master thesis mission and thermal analysis of the upc …the cubesat that is planning to launch the...

MASTER THESIS

Mission and Thermal Analysis of the UPCCubesat

Pol Sintes Arroyo

SUPERVISED BY

Josep J. Masdemont Soler

Universitat Polit ecnica de CatalunyaMaster in Aerospace Science and Technology

14 de desembre de 2009

Mission and Thermal Analysis of the UPCCubesat

BY

Pol Sintes Arroyo

DIPLOMA THESIS FOR DEGREE

Master in Aerospace Science and Technology

AT

Universitat Politecnica de Catalunya

SUPERVISED BY:

Josep J. Masdemont Soler

Matematica Aplicada I

ABSTRACT

The Project is envisioned as a mission control analysis and a thermal control analysis ofthe Cubesat that is planning to launch the UPC (Universitat Politecnica de Catalunya).A Cubesat is a 10x10x10 cm cubic satellite that weights no more than 1 kg and that iscurrently used in many countries and educational institutions as an easy access to space.

The primary work to do would be the analysis of the orbit the satellite would perform. Inthis way, the STK (Satellite Tool Kit) software would provide the mechanism to perform thisanalysis. Starting with the known values of the project, simulations have been carried out inorder to obtain the trajectory the satellite will would perform. Additionally, perturbations inthe orbit, comparatives with other models and simulations with different parameters wouldbe studied. All this practical work is completed with a theoretical explanation of what arethe models used by the software, what are the parameters used and why we use this onesand no other ones.

The second part of the project presents the thermal analysis of the satellite. In this section,draft calculations of the thermal balance of the satellite are presented along with simula-tions with the SEET (Space Environment and Effects Tool) module of the STK. In addition,the necessary theoretical explanations are offered in order to conduct a complete thermalanalysis in future projects.

Essentially, these two sections plus a theoretical background or state of the art of Cube-Sats or the different types of launches form the Master Thesis. Furthermore, extensiveappendixes can be found at the end of the project which act as an ideal complement to thetopics presented in the Master Thesis.

Results obtained from the simulations show similarities with other related-type projectsand with the theory explained. The inclusion of the UPC Cubesat in the existing network ofCubesat developers is advised. HPOP (High Precision Orbit Propagator) is recommendedin future simulations. This propagator shows little differences with SGP4 (Special GeneralPerturbations no 4) but although little, these differences can change significantly the orbitalelements during a year. Atmospheric drag and the non-spherical shape of the Earth arethe ones that affect more the satellite with both secular and periodic changes no matterwhich orbit is being used. Moreover, among other differences, using the two differentshapes of orbit can produce discrepancies in lifetime of 6 or 7 years.

On the other hand results from the thermal analysis show variations of temperature from-85oC to 50 oC for the standard case. Important variations are observed with different val-ues of internal dissipation. Finally, the emissivity/absorptivity ratio is the main parameterwhich we can play in order to change these temperature variations.

Table of Contents

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Chapter 1. Introduction to CubeSats . . . . . . . . . . . . . . . . . . 3

1.1. Definition of a Cubesat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2. History of CubeSats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3. The CubeSat of the UPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2. Mission Analysis . . . . . . . . . . . . . . . . . . . . . . . 11

2.1. Introduction to the STK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2. Theoretical background of the orbital dynamics . . . . . . . . . . . . . . . 13

2.2.1. Orbit Determination . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3. Perturbation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4. Orbit Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.1. SGP4 Propagator . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4.2. HPOP Propagator . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5. Ground Track and Accessibility . . . . . . . . . . . . . . . . . . . . . . . . 24

2.6. Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.7. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7.1. Total and individual access . . . . . . . . . . . . . . . . . . . . . . 26

2.7.2. Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.7.3. Orbit shape comparative . . . . . . . . . . . . . . . . . . . . . . . 30

2.7.4. Elevation angle comparative . . . . . . . . . . . . . . . . . . . . . . 32

2.7.5. Propagator comparative . . . . . . . . . . . . . . . . . . . . . . . . 33

2.7.6. Simulation time comparative . . . . . . . . . . . . . . . . . . . . . 37

2.7.7. Satellite lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.7.8. Orbital elements variation due to perturbations . . . . . . . . . . . . 40

2.7.9. Dispersion analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Chapter 3. Thermal Analysis . . . . . . . . . . . . . . . . . . . . . . . 47

3.1. Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2. Simplified results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2.1. STK simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Appendix A. Cubesat launches and participants . . . . . . . . . . 61

A.1. Past launches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.2. Upcoming launches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

A.3. Cubesat participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Appendix B. Cubesat launch vehicles . . . . . . . . . . . . . . . . . . 67

Appendix C. STK modules . . . . . . . . . . . . . . . . . . . . . . . . . 71

Appendix D. Additional theory for mission analysis . . . . . . . . 73

D.1. The n-body problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

D.2. The trajectory equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

D.3. Type of conics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

D.4. Types of orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

D.5. Perturbation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

D.6. HPOP force models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Appendix E. STK user’s guide . . . . . . . . . . . . . . . . . . . . . . . 91

Appendix F. Simulation tables of the mission analysis . . . . . . 99

F.1. Individual access analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

F.2. Orbit shape comparative . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

F.3. Propagator comparative . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

F.4. Elevation angle comparative . . . . . . . . . . . . . . . . . . . . . . . . . . 104

F.5. HPOP vs. SGP4 comparative . . . . . . . . . . . . . . . . . . . . . . . . . 104

Appendix G. Thermal analysis information . . . . . . . . . . . . . . 107

G.1. UPCSat Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

G.2. Thermal analysis methodology . . . . . . . . . . . . . . . . . . . . . . . . 108

G.3. Software available . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

List of Figures

1.1 Typical Cubesat. Source [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Standard P-POD. Source [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Orbital elements. Source [12]. . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Forces taken into account by each propagator . . . . . . . . . . . . . . . . . 212.3 Description of the umbra and penumbra effects. Source [17]. . . . . . . . . . 252.4 STK map illustrating all the ground stations of the Cubesat network. Source

[STK]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5 Number of accesses for all the ground stations during a year (Part I). . . . . . 282.6 Number of accesses for all the ground stations during a year (Part II). . . . . 282.7 Total duration lighting percentages . . . . . . . . . . . . . . . . . . . . . . . 302.8 Number of accesses vs. orbit shape comparative for UPC, NTNU and Malaysia 312.9 Lighting properties comparative for a 1200x350 and a 350x350 km orbit . . . 322.10 Access scheme for different elevation angles . . . . . . . . . . . . . . . . . 332.11 Access comparative for different elevation angles for UPC, NTNU and Malaysia

ground stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.12 Mean access duration/day comparative for each propagator for UPC, NTNU

and Malaysia ground stations . . . . . . . . . . . . . . . . . . . . . . . . . 352.13 Lighting properties comparative for each propagator . . . . . . . . . . . . . 362.14 SGP4 and HPOP mean access duration/day comparative for UPC, NTNU and

Malaysia ground stations for a 1200x350 km orbit . . . . . . . . . . . . . . . 372.15 SGP4 and HPOP lighting properties comparative for a 1200x350 km orbit . . 372.16 Apogee, perigee and eccentricity variation during the HPOP 1200x250 km

satellite lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.17 i comparative between a spherical (blue) and an elliptical (green) model of Earth 412.18 ω comparative between a spherical (blue) and an elliptical (green) model of

Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.19 e variation for an elliptical model of Earth . . . . . . . . . . . . . . . . . . . 412.20 e variation for a complex model of Earth . . . . . . . . . . . . . . . . . . . . 412.21 e variation produced by third-bodies effects . . . . . . . . . . . . . . . . . . 422.22 Ω variation produced by third-bodies effects . . . . . . . . . . . . . . . . . . 422.23 a variation produced by atmospheric drag . . . . . . . . . . . . . . . . . . . 422.24 ω variation produced by atmospheric drag . . . . . . . . . . . . . . . . . . . 422.25 a variation produced by SRP . . . . . . . . . . . . . . . . . . . . . . . . . . 422.26 Ω variation produced by SRP . . . . . . . . . . . . . . . . . . . . . . . . . 422.27 a variation produced by all perturb forces . . . . . . . . . . . . . . . . . . . 432.28 e variation produced by all perturb forces . . . . . . . . . . . . . . . . . . . 432.29 i variation produced by all perturb forces . . . . . . . . . . . . . . . . . . . . 432.30 Initial conditions of the dispersion analysis . . . . . . . . . . . . . . . . . . . 442.31 Position of the satellites seven days later . . . . . . . . . . . . . . . . . . . 442.32 Final positions of the satellites . . . . . . . . . . . . . . . . . . . . . . . . . 442.33 Range variation between UPCSAT and UPC1 for 50m separation . . . . . . 452.34 Range within the satellite will be for a 50m margin . . . . . . . . . . . . . . . 46

3.1 Incident light characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2 Heat fluxes of a typical satellite orbiting Earth. Source [20]. . . . . . . . . . . 493.3 Temperature evolution for the Al. with Kapton with 0.5 W of internal dissipation 54

B.1 Vega launch vehicle. Source [6]. . . . . . . . . . . . . . . . . . . . . . . . . 69

D.1 Orbital plane angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78D.2 Types of conic sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80D.3 Orbital element perturbation changes. Source [19]. . . . . . . . . . . . . . . 83D.4 Nodal regression. Source [19]. . . . . . . . . . . . . . . . . . . . . . . . . . 86D.5 Apsidal rotation. Source [19]. . . . . . . . . . . . . . . . . . . . . . . . . . 86D.6 Typical dacay of a satellite for a 300 km circular orbit . . . . . . . . . . . . . 87

E.1 STK window with main commands . . . . . . . . . . . . . . . . . . . . . . . 91E.2 Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92E.3 Satellite geographic coordinates . . . . . . . . . . . . . . . . . . . . . . . . 92E.4 Facility constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93E.5 Propagator page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94E.6 Force models page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94E.7 Access page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95E.8 Access report example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96E.9 Lighting report example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96E.10 Lifetime page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97E.11 Lifetime graphic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

G.1 Typical operational limits of components of a satellite. Source [23]. . . . . . . 109

List of Tables

1.1 Current CubeSat status history . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Data used in the simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2 Access time comparative between UPC and global network . . . . . . . . . 272.3 Access time comparative between the more an less accessed ground stations 272.4 Lighting properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.5 Number of accesses vs. orbit shape for UPC, NTNU and Malaysia . . . . . . 312.6 Lighting properties for a 1200x350 km orbit . . . . . . . . . . . . . . . . . . 312.7 SGP4 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.8 Mean access duration/day vs. propagator for UPC, NTNU and Malaysia ground

stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.9 HPOP data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.10 Simulation time comparative for different gaps of one year for the accessibility

properties of the UPC ground station . . . . . . . . . . . . . . . . . . . . . 382.11 SGP4 and HPOP lifetime comparative for different shapes of orbit. Launch

date: 1 Jul 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.12 Accessibility evolution of the first four years for the UPC ground station . . . . 392.13 Theoretical orbital elements changes due to each perturbation force. Source

[19]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.14 Range variations between UPCSAT and UPC1 for different initial separations 45

3.1 Data used in the hot and cold case calculations . . . . . . . . . . . . . . . . 503.2 Hot and cold case temperatures for different materials . . . . . . . . . . . . 513.3 Hot and cold case temperatures for different materials with no internal dissi-

pation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4 Hot and cold case temperatures for the Al. with Kapton . . . . . . . . . . . . 53

A.1 CubeSats past launches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A.2 CubeSats upcoming launches . . . . . . . . . . . . . . . . . . . . . . . . . 63A.3 List of Cubesat participants. Source [2]. . . . . . . . . . . . . . . . . . . . . 64

B.1 Launch vehicles comparative. Source [21]. . . . . . . . . . . . . . . . . . . 69

D.1 Relative accelerations form other bodies to a LEO satellite . . . . . . . . . . 75D.2 Realationship between the type of conic and e, a and ε . . . . . . . . . . . . 80D.3 Most important accelerations form other bodies to a LEO satellite . . . . . . 84D.4 Force models available in the HPOP . . . . . . . . . . . . . . . . . . . . . . 88

F.1 Complete list of the individual access analysis for all ground stations . . . . . 99F.2 Accessibility analysis vs. orbit shape for UPC ground station . . . . . . . . . 101F.3 Accessibility analysis vs. orbit shape for NTNU ground station . . . . . . . . 101F.4 Accessibility analysis vs. orbit shape for Malaysia ground station . . . . . . . 101F.5 Lighting analysis vs. orbit shape . . . . . . . . . . . . . . . . . . . . . . . . 102F.6 Accessibility analysis vs. propagator for UPC ground station . . . . . . . . . 102F.7 Accessibility analysis vs. propagator for NTNU ground station . . . . . . . . 102F.8 Accessibility analysis vs. propagator for Malaysia ground station . . . . . . . 103

F.9 Lighting analysis vs. propagator . . . . . . . . . . . . . . . . . . . . . . . . 103F.10 Elevation angle accessibility analysis for UPC ground station . . . . . . . . . 104F.11 Elevation angle accessibility analysis for NTNU ground station . . . . . . . . 104F.12 Elevation angle accessibility analysis for Malaysia ground station . . . . . . . 104F.13 HPOP and SGP4 accessibility analysis for UPC ground station . . . . . . . . 105F.14 HPOP and SGP4 accessibility analysis for NTNU ground station . . . . . . . 105F.15 HPOP and SGP4 accessibility analysis for Malaysia ground station . . . . . . 105F.16 HPOP and SGP4 Lighting comparative . . . . . . . . . . . . . . . . . . . . 105

G.1 Emissivity and absorptivity of different parts of the Cubesat . . . . . . . . . . 107G.2 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

1

INTRODUCTION

The necessity to achieve new goals has kept mankind occupied during his whole history.From immemorial times, men have tried to reach the most extremes points of the planetuntil deciding to reach the air and later Space. What at the beginning you spent monthsto arrive to, you now only need a few hours. What in the first times only rich people couldafford, it is now open for all the population.

Nowadays, access to Space is limited to a few and launching an object into orbit is veryexpensive. Minimizing this cost and making Space accessible to everyone is the objectiveof the CubeSats.

CubeSats are small satellites weighting no more than 1 kg which have the purpose ofmaking Space available to small projects, mostly from educational institutions. Precisely,UPC is currently developing a project to launch a Cubesat through the launches of oppor-tunity that offer ESA (European Space Agency). In spite of the dimensions of the satellite,CubeSats need the standard subsystems to work. Depending on the type of the missionone or other subsystems will be necessary. Moreover, in every space mission the contactwith the satellite is desired in order to have success. This contact is established by meansof the position of the satellite in space so this position must be known and studied. Themission analysis is the one in charge of the study of this position, the calculation of theorbit and the possible perturbations that will affect the satellite.

This project deals with some of the aspects of the mission analysis of the future Cubesatof the UPC. In order to study the orbit, the theory necessary to understand the simulationsperformed is explained. These simulations provide an extensive knowledge of the perfor-mance of the satellite and have been carried out using a commercial software called STK.Moreover, from these simulations it is explained the influence of the different parametersof the satellite in its orbit apart from explaining how it is affected by the external perturba-tions. Furthermore, an introduction to the thermal analysis is also present at the end ofthe project. The thermal analysis pretends to introduce the first steps in order to have acomplete knowledge of the variation of temperature during the lifetime of a satellite alongwith its importance to the mission.

The project is structured in three chapters. The first chapter introduces the concept ofCubeSats giving information about their state-of-the-art and of the project of the UPC aswell. The second chapter is centered in the mission analysis, explaining the necessarytheory and the results obtained and finally the third chapter introduces the thermal analy-sis of the satellite and first simplified calculations of the variation of temperature that willexperience the satellite in orbit. It is also important to recall that there also exist someappendixes that try to complete the information of the main body of the project.

2 Mission and Thermal Analysis of the UPC Cubesat

Introduction to CubeSats 3

Chapter 1

INTRODUCTION TO CUBESATS

1.1. Definition of a Cubesat

The CubeSat concept was developed by the California Polytechnic State University (CalPoly)and the Space Systems Development Laboratory of Stanford University [1]. It had the pur-pose of creating space research opportunities for universities previously unable to accessspace by defining a standard mechanical interface and deployment system.

A CubeSat (Fig 1.1) is a 10 cm cube with a mass of up to 1 kg and functions fully au-tonomously. Worldwide over 60 universities, high schools and industries are involved inthe development of CubeSats [2], with payloads covering a wide range of scientific, engi-neering and industrial objectives. The low prize of the satellite and the launch opportunitiesoffered by major satellites launch providers and manufacturers make them an ideal methodfor educational purposes. Space is fully open to everyone with this concept.

The idea of the launch opportunity reduces the cost of the launching to zero in most of thecases. This concept is based in the utilization of a small part of the launcher that has asthe primary mission the launching of a satellite (the normal size concept of satellites). Thelaunch cost is just a little bit higher because you only add 1 kg for each CubeSat but theadvantages are really enormous. So the idea is that you launch the CubeSats using thecurrent launches of ’standard’ satellites.

Moreover, the device chosen to deploy the CubeSats will be standard flight-proven Cube-Sat deployment systems. The idea of a standard system has huge advantages. Thesystem would add integrity so the people involved in the project would only deal with onlyone type of system and they would be able to use the maximum number of launch vehiclesas possible. The standardization would benefit both the manufacturers and the launchercompanies. The most common standard system is the P-POD (Fig 1.2) (Poly Pico-satelliteOrbital Deployer) from CalPoly. Each P-POD is designed to carry three standard CubeSatsand serves as the interface between the CubeSats and the launch vehicle. It is a rectangu-lar aluminum tubular frame with an electrically activated spring-loaded door mechanism.After the door is opened the CubeSats are pushed out by a spring along guidance rails,ejecting them into orbit with a separation speed of a few m/s. There are also other ver-sions of the system such as the X-POD from UTIS-SFR (Toronto) that has an independentrelease mechanism for the spring deployer and feedback to indicate deployment has takenplace.

The concept of standardization is often related with flexibility. Pre-qualified P-POD andlaunch vehicles interfaces maximize the number of compatible missions, reduce the in-tegration time and minimizes costs. It also minimizes design, analysis and testing forsubsequent mission with the idea of repetition. There are other advantages such as thepossibility to transfer the CubeSats to a different launch vehicle if the launch is delayed orcancelled.


The standard 10x10x10 cm basic CubeSat is often called a ’1U’ CubeSat meaning oneunit. CubeSats are scalable in 1U increments and larger. CubeSats such as a ’2U’ Cube-Sat (20x10x10 cm) and a ’3U’ CubeSat (30x10x10 cm) have been both built and launched.

Since CubeSats are all 10x10 cm (regardless of length) they can all be launched anddeployed using the common deployment system. P-PODs are mounted to a launch vehicleand carry CubeSats into orbit and deploy them once the proper signal is received from thelaunch vehicle. P-PODs have deployed over 90% of all CubeSats launched to date sincethe first one launched in June of 2003(including un-successful launches), and 100% of allCubeSats launched since 2006. The P-POD has capacity for three 1U CubeSats, howeversince three 1U CubeSats are exactly the same size as one 3U CubeSat, and converselytwo 1U CubeSats are the same size as one 2U CubeSat; the P-POD can deploy 1U, 2U,or 3U CubeSats in any combination up to a maximum volume of 3U.

All educational payload elements shall have their own power supplies and communicationfacilities. There is no electrical interface to the CubeSats either from the POD or the mainpayload, and once the CubeSat is installed in the POD prior to launch there will be noopportunity for further battery charging. The CubeSats are expected to be electrically inertonce inserted into the POD, with no power dissipation or RF emissions. They are expectedto utilize the sensors in the feet of the CubeSat structure to determine launcher separationand begin operations.

Although launch prices have risen quite substantially across the board of launch providers,a CubeSat still forms the most cost-effective independent means of getting a payload intoorbit. Several companies and research institutes offer regular launch opportunities in clus-ters of several cubes. The concept of the distribution of costs is commonly used. Thisconcept says that in order to reduce the costs, you need to distribute them over many cos-tumers is needed, deploy multiple spacecrafts per mechanism and use identical, standardsystems and not mission specific devices.

In conclusion, the objectives of the P-POD are the protection of the launch vehicle and theprimary payload, the safe and reliable deployment of the CubeSats and the compatibilitywith many launch vehicles.

Figure 1.1: Typical Cubesat. Source [2]. Figure 1.2: Standard P-POD. Source [2].


1.2. History of CubeSats

CubeSats were first conceptualized in 1999 by Stanford and Cal Poly as said in the pre-vious section driven by need for student opportunities. The idea was born in the mindsof Jordi Puig-Suari and Bob Twiggs. The first, a Catalan aerospace engineer, says in aninterview [3] that he moved to the California Polytechnic State University from the ArizonaState University with lots of problems and solutions for the satellite engineering. The im-plication of students in the development of satellites was not new but the problems in costand time were really big. They were building huge satellites of 20 and 30 kilograms, whichmake the students impossible to finish their thesis before launching the satellites. Then,with the help of Professor Bob Twiggs of the Aeronautic and Astronautic Department ofStanford University, he was able to solve that major problems of the aerospace engineer-ing bringing to life the first version of the CubeSat. Since then, more than 100 projects ofCubeSats worldwide have been developed.

Moreover, Cal Poly’s current role is to provide standard interface and systems for deployingCubeSats (P-POD), maintain the CubeSats standard, coordinate launch opportunities andnetworking ground stations around the world dedicated to CubeSat operations [2]. Fromthe 51 launches of CubeSats, 35 are or were in orbit. The others were lost in two launchfailures in Russia and in the United States.

The applications of the CubeSats payloads range from astrobiology experiments to Earthscience research. In this field it should be remarked the GeneSat mission as an astrobiol-ogy experiment, the ionospheric research of the QuakeSat mission or the Pico-inspectortesting mission of Aerospace Corporation. A short list of CubeSats applications is shownbelow giving examples of CubeSat missions with the corresponding application [4].

• Development of CubeSat technology (Testing)

– AAU CubeSat

– CanX-1

– AeroCube

– CubeSat TestBed 1

• Earth remote sensing

– Libertad-1

– AAUsat-2

– Quakesat

• Tether experiments

– MAST

• Biology

– GeneSat 1

– Pharmasat-1


All these experiments validate the CubeSat concept to be used in all kind of applicationsand not only with educational purposes but in industry and research also. A brief descrip-tion of the missions already launched is shown in Table 1.1 but the complete list of past,current and future missions can be explored in Appendix A.

Table 1.1: Current CubeSat status history

Batch # Date LV No Cont Semi Cont Full Cont Total

1 30 Jun 2003 Rokot 2 1 3 (1 3U) 6 (1 3U)2 27 Oct 2005 Kosmos-3M 1 0 2 33 22 Feb 2006 M-V 0 0 1 (2U) 1 (2U)4 26 Jul 2006 DNEPR

(failure)0 0 0 14 (1 2U)

5 16 Dec 2006 Minotaur I 0 0 1 (3U) 1 (3U)6 17 Apr 2007 DNEPR 1 4 (1 3U) 2 7 (1 3U)7 27 Apr 2008 PSLV 0 0 6 (1 2U +

2 3U)6 (1 2U +2 3U

8 03 Aug 2008 Falcon-1(failure)

0 0 0 2

9 23 Jan 2009 H-IIA 2 0 1 310 19 May 2009 Minotaur I 0 0 4 (1 3U) 4 (1 3U)11 23 Sep 2009 PSLV 0 0 4 4

TOTAL Up to 10/09 16 (1 2U) 6 5 (1 3U) 24 (2 2U+ 5 3U)

51 (3 2U+ 6 3U)

Batch #: Number of the CubeSat group launch (CubeSats are typically launched in group)

LV: Launch Vehicle

No Cont: Number of CubeSats of the corresponding batch that had no contact with the GS (ground station)

Semi Cont: Number of CubeSats of the corresponding batch that had contact for a short time with the GS

Full Cont: Number of CubeSats of the corresponding batch that had full contact with the GS

Total: Total number of CubeSats of the corresponding batch that didn’t had a launch failure

It can be observed from Table 1.1 that if the failures due to launch vehicles are not takeninto consideration the success rate of CubeSats missions is really high. From the 35 thatare in orbit now, in 29 there was contact between the satellite and the ground station andform that 29, in 24 there was full contact and most of them are still in operation. It canbe deduced from this data that indeed these satellites can be useful for many applicationsand that cannot be seen just as ’student toys’.

There are going to be upcoming launches in the next months and every year this technol-ogy would be accepted more and more as part of the normal Space world. In the secondquarter of 2009 there was planned a new launch of the Falcon-1 of SpaceX which carriedthe RazakSat as the primary payload and was supposed to carry also two triple CubeSatsas secondary payload. Due to a last minute problem with vibrations, a mitigation devicewas installed in the place where the CubeSats were supposed to be [5]. This problem hasdelayed the two CubeSats to a later launch during 2010 on-board of a Falcon-1 or a stillnot demonstrated Falcon-9.


Also, late in 2009, the maiden flight of the European Vega LV was planned. This flight hasbeen delayed different times, being October 2010 its current launch date. This LV will carry11 CubeSats missions as part of the ESA launch opportunity contest [6]. Other missionsplanned for 2010 are one in the new Minotaur IV with 2 triple CubeSats and another one inthe Taurus-XL that will carry 3 CubeSats more. There is a clear increase in the launchesof CubeSats and in a few years there would be even a higher increase which means thatSpace will be open to everyone with a good team, good ideas and willing to work hard.

Although the obvious thing when examining if the CubeSats technology is having successor not is the amount of satellites now in operation in orbit there are others factors to takeinto consideration. The CubeSat concept was born as an idea to facilitate the access tospace to universities or organizations without the resources to do it. As part of this idea,the concepts of networking and standardization were needed. What if all the universitiesand private and public research institutions building CubeSats share their resources to ob-tain better results? This is the primary objective of the CubeSat Community [2]. There aremore than 80 universities, private companies, government organizations building Cube-Sats and most of them have antennas and tracking devices to follow their satellites in thesky. With this community, each of these institutions shares their capabilities to follow all theCubeSats in orbit. The advantage is incredible because instead of following your satellitesome minutes during the day, you can now watch it 10 times more. A complete list of heinstitutions involved in the CubeSat community can be found in Appendix A.3..

This program is also designed so that students can participate in entire life cycle of a spacemission, from the first idea of the concept to the launch of the satellite and the study of thedata obtained.

In conclusion, the accomplishments made within just 8 years have been spectacular. Thereare 20 completely operational CubeSats in orbit and just 6 total failures of the CubeSats(not taken into account the failures due to the launch vehicle). There have been success-ful coordination and launch of 31 satellites on worldwide launch vehicles and each yearthere is an increase in the number of launch opportunities for CubeSats. Finally and veryremarkable, there has been established an international Earth station networking.

1.3. The CubeSat of the UPC

In this context, the Polytechnic University of Catalonia is planning to build a CubeSat andlaunch it through the ESA launch opportunities. ESA’s launch opportunities are a call forEuropean universities to launch their projects with the new Vega launch vehicle [7]. Theopportunity to fly CubeSats on the Vega maiden flight is proposed by the ESA EducationOffice with the purpose of giving students from European universities and other educa-tional institutions wishing to pursue a career in the space domain a valuable hands-onexperience. They can take part in this end-to-end space project including educationalactivities from design, integration, verification, launch and operations. The educationalpayloads will be entirely developed by educational institutions, with advice from ESTECexperts if requested and deemed appropriate by the Education Office. All payloads shallfully comply with the Vega general specification for qualification and acceptance test ofequipment.


A first Announcement of Opportunity (AO) was published on the education pages of theESA web portal on 9 October 2007 and the first nine CubeSats selected (with two back-upsatellites) were announced in 2008 [6]. Although the launch date was planned to be during2009, the new estimate date is in the end of 2010.

Vega is ESA’s new small launch vehicle which is being developed under the manage-ment of the Vega Programme (LAU-PV) in the framework of an ESA optional programmefunded by Belgium, France, Italy, Spain, Sweden, Switzerland and The Netherlands. Vegais designed to launch a wide range of missions and payload configurations in order to re-spond to different market opportunities and therefore provide the flexibility needed by thecustomers. In particular, it can launch payloads ranging from a single satellite up to onemain satellite plus six microsatellites. It is compatible with payload masses ranging from300 to 2500 kg and can provide launch services for a variety of orbits, from equatorial toSun-synchronous.

The primary scientific payload on the maiden flight is the LAser RElativity Satellite (LARES)for testing a prediction following from Einstein’s theory of General Relativity, the so-called’frame-dragging or Lense-Thirring effect’. An educational payload of nine European Cube-Sats is foreseen to be accommodated in three P-PODs, each containing three CubeSats,attached to and deployed from the qualification payload. The AVUM multi-burn facility willbe utilized to put the CubeSats into either a 1200x350 km elliptical orbit or a 350 km circu-lar orbit (still to be confirmed). The qualification payload will be separated from the AVUMafter the orbital maneuvers.

Regarding the orbital parameters, the LARES satellite is supposed to be placed by Vegainto a circular orbit with an altitude of 1200 km and an inclination of 71o. Thereafter, theorbit will be changed by a de-orbit boost of the AVUM. The new orbit will have a perigeeof 350 km and an apogee of 1200 km, the inclination is 71o as before. This orbit is morecompatible with the capabilities of the planned CubeSats ground stations. The brakingeffect of the residual atmosphere will lower the apogee by about 40 km per month (this isjust a rough estimate, more detailed calculations are ongoing). In this new orbit, the lifetimewill be much less than 25 years, therefore compliant with international requirements relatedto space debris. Currently under investigation is the possibility to change the 350x1200km orbit to a 350x350 km orbit by an additional firing of the AVUM liquid propellant engine.

At this time it is not known if the deployment will take place in sunlight or eclipse. This mayindeed not be known until after the lift off, as a last-minute launch delay could affect thedeployment position relative to the sun.

In order to select the CubeSats of the ESA launch opportunities, the criteria include,amongst others:

• The educational content, technical maturity and project objectives of the proposals.

• Letters of commitment by the funding bodies (institutions and/or industry).

• Compliance of the development schedules with the Vega Flight schedule.

• Signing of relevant agreements between the educational institutions (universities)and the Education Office.


The idea to launch the UPC CubeSat is to do it through another launch opportunity ofthe ESA. The process will be very similar to the first one so analyzing the steps the otherteams have made in this first opportunity will be extremely positive to have success in thisupcoming mission.

The project is known to be called UPCSat and is currently being developed by the CRAE(Aeronautics and Space Research Center) of the UPC. The project is directed by Adri-ano J. Camps Carmona of the Signal Theory and Communications Department (TSC) butencloses other people and departments of the UPC [8].

CRAE is a specific research centre that encloses 90 researchers from 28 different researchgroups inside the UPC. UPC has extensively knowledge in the aerospace field but is cur-rently behind other Universities in the development of this kind of technology. This projectwould benefit the entire University because there is a wide range of payloads and subsys-tems that can be developed by the research groups of UPC, using the CubeSats as testplatforms for their technologies. Moreover, the strategy would be simple. The first missionswill be focused in just flying the satellite. No attitude control will be installed in the satelliteand the required subsystems will be bought as many as it can be in order to have a quickstart-up. Future missions will replace these subsystems with others developed entirelyin the University including also, new developments that could be used simultaneously forother scientific experiments. The ground station will also be bought form ISIS Companyand installed in one of the faculties of the UPC. Finally testing of the technology will becarried out in some labs of the University and in some external labs of private companies.

The main goal of this project, though, is the collaboration between groups within UPC inspace related activities, retain and attract students for final project and potentially for Ph Dand provide visibility of UPC space-related activities to the society.

Mission Analysis 11

Chapter 2

MISSION ANALYSIS

2.1. Introduction to the STK

In order to understand the different explanations in this section, some basic definitionsshould be defined.

Mission analysis is the term used to describe the mathematical analysis of satellite orbits,performed to determine how best to achieve the objectives of a space mission.

Celestial mechanics is a division of astronomy dealing with the motions and gravitationaleffects of celestial objects. The field applies principles of physics, historically Newtonianmechanics, to astronomical objects such as stars and planets. It is distinguished fromastrodynamics, which is the study of the creation of artificial satellite orbits.

Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as de-termined from Sir Isaac Newton’s laws of motion and his law of universal gravitation. Itis a specific and distinct branch of celestial mechanics, which focuses more broadly onNewtonian gravitation and includes the orbital motions of artificial and natural astronomi-cal bodies such as planets, moons, and comets. Astrodynamics is principally concernedwith spacecraft trajectories, from launch to atmospheric re-entry, including all orbital ma-neuvers, orbit plane changes, and interplanetary transfers.

Astronautics is the branch of engineering that deals with machines designed to work out-side of Earth’s atmosphere, whether manned or unmanned. In other words, it is the scienceand technology of space flight. To perform the mission analysis, some kind of software isneeded. The amount of data and calculations needed make it difficult and in some wayimpossible to achieve without specific software.

There are ways to create your own software by means of programming languages such asC++, Fortran, FreeMat, Numerit Pro or the most common of them Matlab but the missionanalysis performed in this project has been done by a commercial software named SatelliteTool Kit.

Satellite Tool Kit, often referred to by its initials STK, is a software package from Ana-lytical Graphics, Inc. (AIG) that allows engineers and scientists to design and developcomplex dynamic simulations of real-world problems [9]. Originally created to solve prob-lems involving Earth-orbiting satellites, it is now used in both the aerospace and defensecommunities.

STK has more than 32,000 installations worldwide, with organizations such as NASA,ESA, CNES, Boeing, JAXA, Lockheed Martin, Northrop Grumman, EADS, DOD, and CivilAir Patrol.

The product is currently used in such areas as:


• Battlespace Management

• Communications Analysis

• Space Exploration

• Electronic Warfare

• Geospacial Intelligence

• Spacecraft Mission Design

• Missile Defense

• Unmanned Systems (UAVs)

• Spacecraft Operations

In 1989, the three founders of Analytical Graphics, Inc - Paul Graziani, Scott Reynoldsand Jim Poland, left GE Aerospace to create Satellite Tool Kit (STK) as an alternative tobespoke project-specific aerospace software.

The original version of STK ran only on Silicon Graphics computers, but as PCs becamemore powerful, the code was converted to run on Windows. STK was first adopted bythe aerospace community for orbit analysis and access calculations but as software wasexpanded, more modules were added that included the ability to perform calculations forcommunications systems, radar, interplanetary missions and orbit collision avoidance.

The addition of 3D viewing capabilities lead to the adoption of the tool by military users forreal-time visualization of air, land and sea forces as well as the space component. STKhas also been used by various news organizations to graphically depict complex eventsto a wider audience. The interface to STK is a standard GUI display with customizabletoolbars and dockable maps and 3D viewports. All analysis can be done through mouseand keyboard interaction.

Each analysis or design space within STK is called a scenario. Within each scenario anynumber of satellites, aircraft, targets, ships, communications systems or other objects canbe created. Each scenario defines the default temporal limits to the child objects, as wellas the base unit selection and properties. All of these properties can be overridden foreach child object individually, if necessary. Only one scenario may exist at any one time,although data can be exported and reused in subsequent analysis.

For each object within a scenario, various reports and graphics (both static and dynamic)may be created. Relative parameters, between one object and another can also be re-ported and the effect of real-world restrictions (constraints) enabled so that more accuratereporting is obtained. Through the use of the constellation and chains objects, multiplechild objects may be grouped together and the multipath interactions between them inves-tigated.

STK is a modular product, in much the same way as Matlab allows you to add modules tothe baseline package to enhance specific functions.

Mission Analysis 13

Since the release of STK 8.0, the STK product range has been reorganized into Editionswith additional add-on modules. A brief summary of the editions and modules is listed inAppendix C.

• STK Basic Edition

• STK Professional Edition

• STK Expert Edition

• STK Specialized Analysis Modules

STK Basic Edition is run by a free license obtained from AIG. This license allows theutilization of the STK Basic in an unlimited way and it also permits the evaluation of theProfessional Edition and Analysis Modules for 30 days.

Moreover, the ’low cost’ of this license is the reason that in this project the main calculationshave been computed with the Basic Edition of STK.

2.2. Theoretical background of the orbital dynamics

It can seem that mission analysis and space engineering is a new development of thispast century but history shows us that this race started long ago, in the Greek times. Itwas Aristarchus who put the first stone in the study of the movement of the celestial bodiesin space. He was a Greek astronomer who lived in the 300 BC and was the first personto present an explicit argument for a heliocentric model of the solar system, placing theSun, not the Earth, at the center of the known universe. Despite his ideas, the geocentricmodel (defended by Ptolemy and Aristotle) was the one used until Nicolaus Copernicus(1473-1543) in the XVI century formulated a comprehensive heliocentric model, whichdisplaced the Earth from the center of the universe. Moreover, the heliocentric modelwas not accepted until Galileo Galilei (1564-1642) in the XVII century discovered the fourmoons in Jupiter that proved the model.

Meanwhile, two different scientists, Johannes Kepler (1571-1630) and Tycho Brahe (1546-1601), studied the movement of the planets and other bodies in very different ways. Thesetwo scientists marked the history of orbital mechanics with two different personalities.While Tycho was a noble who dedicated part of his life to an accurate observation of themotion of the planets, Kepler was a poor and sickly mathematician who was gifted with thepatience and the innate mathematical perception needed to unlock the secrets hidden inTycho’s data. Thanks to the observational data of Tycho, Kepler could finally demonstratehis three laws of the movement of celestial bodies in 1609.

• 1st law : The orbit of each planet is an ellipse, with the sun at one focus.

• 2nd law : The line joining the planet to the sun sweeps out equal area in equal times.


• 3rd law : The square of the period of a planet is proportional to the cube of its meandistance from the sun (1619).

The three Kepler’s laws were just a description, not an explanation of planetary motion. Itremained still someone to unveil the mystery.

In 1642, the same year Galileo died, a child born in England was about to change thehistory of physics and to alter the thought and habit of the world. Isaac Newton (1642-1727)published his ’Principia Mathematica’ in 1687. In this work, Newton described universalgravitation and the three laws of motion which dominated the scientific view of the physicaluniverse for the next three centuries. Newton showed that the motions of objects on Earthand of celestial bodies are governed by the same set of natural laws by demonstrating theconsistency between Kepler’s laws of planetary motion and his theory of gravitation, thusremoving the last doubts about heliocentrism and advancing the scientific revolution.

In Book 1 of the principia Newton introduces his three laws of motion:

• 1st law : Every body continues in its state of rest or of uniform motion in a straightline unless it is compelled to change that state by forces impressed upon it.

• 2nd law : The rate of change of momentum is proportional to the force impressedand is in the same direction as that force

• 3rd law : To every action there is always opposed an equal reaction.

Newton also formulated his Law of Universal Gravitation by standing that any two bodiesattract one another with a force proportional to the product of their masses and inverselyproportional to the square of the distance between them. This law is expressed in Eq. 2.1.

Fg = −GMm

r2 ·r

r(2.1)

In Eq. 2.1 Fg is the force on mass m due to mass M and r is the vector from M to m. Theuniversal gravitational constant G, has the value of 6.67428·10−11 m3/kg·s2 .

The application of Newton’s Law of Universal Gravitation to his second law of motion orig-inated the equation of motion for planets and satellites which the N-body problem is a firstapproximation.

Basically, the N-body problem studies the gravitational force that these N bodies exert toone of them [10]. Moreover, it takes the positions, masses, and velocities of some set ofn bodies, for some particular point in time, and determines the motions of the n bodies,and find their positions in time. Note that in Appendix D there is the explanation of all thetheory commented in this section.

The expression obtained is a second order, nonlinear, vector, differential equation of mo-tion that with some simplifying assumptions can be reduced to Eq. 2.2.

Mission Analysis 15

r = −Gn

∑j=1j 6=i

mj

r3ji

r ji (2.2)

However, in this project it is of interest the study of the motion of a near Earth satellite thusthe CubeSat will orbit around the Earth at a low altitude. Therefore, let us rewrite Eq. 2.2in a different form. If m1 is the Earth m2 is the satellite and all the other masses may bedifferent celestial bodies as the Moon, the Sun, or other planets in the Solar System, thenthe expression is resduced to Eq. 2.3.

r12 = −G(m1 +m2)

r312

r12−n

∑j=3

Gmj(r j2

r3j2

−r j1

r3j1

) (2.3)

The first term of Eq. 2.3 is the force acting between the two main bodies (the Earth andthe satellite). The other term is the perturbation of the other bodies affecting the force ofthe two main ones. However, the acceleration coming from other bodies different from theEarth is very little. Just the effect of the Sun and the Earth oblateness have a considerablevalue. It is for this reason that some assumptions can be made. Simplification hypothesisare made in order to obtain a simpler solution. If just the satellite and the Earth are theonly ones in study and they are spherical and homogenous, we obtain:

r = −G(M +m)

r3 r (2.4)

Moreover, the mass of the satellite is very little compared to the mass of the Earth (M ≫m). If a parameter µ= G(M +m) ≈ GM is defined, we obtain:

r +µr3 r = 0 (2.5)

This equation is the two-body equation of motion. This equation can be solved analytically,in contrast to the three body problem or higher that can only be solved numerically. Thisequation must be derived to obtain the trajectory equation.

Taking into account the conservation of the mechanical energy and the angular momen-tum and operating them with the two-body equation of motion, the trajectory equation isobtained:

r =h2/µ

1+ Bµ cosv

(2.6)

If e= B/µ, we obtain the polar equation of a conic section (Eq. 2.7), that it is mathematicalequal in form to the trajectory equation and widely used in the study of orbits.

r =p

1+ecosv(2.7)


In Eq. 2.7 p is the parameter of the orbit and e is the eccentricity. The eccentricity deter-mines the type of conic section that represents the orbit. A review of conic sections can befound in Appendix D.3..

2.2.1. Orbit Determination

Since the first method to determine the orbit, the Newton’s one that Halley used to deter-mine when would a comet pass near the Earth, many scientists such as Euler, Lambert,Lagrange, Laplace or Gauss among others have studied the celestial bodies and provedmany theories and methods.

In order to determine an orbit, the orbital elements are defined. Orbital elements are theparameters required to uniquely identify a specific orbit [11]. Given an inertial frame ofreference and an arbitrary epoch (a specified point in time), exactly six parameters arenecessary to unambiguously define an arbitrary and unperturbed orbit. This is becausethe problem contains six degrees of freedom. These correspond to the three spatial di-mensions which define position, plus the velocity in each of these dimensions. These canbe described as orbital state vectors, but this is often an inconvenient way to represent anorbit, which is why Keplerian elements are commonly used instead.

The Keplerian orbital elements are (Fig. 2.1):

• Semi major axis (a) - Distance between the geometric center of the orbital ellipsewith the perigee, passing through the focal point where the center of mass resides.

• Eccentricity (e) - Shape of the ellipse, describing how flattened it is compared with acircle. (not marked in diagram)

• Inclination (i) - Vertical tilt of the ellipse with respect to the reference plane, measuredat the ascending node (where the orbit passes upward through the reference plane).

• Right ascencion of the ascending node (Ω) - Represents the angle between thevernal equinox and the point where the orbit crosses the equatorial plane (goingnorth)

• Argument of perigee (ω) - Defines the orientation of the ellipse (in which directionit is flattened compared to a circle) in the orbital plane, as an angle measured fromthe ascending node to the perigee.

• True anomaly (ν) - defines the angle in the plane of the ellipse, between perigee andthe position of the orbiting object at any given time.

There are several ways to calculate r and v from the classical orbital elements or in theother way, to calculate the orbital elements form r and v. The following equations are usedto pass from r and v to the orbital elements and vice versa.

1. Orbital elements from r and v

Mission Analysis 17

Figure 2.1: Orbital elements. Source [12].

h = r× v (2.8)

n = k× h (2.9)

k = (0,0,1) (2.10)

e =1v

[(

v2−vr

)

r − (r ·v)v]

(2.11)

p =h2

µ(2.12)

e= |e| (2.13)

cosi =hk

h(2.14)

cosΩ = nin n j>0→ Ω<180o

(2.15)

cosω = n·en·e ek>0→ ω<180o

(2.16)


cosν = r·er·e r ·v>0 → ν<180o

(2.17)

2. r and v from the orbital elements

r = rcosνP+ rsinνQ (2.18)

r =p

1+ecosν(2.19)

v =

√

µp[−sinνP+(e+cosν)Q] (2.20)

These equations are in the Perifocal coordinate system where P and Q are unit vectorsin the direction of xω (perigee) and yω (90o rotated axis in the direction of orbital motionand lies in the orbital plane). Rotations are needed in order to obtain r and v in differentcoordinates systems.

2.3. Perturbation Techniques

The two-body problem is a good approximation to reality in order to study the motion of asatellite in space, but reality is more complex than that. There exist some forces differentfrom the gravitation of the main body such as the atmospheric drag that perturb the orbit indifferent ways and that in order to have a complete knowledge of the motion of a satellite inspace, must be studied and taken into account. These forces can be summarized in fourmain ones:

• Non-spherical Earth

• Third-body perturbation

• Atmospheric drag

• Solar radiation pressure

A descrpition of the four types of perturbating forces can be found in Appendix D.5.. More-over, unperturbed orbits have constant orbital elements. When perturbing forces are con-sidered, the classical orbital elements vary with time. To predict the orbit this time variationmust be determined using techniques of either special or general perturbation.

General perturbation techniques are an approach to analytically solving some aspects ofthe motion of a satellite subjected to perturb forces [11] [13]. The original equations ofmotion are replaced with an analytical approximation, which permits analytical integration.

Mission Analysis 19

Because the orbital elements are nearly constant, general perturbation techniques usuallysolve directly for the orbital elements rather than the inertial position and velocity.They aremore difficult and approximate, but they allow a better understanding of the perturbationsources and their effects because the output provides a qualitative analysis of the orbitalpath. Much faster solutions can also be obtained compared with the special perturbationtechniques. The underlying concept of the analytical or general approach is the Variationof Parameters (VOP). Based on this method, the solution of the unperturbed system canrepresent the solution of the perturbed system, provided that the constants in the solutioncan be generalized as time-varying parameters.

Special perturbations, on the other hand, employ direct numerical integration of the equa-tions of motion, in which the accelerations are integrated directly to obtain velocity andposition [11] [13]. The special techniques are defined in terms of specific force modelsand initial conditions. These methods have lately become more popular because of theenhancement in the computational power available to scientists and engineers which re-duces the computation time. These types of perturbations use different techniques tocalculate the orbit such as the Cowell and the Encke method.

Cowell is the simplest and most straight-forward of all the perturbation techniques [11].It was developed in the early 20th century but it has been rediscovered in many formsmany times. Cowell method simply writes the equations of motion of the object in studyincluding all the perturbations and then integrates them step-by-step numerically. Themain advantage of this method relays in the simplicity of formulation and implementation.Any number of perturbations can be handled at the same time but the cost of computationis bigger than that of Encke method especially when it gets close to large attracting bodies.More precisely, this method is in general 10 times slower than Encke method, which is anaspect to take into consideration while designing the mission analysis.

Encke method is in general far more complex than Cowell, although it appeared half acentury earlier [11]. In contrast to Cowell, where the sum of accelerations is integratedtogether, in the Encke method the difference between the primary acceleration and allperturbing accelerations is integrated. Encke method is much faster than Cowell due tothe ability to take larger integration step sizes when it is near a large attracting body, whichat the end reduces the number of integration steps. Although this method is normally 10times faster than Cowell, this is only applied to interplanetary trajectories. When talkingabout Earth satellites, the difference is reduced considerably since Encke is only 3 timesfaster than Cowell.

Cowell and Encke methods are ways to calculate the same parameters but they both needthe integration of their equations in order to get results. Therefore a discussion of numericalintegrators is appropriate. This integration can be performed in different ways dependingon the problem you are considering. The decision of choosing the best integrator to yourproblem is extremely important. There are two main types of numerical integrators, single-step and multi-step.

Runge-Kutta is an example of single-step method [11]. It is actually a family of varyingorder methods where higher ones have higher accuracy. These methods are stable anddo not require a starting procedure. They are relatively simple, easy to implement, have asmall truncation error and the step size is easily changed.


The multi-step integrators are predictor-corrector type, where the predictor gives an initialestimate, and the corrector further refines the result [11]. The predictor-corrector typesare known to give better accuracy but at the expense of more complexity. Gauus-Jacksonis an example of this type of integration methods. It is also known as the sum squaredmethod and it is one of the best and most used numerical integration methods for trajectoryproblems of the Cowell and Encke type. Its predictor alone is more accurate than most ofthe other predictor-corrector methods.

For both methods, the ultimate accuracy is obtained by varying the integrator’s step-size.

2.4. Orbit Prediction

Predicting the orbits of satellites is an essential part of the mission analysis and has im-pacts on the power system, attitude control and thermal design of the satellite.

Furthermore, it is the starting point in planning whether a proposed mission is feasibleand how the satellite needs to be designed. The computation of the orbits of artificialsatellites around planets such as the Earth has been studied in detail in the last century.The problem of computing the orbits of satellites, however, is not straight forward. Themain factors affecting the orbit of a satellite are the perturbations studied in the previoussection. These effects have important considerations for different types of satellite orbits.For example satellites in LEO are strongly affected by the non-spherical nature of the Earthand even atmospheric drag. Satellites out in geostationary orbit, however, are sufficientlyfar from the Earth and these effects are much more little. The gravitational pull of the Sunand Moon, however, does play a significant role in the evolution of their orbits. Effects suchas atmospheric drag and radiation pressure are also very dependent upon the shape, sizeand mass of the satellite.

Orbits and their models are not perfect, and so are calculated analytically or simulatednumerically for future time steps to predict where a satellite will be in the future as wehave seen with the perturbations techniques. The purpose of these orbit propagatorsis to provide high accuracy in predicting the position of a satellite. There exist a widerange of propagators, each one with different levels of accuracy, depending on how manyperturb forces are taking into consideration. A list of the propagators used by the simulationsoftware STK is presented below.

• Two-body

• J2

• J4

• HPOP (High Precision Orbit Propagator)

• SGP4 (Simplified General Perturbations)

• LOP (Long Term Propagator)

Mission Analysis 21

• Astrogator

Fig. 2.2 illustrates which perturbating forces each propagator is considering.

Figure 2.2: Forces taken into account by each propagator

Depending on the STK version available for the user, some of the propagators cannot beused. This affect the outputs obtained thus not all the propagators have the same accuracy.Let’s explain first the general differences between them further than analyzing the forceseach one takes into account.

Extracting the conclusions from Vallado [14] regarding the accuracy of the propagationmethods, the propagation techniques can be classified in low, medium or high accuracy.A breakout like this distinguishes the state-of-the-art (high), from the routine numericaloperations (med), and from the analytical ones (low).

• Low >500 m

• Medium 500-10 m

• High <10 m

Low routines are designed for general propagation techniques. The accuracy can be quitelimited (as in the two-body case), or have some approximations for drag, resonance, etc,as in the SGP4 examples. The mean element theory in particular can be tailored to givemore or less accuracy, depending on the mission needs. Examples of these classes ofpropagators are the analytical ones of the two-body, J2, J4 or SGP4.

Medium accuracy force models are the ones using the 4th order Runge-Kutta and highaccuracy methods are those using the numerical integration of the 8th or 12th order Gauss-Jackson or Adams-Bashforth among others.

An example of ’high’ accuracy method in STK is the HPOP propagator. HPOP uses anumerical integration method to propagate the satellite state in the J2000 reference frame.Available integration techniques in STK are the Runge-Kutta method of 7th or 8th order,the Burlirsch-Stoer method and the Gauss-Jackson method of 12th order.


The two-body model introduced and analyzed by Kepler is perhaps the first mathematicalmodel for any orbit determination. This model can be described as the basic propagator.It does not consider any perturbation so secular and periodic changes are absent.

The J2 and the J4 propagators take in consideration the non-spherical Earth. J2 Pertur-bation includes the point mass effect as well as the dominant effect of the asymmetry inthe gravitational field. J4 additionally considers the next most important oblateness effects(the second order of J2 term and the J4 in addition to J2). None of these propagatorsmodel atmospheric drag, solar radiation pressure or third body gravity but are an advanceto the basic two-body propagator.

These propagators are often used in early studies to perform trending analysis. J2 is of-ten used for short analyses (weeks) and J4 for long analyses (months, years). Moreover,the solutions produced by these two propagators are approximate, based upon Keplerianmean elements. In general, forces on a satellite cause these elements to drift over time(secular changes) and oscillate (periodic changes). In particular, the J2 and J4 termscause only periodic oscillations to semi-major axis, eccentricity and inclination, while pro-ducing drift in argument of perigee, right ascension and mean anomaly. In contrast, STK’sJ2 and J4 propagators model only the secular drift in the elements.

Because the main propagators used in the simulations are the SGP4 and the HPOP dueto they have been analyzed more precisely.

2.4.1. SGP4 Propagator

SGP4 is an acronym for Simplified General Perturbations No. 4. The SGP4 is a semi-analytical propagator that uses the two-line mean element (TLE) sets to propagate a satel-lite’s orbit over time.

The original analytic theory, Simplified General Perturbations (SGP), was developed byAeronutronic-Ford. In 1965, Max Lane began developing a slightly different analytic theory.His work, along with contributions by Ken Cranford, resulted in the Simplified GeneralPerturbations Theory No. 4 (SGP4). In the early 1970s, the original SGP analytic theorywas replaced by a version of the Air Force General Perturbations Theory No. 4 [15].

In 1980, the equations for a form of analytical propagation (SGP4) were presented in theSpacetrack Report Number 3 [16]. The report contained both equations, and FORTRANsource code. The form of the two-line element sets describing the satellite orbital param-eters remains the same today as in 1980. It was not until 1998 that a follow-on paper wasfinally published that summarized the current mathematical theory of SGP4. The paper(Hoots, 1998) was presented at the US Russian workshop, and it is significant for severalreasons, not the least of which is the availability of the mathematical technique for the firsttime in almost 20 years. It will take time to modify any one of the multitudinous versionsof SGP4 that exist on the Internet today because no intermediate formulations were avail-able. This is a quite strange example of a propagator because it has become a ’standard’even though very little information is generally available.

Regarding Vallado, the accuracy of SGP4 is typically about 1 km in position [14]. At a

Mission Analysis 23

distance of for example 300 km this could cause a pointing error of up to 0.2 deg. TLEdata older than a few days are likely to be considerably less accurate than this.

While sensor sites and most military users have changed to SGP4, the practice of providingelement set data that can be used in either SGP or SGP4 has been preserved. Theprimary difference between the two element sets is the formulation of mean motion andthe atmospheric drag representation. While the SGP is a Kozai-based theory, SGP4 is aBrouwer-based theory.

The Brouwer-based theory is based on the Mean Element Theory. This theory began withthe work of Lagrange himself, and has been developed further by many people over manyyears. It is a formal mathematical theory for approximating motion by separating the effectsof fast motions and slow motion.

Moreover, the most widely used form of mean element theory is based upon averaging thedifferential equations of motion over a fast-moving angular variable, and then using theseaveraged equations to predict the motion of the slowly varying elements. The term ”meanelement” does not refer to a numerical average of a sampling of the element and is notrelated to statistics at all.

STK currently implements two mean element theories, the Kozai-based theory and theBrouwer-based theory. The Brouwer-based theory has been implemented in two versions.The Brouwer Short Mean Element Refers to the mean elements considering only the shortperiod terms while the Brouwer Long Mean Element type refers to the mean elementsconsidering both the short period and long-period terms.

2.4.2. HPOP Propagator

The HPOP (High Precision Orbit Propagator) is a high accuracy special perturbation prop-agator. It is not available in the basic edition of the STK. For this reason, the Professionalversion must be used.

The HPOP uses numerical integration of the differential equations of motions to generateephemeris [9] [13]. Several different force modeling effects can be included in the analysis,including a full gravitational field model, third-body gravity, atmospheric drag and solarradiation pressure. Several different numerical integration techniques and formulationsof the equations of motion are available. The different formulations aid in computationalefficiency while preserving accuracy. Because of the many parameter settings availablefor the user, a precise model of the force model environment for almost any satellite canbe specified, and thus a highly precise orbit ephemeris can be generated.

Note that a high precision is not without costs because of two reasons. First, the useris responsible for choosing force model settings appropriate to the situation being mod-eled and second, ephemeris generation takes more computational time and effort thananalytical propagation, which simply evaluates a formula.

Force models can be used to define a precise representation of a satellite’s force environ-ment for use in HPOP analysis. A complete list of the available force models is presented


Appendix D.6..

2.5. Ground Track and Accessibility

When designing a satellite, you do not only expect to launch it into orbit but to also contactit while it is in space and obtain data, give him orders or whatever the type of missionrequires. It is in this context where the ground track of the satellite becomes important.

A ground track is the projection of the satellite’s orbit onto the surface of the Earth. A satel-lite ground track is an imaginary path along the Earth’s surface which traces the movementof an imaginary line between the satellite and the center of the Earth. In other words, theground track is the set of points at which the satellite will pass directly overhead, or crossthe zenith, in the frame of reference of a ground observer.

So the importance of it, relay in the fact that the satellite can only be contacted from Earthfrom parts of the planet that can ’see’ the satellite, which it is in fact, close to the groundtrack of the satellite. This ability to contact the satellite can be defined as accessibilityand the bases where the satellite can be ’seen’ from Earth as ground station. STK allowsintroducing some constraints to the accessibility. Examples of constraints are the azimuthand elevation angle or the range.

The number of ground stations distributed all over the world would define the probabilitythat a certain satellite can be contacted in a period of time. This probability would alsodepend on the type of mission (orbit) of the satellite and on the geographical conditions ofthe ground stations. By simulating these parameters, the accessibility of a satellite can beobtained.

2.6. Lighting

When the satellite is orbiting the Earth, its position to the Sun is continuously changing.This position affects the satellite in a very important way. If the satellite is directly exposedto the sunlight or it is under the shadow of the Earth will affect in the heat absorbed on thesatellite and the solar radiation pressure perturbation force. This amount and variation ofheat affects in the thermal design of the satellite and its lifetime.

STK allows the users to perform calculations on the time a satellite would be exposed todirect sunlight or lighting, umbra and penumbra (which is partial light and partial shadow)(Fig. 2.3).

Mission Analysis 25

Figure 2.3: Description of the umbra and penumbra effects. Source [17].

2.7. Simulation results

Finally, in this chapter, the simulations performed in the STK are presented in a clear andclean way. The tables and graphics are accompanied by the explanations of the resultsand the conclusion of them.

Different types of simulations have been carried out. It is recalled that a very huge amountof data has been analyzed during the simulations. The impossibility to include all of it inthe final report has caused to only prsenet resuming tables and graphics containing themean results. In order to understand what are the simulations performed and how thissimulations have been conducted, a STK user’s guide is presented in Appendix E.

The data that is provided in the website of ESA is the one that has been taken into accountin the simulations since the UPC Cubesat is expected to be launched in one of the futurelaunch opportunities of the Vega launch vehicle [6]. Moreover, there has been some datathat has been maintained constant in all the simulations while other has been changedto produce comparatives in the simulations. The base data used in the simulation is pre-sented in Table 2.1.

The shape and inclination of the orbit has been extracted from one paper published by ESAwhere they said they were still deciding between the 350 km circular orbit and another oneof 350x1200 km [7]. The comparative of these two orbits can be observed below in thissection.

In addition, some propagators have been used during the simulations. The SGP4 hasbeen the standard one due to its reliability when compared to the other analytical onesand because other ones more interesting are not allowed when using the basic version ofSTK. Moreover, by means of the evaluation license of the STK, another propagator hasbeen used, the HPOP, which is presented and compared with the SGP4 at the end of thissection.


Table 2.1: Data used in the simulations

Standard ValuesOrbit shape 350x350 kmOrbit inclination 71 (fixed)Mean motion 15.7312 revs/dayPropagator SGP4Elevation angle 15

Time of SimulationBeginning 1 Jul 2010End 1 Jul 2011

Finally, simulations have been carried out during a year in order to obtain consistent resultsindependently of the lifetime of the satellite. The beginning of the simulation has beenrandomly chosen in a near future.

Note that additional tables and graphics concerning the simulations of this section can befound in Appendix F.

2.7.1. Total and individual access

In this analysis, the accessibility to the satellite is computed. The Cubesat operator canchoose either to detect the satellite by its own ground station or to cooperate with theexisting worldwide network of Cubesat ground stations. Nowadays, more than eighty uni-versities, colleges and research institutions are involved in it.

Figure 2.4: STK map illustrating all the ground stations of the Cubesat network. Source[STK].

The first step in order to obtain results was to insert in STK the UPC ground station to

Mission Analysis 27

later introduce the entire ground stations of the worldwide network (see Fig 2.4). Accesssimulations were carried out in all the ground stations introduced and then classified in anexcel table sorted by time. In other words, the output reports from each ground station werea set of start and stop times of each occasion the satellite was accessed. A ground stationcan access the satellite an average of 700 times a year, which multiplied by each groundstation, gives a total of 56.000 times a year. The problem resides in the comprehensionof the data because in instance, a ground station maybe is accessing the satellite at thesame moment that another one or maybe more than one. So the total time the satellitewas being accessed was not the sum of all the seconds the ground stations were seeingit since some of these seconds were overlapped with others.

The solution was to sort by start time all the accesses independently of the ground stationthe access was. Then, the last thing to do was to develop a simple algorithm to sum all theseconds comparing if the time to sum was overlapped with the previous accesses. Thisalgorithm gave the total clean time the satellite was accessed during a year. In Table 2.2,a comparative between using the UPC ground station or the entire network is presentedalong with the duration per day, which gives a better understanding of the time the satelliteis being accessed.

Table 2.2: Access time comparative between UPC and global network

Total Duration Mean Duration/DayNetwork 359.3305 sec 9845 sec

UPC 140.095 sec 384 sec

It is beyond any doubt that cooperation is of extremely benefit for everyone. Getting in-volved in the worldwide network can give the UPC operators more than 25 times moreaccess time than using one unique ground station. This time would allow the operatorsand users to better control and use the satellite. Speaking in terms of a day, the UPCsatellite could be operated 2.75 hours instead of 6 minutes a day, which is a considerableincrease in time.

Moreover, simulations regarding the differences of access time between ground stationshave been performed. The importance of the geographical situation of a ground stationalong with the type of orbit of a satellite are the major elements of differences when com-paring ground stations. A table containing the differences on access between groundstations is presented Appendix F. A table (see Table 2.3) showing the difference betweenthe more and the less accessed ground stations and a graphic (see Fig. 2.5) comparingall of them is presented in the main body of the work.

Table 2.3: Access time comparative between the more an less accessed ground stations

Ground Station Number of accessesMax # Accesses NTNU 2130Min # Accesses Malaysia 528


Figure 2.5: Number of accesses for all the ground stations during a year (Part I).

Figure 2.6: Number of accesses for all the ground stations during a year (Part II).

The graphics in Fig. 2.5 and Fig. 2.8 allows us to indicate some conclusions about acces-sibility. It is important to recall that the most accessed ground station, NTNU, is situatedat very high latitudes, about latitude 63o ,and the less accessed one, Malaysia, is located,in contrast, in very low latitudes, about 3o. We can extract from these results that for our

Mission Analysis 29

case the latitude is someway proportional to the amount of time you can access a satel-lite at that point. In fact, this is only validated to our case because a satellite orbiting inan equatorial orbit would only be accessed from ground stations close to the equator. Inother words, the closer the ground station is in latitude to the inclination of the orbit you aretrying to access, the more time you would be able to ’see it’. In our case, the satellite isorbiting with an inclination of 71o, so the ground stations closer to this latitude can accessthe satellite more time.

If we simulate the accessibility to a ground station situated in some random point of theEarth but at latitude 71o, we obtain that you would access the UPC satellite 17.5 minutesa day. That is an increase of 0.3 minutes to the duration per day to NTNU (the mostaccessed one) and of 13 minutes to Malaysia (the less accessed one). This is due to thefact that the radius of the equator is the biggest one in terms of latitude and that the radiusof the latitudes becomes smaller when approaching both poles. So, a satellite with 71o ofinclination would pass through each latitude the same times, but because higher latitudeshave smaller radius than smaller latitudes, the satellite would pass through the same pointmore times in higher ones than in smaller ones. For example, a satellite with a polar orbitwould pass through both poles in each revolution but would have to wait a very long timeto pass through a determinate point in the equator more than one time.

2.7.2. Lighting

Space is a very harsh environment. Temperatures can change in very little time dependingif you are in direct sunlight or in the shadow of some body. In our case, the UPC Cubesatwould orbit in a low orbit so at some points it would face directly the Sun but in othercases, it would be at the shadow of the Earth. Depending on which of these situationsthe satellite is, it would have one temperature or another. The results obtained wouldbe important for the thermal design of the satellite because this subsystem is the onein charge of maintaining a suitable temperature for all the components of the satellite atany time. Tables and graphics about the time the satellite is at lighting (direct sunlight),penumbra (partial sunlight) and umbra (total shadow of the Earth) are presented in Table2.4 and in Fig. 2.7. Remember that these results are valid for simulations of one year.

Table 2.4: Lighting properties

Max Dur. Min Dur. Mean Dur. Total Dur. Mean Dur./DayLighting 9.7 days 6.4 min 64.5 min 20949334 sec 15.94 h.

Penumbra 40.8 min 0.13 min 0.24 min 152889 sec 0.12 h.Umbra 36.4 min 0.4 min 32.2 min 10434988 sec 7.94 h.

Results show us that more than a 66% of the time the satellite is orbiting the Earth, it isdirectly facing the Sun. It is also of notice that the maximum continuous time the satellitewould be facing the Sun is of 9.7 days. This is due to the fact that the orbit at some pointwould have an orientation in the sense that it would all face to the Sun in some subsequentrevolutions.

So this value, 9.7 days, would be the reference value that would be used during the ther-


Figure 2.7: Total duration lighting percentages

mal analysis of the Cubesat. If the components of the satellite can handle the amount ofupcoming heat fluxes for 9.7 days without pause, the satellite would resist all other situa-tions.

2.7.3. Orbit shape comparative

The inconsistence of the data given by ESA about the characteristics of the orbit is aproblem when designing the mission analysis of the UPC Cubesat. Information givenshow that it has not been decided yet which orbit the Cubesat would have [7]. At first, acircular orbit of 350 km of altitude seemed to be the final decision but they later stated thatmaybe they would switch to an elliptical one with a perigee of 350 km and an apogee of1200 km. In this section of the results, a comparative between these two orbits is madealong with the advantages and drawbacks of each one. Simulations are done with respectto the changes that would occur in accessibility and lighting due to the fact that these twoparameters are of great interest in the context of the project but it is important to state thatmore comparatives regarding other parameters can be performed.

1) Accessibility

Depending on the time you can access the satellite, the operators would be able to performgive more orders to the satellite, download more data or just have more time to controlit. The shape of the orbit affects this time independently of its inclination. Simulationresults with the most and less accessed ground stations and the UPC ground station arepresented in Table 2.5 and Fig. 2.8.

Results prove that indeed, a higher altitude would benefit the control of the satellite. TheUPC Cubesat would be able to be seen more time during the day, which is translated tomore security to the Cubesat. The main drawback of increasing the orbit apogee to 1200km would be the more difficult communication with it. A major distance means a bigger

Mission Analysis 31

Table 2.5: Number of accesses vs. orbit shape for UPC, NTNU and Malaysia

UPC NTNU Malaysia350x350 km 732 2130 5281200x350 km 1250 2397 901

Figure 2.8: Number of accesses vs. orbit shape comparative for UPC, NTNU and Malaysia

power to transmit and which nearly all the times is translated to a bigger antenna whichalso means more weight to the satellite. It is true that this increase in distance is not a verybig problem to deal with but it is important to take it into account.

2) Lighting

Table 2.6: Lighting properties for a 1200x350 km orbit

Max Dur. Min Dur. Mean Dur. Total Dur. Mean Dur./DayLighting 17.4 days 2.3 min 88.2 min 23437346 sec 17.84 h.

Penumbra 40.5 min 0.12 min 0.27 min 142178 sec 0.11 h.Umbra 36.6 min 1.6 min 30.2 min 7957779 sec 6.05 h.

The comparative (see Table 2.6 and Fig. 2.9) shows that with a higher orbit, the amountof lighting is increased considerably. The effect of this increase in direct upcoming solarradiation is translated in a harsher environment to the Cubesat. The maximum duration ofdirect sunlight is increased from 9.7 to 17.4 days, which is almost the double. The thermalcontrol of the satellite should be more effective and important in this situation because thecomponents inside the satellite would be operating in a wider range of temperatures.

Moreover, umbra and penumbra times are smaller now due to the fact that the satellite ismore far away from the Earth and the shadow of it would be smaller. Anyway, values arenearly the same as in the 350 km circular orbit so little changes to the thermal design ofthe UPC Cubesat should be considered because of umbra and penumbra effects.


Figure 2.9: Lighting properties comparative for a 1200x350 and a 350x350 km orbit

2.7.4. Elevation angle comparative

The elevation angle is the constraint we insert in the simulations in order to obtain a givendegree of reliability of the results. A picture describing this effect is shown in Fig. 2.10.

This elevation angle can have any value you want to insert from 0o to 90o. In a lot ofsimulations and reports this elevation angle is set to 15o. This angle is thought to be theone where objects orbiting around the Earth can be ’clearly seen’. In other simulations thisangle is reduced to 10o, 5o or even 0o, which is the line of sight, because the equipmentand the simulations they are performing allow doing that. In the UPC Cubesat simulationsthe default value is 15o but we wanted to compare what differences arise when changingthe elevation angle to 5o and 0o (See Fig. 2.11).

The lighting of the satellite would not be affected due to this angle so accessibility is theonly parameter this comparative is considering. Note, that a comparative with respect tothe shape of the orbit or other parameters can be also performed.

Clearly, a smaller value of elevation angle is translated to more accessibility. It is enormousthe change with only 15o but certainly, the mean values show that with an elevation angleof 5o, we get almost 3 times more access time than with the default value of 15o. Moreover,if the constraint applied is the one of the line of sight, 0o, which means indeed no constraintbut the one of the Earth, we get about 5 times more access time than with 15o. So thequestion is why the constraint is not applied to the lower one, and the answer is clear,

Mission Analysis 33

Figure 2.10: Access scheme for different elevation angles

because the data obtained during the time the satellite is between 0o and 15o it is notreliable due to reception and transmission errors.

2.7.5. Propagator comparative

STK basic edition allows the user to simulate using four different propagators. These arethe two-body, the J2, the J4 and the SGP4 propagators. Each one has different levelsof reliability depending on which perturbations effects take into account as seen in theprevious section. The values used with the SGP4 propagator are resumed in Table 2.7.

Table 2.7: SGP4 data

B*term 8e-5 (fixed)Atmospheric density 6.98e-12 (fixed)Cd 2.2 (fixed)

SGP4 computes the atmospheric drag with a simple model that uses parameters such asthe B* term (only used in the SGP4 code) [15] [18]. The B* term is related to the ballisticcoefficient of the satellite and needs the value of the drag coefficient of the satellite andthe atmospheric density at the altitude of the orbit to be computed. These three values,the B* term, the drag coefficient and the atmospheric density have been used only whenperforming simulations with the SGP4 propagator and have been set to the fixed valuesshown in Table 2.7.

A comparative to show the differences between the propagators of the basic edition isperformed along with a comparative between the SGP4 the HPOP propagator. As in theprevious comparative, simulations are performed with respect to accessibility and lightingfor one year.

1) Accessibility


Figure 2.11: Access comparative for different elevation angles for UPC, NTNU andMalaysia ground stations

Results (see Table 2.8 and Fig. 2.12) show different aspects of the simulations done. First,it can be concluded that the J2 and the J4 propagator give nearly the same results. The J4term is really little compared to the J2 term so when simulating, very little differences areobtained from them. Moreover, the two-body propagator also gives very similar results tothe first two ones. This propagator does not take into account any perturb force other thanthe gravitational force between the satellite and the Earth. Results are similar to the J2 andthe J4 propagator but it is true that are significantly different due to this fact. The two-bodypropagator simulation gives more access time to the satellite in all ground stations.

Finally, the SGP4 propagator does give considerably different results than the other threepropagators. This propagator is the most accurate of the four because it takes into ac-

Table 2.8: Mean access duration/day vs. propagator for UPC, NTNU and Malaysia groundstations

UPC NTNU MalaysiaSGP4 6.397 min 17.213 min 4.469 min

J4 8.216 min 22.568 min 5.612 minJ2 8.215 min 22.566 min 5.612 min

Two-Body 8.225 min 22.596 min 5.614 min

Mission Analysis 35

Figure 2.12: Mean access duration/day comparative for each propagator for UPC, NTNUand Malaysia ground stations

count not just the gravitational force from the Earth, the J2 and the J4 terms but also theatmospheric drag and the gravity coming from the Sun and the Moon. Because of all theseeffects, the duration a ground station is accessing the satellite is smaller than that of theother propagators. In each revolution, the satellite is closer to the Earth because of theatmospheric drag so the time passing through the ground stations would be smaller eachtime.

2) Lighting

When simulating the effects of propagators in lighting (see Fig. 2.13), similarities arisefrom those regarding accessibility. J2 and J4 propagators have nearly exact results whilethe other ones, the two-body and the SGP4 propagators are significantly different. We canextract from Fig. 2.13 that when using the SGP4 propagator less lighting is obtained dueto the constant approach to the Earth because of the effect of the atmospheric drag. Usingthe two-body propagator, we obtain also less lighting probably because of the inconsis-tency of the data thus just the gravitational force of the Earth is taken into account as aperturb acceleration.

3) SGP4 vs. HPOP

Basic simulations have been performed using the SGP4 propagator but because this isnot the most accurate one, STK professional has been used in order to be able to usea more accurate one, in this case the HPOP, described in section 2.4.2.. A comparativebetween these two propagators in accessibility and lighting is performed. Values used


Figure 2.13: Lighting properties comparative for each propagator

in this comparative are the previous mentioned for the SGP4 propagator. For the HPOPpropagator the values used are resumed in Table 2.9.

Table 2.9: HPOP data

Force model WGS84 EGM96Radiation coefficient 1.5Shadow model Dual coneThird bodies Sun and MoonIntegrator Gauss-Jackson 12thInterpolation LagrangeCd 2.2 (fixed)Atmospheric model Jacchia-Roberts

Note that in contrast to the previous propagator comparative, this one has been carried outusing the 1200x350 km orbit because in order to simulate the circular 350 km orbit usingHPOP it is necessary to reach at least one year of lifespan, which it is not obtained, as itwill be seen in the lifespan simulation.

Significant differences (see Fig. 2.14) are observed between the two propagators in termsof accessibility which are due to the accuracy of each of them. HPOP in contrast to theSGP4 propagator takes into account the solar radiation pressure. Moreover, the atmo-spheric drag simulation is more accurate in the HPOP thus the SGP4 one uses a verysimple one. Also, the HPOP propagator uses a numerical simulation in contrast to theanalytical one used in the SGP4. This numerical simulation gives us a better accuracy butin the other hand needs more computational time to obtain the results.

Lighting (see Fig. 2.15) is observed to be the same no matter which propagator is being

Mission Analysis 37

used so when referring to the thermal analysis of the satellite it is not a big problem whichpropagator is being used.

Figure 2.14: SGP4 and HPOP mean accessduration/day comparative for UPC, NTNUand Malaysia ground stations for a 1200x350km orbit

Figure 2.15: SGP4 and HPOP lighting prop-erties comparative for a 1200x350 km orbit

2.7.6. Simulation time comparative

Up to this point, all the simulations have been carried out for the same time duration, oneyear, as it has been said at the beginning of this section. In this subsection, differentstart and stop times, all of them with duration of one year, will be simulated in order tounderstand the importance of the launch date. Table 2.10 shows the comparative betweenfive different simulations times.

Little differences are observed from the simulations performed for the UPCSat. It is im-portant to know which is the exact launch date but this parameter is not vital in order toconduct the simulations for the accessibility of a satellie. Moreover, the launch date is aflexible parameter due to the fact that the launch depends of lots of factors such as theweather conditions for instance. By all these reasons, a perfect simulation is impossobleto perform until the launch is finally performed.

2.7.7. Satellite lifetime

The lifetime or lifespan of a satellite is one of the most important issues while designing themission analysis. This is the time the satellite will be orbiting the Earth without falling to theatmosphere and burn up. The satellite decay is influenced by the atmospheric drag of the


Table 2.10: Simulation time comparative for different gaps of one year for the accessibilityproperties of the UPC ground station

Start time - Stop time # AY # AD TDY (sec) MDA (sec) DD (min)

1/07/2010-1/07/2011 1352 3.704 618909.291 457.773 28.2601/07/2011-1/07/2012 1353 3.706 619918.150 458.180 28.3061/07/2012-1/07/2013 1352 3.704 619269.088 458.039 28.2771/07/2013-1/07/2014 1352 3.704 619521.971 458.226 28.2881/07/2014-1/07/2015 1356 3.715 619681.348 456.992 28.295

AY: Access/year

AD: Access/day

TDY: Total duration/year

MDA: Mean duration/access

DD: Duration/day

Earth. This atmospheric drag is greater the more closer you are to the Earth, so satellitesorbiting in LEO will be more prone to this effect. In other words, if you want your satellite inLEO to have a lifetime of many years you need a propulsion system in order to power upyour satellite when approaching to dangerous altitudes. Moreover, this propulsion systemis most of the times so heavy that Cubesat cannot handle it so no propulsion can be addedto them. In conclusion, CubeSats would have a little lifespan that has to be calculated inorder to define the mission duration.

To simulate this parameter the Lifetime module form the STK professional edition is neededso it has been simulated using the evaluation license provided by STK. Propagators usedin this simulation have been the SGP4 and the HPOP, previously commented. Moreover,simulations have been performed in the two cases of the orbit shape. The atmosphericdensity model and the radiation coefficient used is the same as for the HPOP simulations.

Table 2.11: SGP4 and HPOP lifetime comparative for different shapes of orbit. Launchdate: 1 Jul 2010

Propagator Reentry Date # orbits Lifetime350x350

SGP4 23 Nov 2010 2313 145 daysHPOP 04 Oct 2010 1522 95 days

1200x350SGP4 05 Jan 2018 40962 7.5 yearsHPOP 02 Sep 2016 33745 6.2 years

The difference in lifespan (see Table 2.11) is considerable different when orbiting in thecircular 350 km or in the 1200x350 km orbit independently of the propagator used. Adifference of years it is observed which it is due to the effects of the atmospheric drag. Soif the satellite operators want a longer lifespan they must use the 1200x350 km becausewith the other one they would only be able to operate the satellite less than half a year.

The propagator comparative shows that using the HPOP it is obtained a lower lifetime.The difference between them relays mainly in the different atmospheric drag model used

Mission Analysis 39

by each one. These models are commented previously and this gives the difference it isobserved in lifespan. In case of doubt, it is advised to take for real the value of the HPOP,which it has a more reliable drag model. A graphic of the apogee, perigee and eccentricityvariation of the 1200x350 km orbit using the HPOP propagator is presented in Fig. 2.16.

Figure 2.16: Apogee, perigee and eccentricity variation during the HPOP 1200x250 kmsatellite lifetime

Finally, an analysis of the evolution of the accessibility during the lifetime of the satelliteadviced. The satellite will be colser to the Earth in each revolution, and this variationin altitude will cause a change in the accessibility to the satellite. Table 2.12 shows theaccessibility variation in the UPC ground station for its fisrt four years of lifetime. Thesimulations have been carried out for the 1200x350 km orbit with the HPOP. Note thatevery year that passes, the access time to the ground station is lower due to the fact thatthe apogee is lower. The explanation is similar to the one of the orbit shape comparativesubsection.

Table 2.12: Accessibility evolution of the first four years for the UPC ground station

Year # AY # AD TDY (sec) MDA (sec) DD (min)

1st year 1352 3.704 618909.291 457.773 28.2602nd year 1197 3.279 472752.965 394.948 21.5863rd year 1109 3.038 382026.196 344.478 17.4444th year 985 2.698 283595.182 287.914 12.949AY: Access/year

AD: Access/day



DD: Duration/day


2.7.8. Orbital elements variation due to perturbations

The variation of the classical orbital elements due to each of the perturb forces is studiednow. The HPOP allows to choose which perturb forces are considered during the simula-tions. Simulations comparing the changes that the perturb forces produce in each orbitalelement are performed along with the conclusions that can be extracted from it.

Changes can be either secular or periodic. Existent literature has proved that thesechanges can be summarized in Table 2.13 [19].

Table 2.13: Theoretical orbital elements changes due to each perturbation force. Source[19].

Non-spehrical Third-bodies Atm. drag SRPa P P P S Pe P P P S Pi P P P S P

Ω P S P S P P Sω P S P S P P Sν P S P S P P S

S: Secular

P: Periodic

Some of these variations are very little compared to other ones but at the end, little or big,these should be the variations that would appear in the simulations.

Furthermore, several simulations have been performed with the HPOP in the 1200x350km orbit in order to understand the effects produced by the non-spherical Earth, the third-bodies, the atmospheric drag and the solar radiation pressure.

Simulations have started with no perturbations and then the perturb forces have beenadded gradually in order to understand which effects are producing to the orbital elements.The effects of perturbations in the orbital elements have been compared when they areapplied and when the Earth does not have any perturbations.

So the first thing that has been done, has been to deactivate the effects produced by third-bodies, atmospheric drag and solar radiation pressure. Then the only thing to changeis the shape of the Earth. To simulate the effects of a spherical Earth, the central bodygravity of the Earth has been changed. In the potential gravity model (see Eq. 2.21), n isthe degree of the harmonics and m is the number of the harmonics. By giving values tothese two terms, you are telling STK where to truncate the series.

U =µr[1−

∞

∑n=2

n

∑m=0

Jnm(R⊕

r)2ρnm(senφ)cos(m(λ−λnm))] (2.21)

Simulations have been performed for the spherical model of the Earth (n=1), the ellipsoidal(n=2) and the default value of STK (n=21).

Mission Analysis 41

Results prove that a spherical Earth model without perturbations do not produce anychanges to the orbital elements as expected. When simulating for an elliptical model anda more complex (n=21) model of Earth, periodic changes appear in the semi-major axis,the eccentricity and the inclination. Secular variations are observed in the argument ofperigee and the right ascension of the ascending node (RAAN). Graphics comparing theinclination and the argument of perigee in a spherical and an elliptical model of Earth arepresented in Fig. 2.17 and Fig. 2.18 respectively.

Figure 2.17: i comparative between a spher-ical (blue) and an elliptical (green) model ofEarth

Figure 2.18: ω comparative between aspherical (blue) and an elliptical (green)model of Earth

Very little differences arise between the elliptical model of Earth and the complex model ofEarth. The secular changes of the argument of perigee and the RAAN are the same. Thesame occur with the periodic changes of the semi-major axis and the inclination. The onlydifference appears in the eccentricity where a new periodic pattern is added as it can beseen in Fig. 2.19 and Fig. 2.20.

Figure 2.19: e variation for an elliptical modelof Earth

Figure 2.20: e variation for a complex modelof Earth

Third-bodies effects produce periodic changes to all orbital elements and also seculareffects to all of them in contrast to what it is said in the theory, where only secular changesare appreciated in the argument of perigee and in the RAAN. It is true, though, that allthis changes are very little and do not produce important consequences. Examples in theeccentricity and the RAAN are presented in Fig. 2.21 and Fig. 2.22 respectively.

When talking about the atmospheric drag, the theoretical assumptions are correct. Peri-odic changes are produced in all orbital elements, being the ones in the semi-major axis,eccentricity and inclination little compared to their secular variations. So, secular varia-tions are produced in those three orbital elements. Graphics presenting the variations in


Figure 2.21: e variation produced by third-bodies effects

Figure 2.22: Ω variation produced by third-bodies effects

the semi-major axis and the argument of perigee are presented in Fig. 2.23 and Fig. 2.24respectively.

Figure 2.23: a variation produced by atmo-spheric drag

Figure 2.24: ω variation produced by atmo-spheric drag

Finally, the solar radiation pressure effect is studied. Effectively, periodic variations occurmainly in the semi-major axis, the eccentricity and the inclination. Curiously, these changeshave a period of exactly one year. Moreover, the argument of perigee and the RAAN havesecular variations and little periodic changes. Examples of it can be seen in Fig. 2.25 andFig. 2.26 where the changes produced by the solar radiation pressure in the semi-majoraxis and the RAAN respectively are presented.

Figure 2.25: a variation produced by SRP Figure 2.26: Ω variation produced by SRP

To conclude this section, the effects produced by all the perturb forces together is simu-lated. Results show that the main perturbations that affect our satellite are those of the

Mission Analysis 43

atmospheric drag and the non-spherical Earth. Although as we have seen, all the perturbforces affect our satellite, the ones of the third-bodies and the solar radiation pressure areso little that are not appreciated when simulated with the other ones. Graphics with thesemi-major axis, eccentricity and inclination are presented in Fig. 2.27, Fig. 2.28 and2.29 respectively. The argument of perigee and the RAAN are mostly the same as in thenon-spherical Earth simulation.

Figure 2.27: a variation produced by all per-turb forces

Figure 2.28: e variation produced by all per-turb forces

Figure 2.29: i variation produced by all perturb forces

2.7.9. Dispersion analysis

Finally, a dispersion analysis is performed for our satellite. We define as dispersion thedifferences observed between two or more bodies relatively close to each other in a de-terminate period of time. In other words, we have simulated the orbits of three satellitesand then we have observed the variations in their position relative to each other duringone week. The main satellite is the UPCSat and the two other ones (UPC1 and UPC2) arepossible variations of the CubeSat separated 50 m up and down respectively of the mainone (see Fig. 2.30).

In order to simulate the dispersion, the inputs introduced in STK are in the spherical coor-dinate type, only changing the value of the range for the two additional satellites. Simula-tions, as have been said previously, have been performed for seven days and the resultsobtained can be seen in Fig. 2.31. The propagator used is the HPOP for a 1200x350 kmorbit.

In just seven days, a difference in range of approximately 90 km is observed. It is importantto mention that this difference is not in altitude. If we compute the altitude difference in one


Figure 2.30: Initial conditions of the dispersion analysis

Figure 2.31: Position of the satellites seven days later

week, the results have a lower value as can be seen in Fig. 2.32. The evolution of therange in time can be seen in Fig. 2.33 for the difference between the UPCSat and UPC1.It is important to underline that there is an increasing periodic variation along with the linearsecular variation of about 12 km/day. Changing the perturbations taken into account doesnot make visible changes to the results so only the distance travelled by the satellite is theone affecting these differences in range. It is important to mention though, that satellitesplaced at 50 m. in the longitudinal plane of the main satellite will only have small periodicvariations and no secular variations. It can be said, that the distance will keep constant atthe initial range.

Figure 2.32: Final positions of the satellites

Changing the initial values of separation gives different results (see Table 2.14). It is evi-dent that for less initial range, fewer differences in time will be obtained.

Mission Analysis 45

Figure 2.33: Range variation between UPCSAT and UPC1 for 50m separation

Table 2.14: Range variations between UPCSAT and UPC1 for different initial separations

Initial Range Final Range10 m 13.5 km50 m 85 km100 m 176 km500 m 900 km1 km 1790 km

Moreover, the dispersion analysis can be seen as a ’safety’ simulation for the UPCSatbecause it tells you the possible difference you will obtain with a certain margin, in thiscase, a margin of 50 meters. In other words, the simulations are not perfect and so aresimulated with some safe margins in order to obtain a range of values where the resultscan be. This margin can be more or less constraint that would depend on the reliability ofthe data and the simulator.

For the UPCSat, a margin of 50 meters has been studied for a simulation of seven days. Itis highly probable that the real position of the satellite in these seven days will be within therange obtained. It is necessary to distinguish between the vertical range and the horizontalrange, which is defined in Fig. 2.34.

The ellipsoid presented is the range within the values of the real position of the Cubesatwill be in seven days in the future.


Figure 2.34: Range within the satellite will be for a 50m margin

Thermal Analysis 47

Chapter 3

THERMAL ANALYSIS

3.1. Theoretical Background

Thermal analysis is a branch of materials science that studies the properties of materialsas they change with temperature. Moreover, in a satellite definition, the thermal subsystemhelps protect electronic equipment from extreme temperatures due to intense sunlight orthe lack of sun exposure on different sides of the satellite’s body.

In general, there are three main heat transfer modes [20]: conduction, radiation and con-vection. In space, due to the extremely low residual pressure, only conduction and radia-tion modes are present.

Conduction is the process by which heat is transferred through a solid and it is governedby Fourier’s Law (see Eq. 3.1).

q = −k∇T (3.1)

Where q is the heat flow rate vector, k the thermal conductivity and T the temperature.

On the other hand, radiation heat transfer is governed by Stefan-Boltzmann’s Law statingthat the black-body irradiance is proportional to the fourth power of its temperature (seeEq. 3.2).

E = σ ·T4 (3.2)

Where σ is the Stefan-Boltzmann constant, 5.67·10−8W/m2K4.

All these formulas concern the black-body which is an idealized object absorbing all radiantenergy from any direction or wavelength and emitting in any direction isotropically. Theradiated energy of the black-body only depends on its temperature, but a real body canabsorb, reflect and transmit radiation energy so that absorptivity a, transmittivity t andreflectivity r quantities are defined, all wavelength and angular dependent (see Fig. 3.1)[20].

As there is no perfect black-body in practice, the emissivity ε(l) is defined as the ratiobetween the energy emitted by a surface to that of a black body at the same temperature.

Absorptivity and emissivity can either be hemispherical or directional and either total orspectral. The second Kirchhoff’s law states that for a given direction q, directional spectralabsorptivity and emissivity are equal (see Eq. 3.3).


Figure 3.1: Incident light characteristics

ε(q, l) = α(q, l) (3.3)

But, in general, this is not true with total hemispherical values mainly because of theirstrong wavelength dependence. Both α and ε varies with the angle of incidence but theyare assumed to follow the Lambert’s law stating that directional absorptivity/emissivity isproportional to cos(q) (maximum for normal incident angles and null for tangential ones).

The source temperature of incident radiation is different to that of the satellite, so it is impor-tant to distinguish the spectra that it is being used in every moment. As the temperature ofa spacecraft lies in the 70K-700K range, the emitted radiation is infrared (IR wavelengthsrange from 5 to 50 µm). But the source of the main incident radiation is the Sun whichcan be considered as a blackbody emitting at 5776K. This temperature lies in the visiblespectrum (UV wavelengths range from 0.2 to 2.8 µm). Actually, thermal engineers adopteda standard convention. These call ε the hemispherical emissivity in infrared wavelengthsand α the solar absorptivity in visible wavelengths. A specific material has specific valuesof α and ε, which determine its thermal behavior.

Furthermore, in order to perform the thermal analysis of a satellite, the heat sources ofthe satellite must be studied. A satellite orbiting Earth has several heat sources [20]. Ascheme of the heat fluxes of a satellit is presented in Fig. 3.2.

• Direct solar flux depending on the distance to the Sun, with a mean value around1367 [W/m2] at 1AU (1414 [W/m2] at winter solstice and 1322 [W/m2] at summersolstice).

• Albedo planetary reflected radiation. For Earth, the mean reflectivity is assumed tobe near 30% .

• Earth infrared radiation. Earth can be modeled as an equivalent black-body emittingat a mean temperature of 255 K with a flux of 237 [W/m2].

• Internal dissipated power in electronic components.

During the eclipse, only two heat sources are still present. These are Earth’s infrared andinternal dissipation and the spacecraft will be cooler. The temperatures of the satellite tend

Thermal Analysis 49

Figure 3.2: Heat fluxes of a typical satellite orbiting Earth. Source [20].

thus to vary in a cyclic way along the orbit, rising in sunshine and dropping during eclipse.The sky, called Deep Space, is the main source of cold and can be seen as a black bodyemitting at 3K. This temperature represents the radiation of the stars, the galaxies and theCosmic Microwave Background.

This change in temperature along the orbit of a satellite is the main reason to require athermal control for a satellite. But why we need it? Mainly because the electronics andequipments of the satellite can only operate in certain temperatures ranges. Typical limitsare:

• Electronics: -15oC - +50oC

• Mechanisms: 0oC - +50oC

• Rechargeable batteries: 0oC - +20oC

So the design goal is to maintain these temperatures ranges. In other words, is to have athermal balance in the satellite (Total of absorbed plus generated heat equal to heat lostto space - see Eq. 3.4) [20].

QSun+QAlbedo+QEarth+Qinternal = Qradiated (3.4)

Q is the heat generated by all these elements. In practice, in a grey body with a determinateemissivity and absorptivity, the heat flux absorbed and radiated (J) would be the ones ofthe expressions of Eq. 3.5 and Eq. 3.6 respectively.

Jabsorbed= α ·Jincident (3.5)

Jradiated= εσT4 (3.6)

So in order to achieve thermal balance we can rewrite Eq. 3.4 as Eq. 3.8 and Eq. 3.8.

Js ·Asolar ·α+Ja ·Aalbedo·α+Jp ·Aplanet·α+Qinternal = Ar · εσT4 (3.7)


T4 =Qinternal+α(Js ·Asolar+Ja ·Aalbedo+Jp ·Aplanet)

Ar · ε ·σ(3.8)

Note that the areas of the Eq. 3.7 and Eq. 3.8 refer to the areas of the satellite facing theupcoming heat flux.

Moreover, by taking a look to Eq. 3.8, it can be assumed that balance temperature canonly be controlled by varying the ratio of α to ε. By calculating this temperature for all thepossible cases the satellite can be involved in, you will get the range of temperatures foreach part of the satellite.

3.2. Simplified results

The thermal balance of a satellite can be computed by several ways by means of the theoryexplained in the previous section. In this section, the thermal balance of the Cubesat ofUPC is computed with some simplifications in its most critical cases. In Appendix G thesteps to follow are shown in order to have a more realistic analysis.

First, the cases for which the satellite will be simulated must be presented. The thermalanalysis is performed to obtain among others the range of temperatures the satellite andits components will be operating in. So, in order to obtain this range, the maximum andminimum temperatures must be calculated, these are the critical temperatures. Thesetemperatures will be obtained when simulating the critical cases.

The critical cases known as cold and hot cases are the ones where there is a minimumand maximum incoming heat flux respectively. In Table 3.1, there is a sample of the valuesused in the two cases.

Table 3.1: Data used in the hot and cold case calculations

Hot Case Cold CaseOrbit Direct sunlight Total eclipse

Solar heat flux 1414 W/m2 0Albedo coefficient 0.35 0.25

Earth heat flux 260 W/m2 220 W/m2

The hot case will be that in which the Sun is constantly radiating the satellite with itsmaximum heat flux, the greatest albedo coefficient and the Earth is also radiating with itsmaximum heat flux. By contrast, in the cold case no incoming heat flux of the Sun wouldappear because the satellite will be in eclipse, there will not be albedo too and the Earthtemperature would emit its lower heat flux.

Note that internal dissipation is not taken into account in the calculations. This is the firstsimplification of the problem. The second simplification of the problem is to assume thesatellite as a sphere of radius r (see Eq. 3.10). With this second simplification we willobtain the same areas for the incident radiation coming from the Sun, the Earth’s albedo

Thermal Analysis 51

and the Earth radiation (see Eq. 3.9). So, the only parameters considered are the heatfluxes of the Sun, albedo and Earth and the values of emissivity and absorptivity of thematerials.

A = Asolar = Aalbedo= Aplanet = πr2 (3.9)

Ar = 4πr2 (3.10)

The heat flux coming from the albedo can be expressed by Eq. 3.11 where F is the viewfactor (fraction of radiation arrives at one surface after leaving another surface).

Ja = Albedocoe f f ·F ·Js (3.11)

We solve the equations for a black-body (emissivity and absorptivity equal to one) consid-ering low thermal inertia (see Eq. 3.12).

T4 =α ·A· (Js+Ja +Jp)

Ar · ε ·σ= (

Js+Ja +Jp

4·σ) ·

αε

(3.12)

HotCase⇒ T4 =Js+Ja +Jp

4·σ=

1414+(0.35·0.15·1414)+2604·5.67x10−8 ⇒ T = 23.16oC

(3.13)

ColdCase⇒ T4 =Js+Ja +Jp

4·σ=

0+(0.25·0.15·0)+2204·5.67x10−8 ⇒ T =−90.94oC (3.14)

So, a satellite considered as a black-body would have a temperature ranges from -91 to23 oC (see Eq. 3.13 and Eq. 3.14) which is quite a lot for the design requirements of thecomponents of the satellite. However, the UPCSat is not a black body so new calculationswill be performed with the values of emissivity and absorptivity the materials of our Cube-sat. Results are exposed in Table 3.2. Note that the values of emissivity, absorptivity andother characteristics of the materials of the UPCSat can be found in Appendix G.1..

Table 3.2: Hot and cold case temperatures for different materials

Surface Al. frame Al. panel (with Kapton) Solar panelsα 0.08 0.87 0.91ε 0.15 0.81 0.81

Hot Case -20oC 28.5oC 32oCCold Case -117.4oC -87.7oC -85.6oC

Temperatures ranges are not that different from the black-body example. The Kaptonlayer used in the aluminum panel has improved the cold case temperature and with the


solar panels can form an interesting multilayer face. However, the temperatures shownare for simulations with no thermal inertia. Thermal inertia is the key property controllingthe diurnal and seasonal surface temperature variations and is typically dependent on thephysical properties of the materials. The temperature of a material with low thermal inertiachanges significantly during the day, while the temperature of a material with high thermalinertia does not change as drastically.

When thermal inertia is taken into account, cold case temperatures are higher due to thefact that the satellite is most of the time in sunlight and the reduction of temperature duringeclipse is slower. Transient analysis is necessary to determine the effects of thermal iner-tia. However, there is still one parameter to take into account. Internal dissipation causesthe temperatures to vary significantly and a most realistic analysis should be performed.This analysis has to be performed after the simplified one and the steps to follow it arepresented in the appendix.

3.2.1. STK simulation

By means of the Space Environment and Effects Tool (SEET) module of STK releasedto commercial uses in the final version of STK at the end of 2009 a more complete ther-mal analysis has been performed. SEET module offers users to perform analysis in thefollowing fields [9].

• Radiation environment

• Vehicle temperature

• South Atlantic anomaly (SAA)

• Magnetic filed

• Particle impacts

Among a wide range of simulations, SEET module can compute the expected radiationdose rate and total dose due to energetic particle fluxes for a range of shielding thicknessesand materials, the spacecraft’s entrance and exit times through the SAA, the total massdistribution of meteor and orbital debris particles that impact a spacecraft along its orbitduring a specified time period or the local magnetic field at the current location. But themost important feature considered in the thermal analysis is the vehicle temperature.

Using the known thermal balancing equations, the vehicle temperature simulation deter-mines the mean temperature of a space vehicle due to direct solar flux, reflected andinfrared Earth radiation, and the dissipation of internally-generated heat energy. The usermay specify spherical objects, or planar objects with particular orientation, for the compu-tation of temperature. SEET treats the spacecraft as a single isothermal node, where theuser specifies bulk thermal characteristics. On the other hand there are several simplifi-cations in the STK calculations. First of all, the satellite is considered as one isothermalnode so no multi-nodal analysis can be performed. Heat transfer analysis can’t also be

Thermal Analysis 53

made because they depend on the shape of the satellite and STK is also considering theCubesat as a sphere.

So once considered all the issues presented above, simulations can be run in STK. Severalsimulations have been performed with different values of emissivity and absorptivity of thematerials presented in this section (see Table 3.3) and with simulations with different valuesof internal dissipation (see Eq. 3.4).

Table 3.3: Hot and cold case temperatures for different materials with no internal dissipa-tion

Surface Al. frame Al. panel (with Kapton) Solar panelsα 0.08 0.87 0.91ε 0.15 0.81 0.81

Hot Case -7oC 50oC 50oCCold Case -100oC -100oC -100oC

Table 3.4: Hot and cold case temperatures for the Al. with Kapton

Q 0 W 0.5 W 1 WHot Case 50oC 50oC 55oCCold Case -100oC -85oC -78oC

Table 3.3 refers to the maximum and minimum temperature for each material with no inter-nal dissipation. We can deduce from the graphics that the cold case temperature does notvary with the type of material but that the hot case temperature has important variations.

When analyzing the effects produced by the internal dissipation of the satellite for a deter-minate material we can conclude that it majorly affects the cold case temperature obtaininglower values for higher internal dissipations. Fig. 3.3 shows the evolution of temperatureduring a year for the Kapton case with 0.5 W of internal dissipation. It can be extractedfrom the results that the maximum temperature is obtained for the maximum incoming so-lar heat flux and the minimum temperature is obtained during the times the satellite is atthe shadow of Earth.

Although the results obtained with STK are more accurate than those done previouslywith de direct application of the equations, these results are still not accurate enough. Amulti-nodal analysis with the specific shape of the satellite must be carried out with otheravailable software. Specific information about the multi-nodal analysis and the availablesoftware can be found in Appendix G.


Figure 3.3: Temperature evolution for the Al. with Kapton with 0.5 W of internal dissipation

Thermal Analysis 55

CONCLUSIONS

The objective of this work has been to analize some aspects the mission analysis of theCubesat the UPC is willing to launch through the launch opportunities of ESA. In order toperform this analysis, a complete theory reminder of orbital dynamics has been explainedalong with the issues concerning propagators and perturbations. Simulations have beenperformed using the commercial software STK which provides a great variety of parame-ters to simulate with really big reliability. As a complement of the mission analysis, the firststeps to perform a thermal analysis have also been presented in this work. Basic theoryof thermal design of the satellite has been explained along with basic calculations of ther-mal balance by means of the equations available. Additionally, the state-of-the-art of theCubesat program has also been explained.

In addition, it is important to remark that this project is one of the first ones regardingthe project of the Cubesat of the UPC. Information contained is not the ultimate one andchanges may arise during the project in the next months or years. In this manner, thisMaster Thesis is one of the first steps of the project, which can be seen as a guideline forfuture studies concerning the UPC Cubesat.

Furthermore, results have shown similarities with other related-type projects and with thetheory explained. The inclusion of the UPC Cubesat in the existing network of Cubesatdevelopers is advised in order to have more time to access the satellite while orbiting theEarth. It is also recommended to use the HPOP in future simulations. This propagatorshows little differences with SGP4 but although little, these differences can change signif-icantly the orbital elements during a year. Perturbations affecting the satellite have beenstudied separately and all together concluding that the atmospheric drag and the non-spherical shape of the Earth are the ones that affect more the satellite with both secularand periodic changes no matter which orbit is being used. Actually, the shape of the orbitis really important in the mission analysis. Among other differences, using the two differentshapes of orbit can produce discrepancies in lifetime of 6 or 7 years.

Alternatively, results from the thermal analysis show variations of temperature from -85oCto 50oC for the standard case. It is important to recall that the results obtained are sim-plified ones, and that important characteristics of the simulation such as the shape of thesatellite and the internal dissipations should be studied deeply. However, important varia-tions are observed for different values of internal dissipation and the emissivity/absorptivityratio is the main parameter which we can play in order to change these temperature vari-ations.

Finally, this project and its results could be a great help and a useful information tool forother studies concerning the Cubesat of the UPC. Further work should be done whenknowing the specific requirements of the launch vehicle in matter of orbit in order to obtainmore accurate results. It is also highly recommended to continue the thermal analysis ofthe satellite form the end point of this project using available simulation tools as ESATAN,ESARAD or ANSYS.

BIBLIOGRAPHY 57

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[21] Astronautix, Encyclopedia Astronautica, http://www.astronautix.com/

[22] The CubeSat Kit of Pumpkin, Inc., http://www.cubesatkit.com/

[23] Jacques, L., Thermal Design of the Oufti-1 nanosatellite, University of Liege, MasterThesis, 2009.

[24] ESA Thermal Control website, http://www.esa.int/TEC/Thermal control/SEMTT0CE8YE 0.html

[25] ANSYS, Inc. webpage, http://www.ansys.com/

[26] ANSYS, Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/wiki/ANSYS

APPENDIXES

Cubesat launches and participants 61

Appendix A

CUBESAT LAUNCHES AND PARTICIPANTS

A.1. Past launches

Table A.1: CubeSats past launches

Batch # Date LV Launch Site Prim. Payload

1 30 Jun 2003 Rokot Plesetsk, Russia MIMOSA, MOST

Name Institution Type Deployer StatusCUTE-1 TITECH Single T-POD OperationalXI-IV U.Tokyo Single T-POD OperationalCanX-1 U.Toronto Single P-POD No ContactDTUsat DTU Single P-POD No ContactAAU CubeSat AAU Single P-POD Some ContactQuakeSat Stanford Triple P-POD Operational

2 27 Oct 2005 Komos-3M Plesetsk, Russia SSETI Express

Name Institution Type Deployer StatusNCube2 NTNU Single T-POD No ContactUWE-1 U.Wurzburg Single T-POD OperationalXI-V U.Tokyo Single T-POD Operational

3 22 Feb 2006 M-V Uchinoura, Japan ASTRO-F (AKARI)

Name Institution Type Deployer StatusCUTE-1.7+APD TITECH Double T-POD Operational

4 26 Jul 2006 DNEPR Baikonur, Kazaskstan Belka

Name Institution Type Deployer StatusION U.Illinois Double P-POD Launch failureSacred U.Arizona Single P-POD Launch failureKUTEsat U.Kansas Single P-POD Launch failureICE Cube 1 Cornell Single P-POD Launch failureRINCON 1 U.Arizona Single P-POD Launch failureSEEDS Nihon Single P-POD Launch failureHAUSAT 1 Hankuk Single P-POD Launch failureNcube 1 NTNU Single P-POD Launch failureMEROPE Montana Single P-POD Launch failureAeroCube-1 Aerospace Single P-POD Launch failureCP2 CalPoly Single P-POD Launch failureCP1 CalPoly Single P-POD Launch failureICE Cube 2 Cornell Single P-POD Launch failureMea Huaka U.Hawaii Single P-POD Launch failure

5 16 Dec 2006 Minotaur MARS,USA TacSat-2Continued on next page


Table A.1 – continued from previous pageBatch # Date LV Launch Site Prim. Payload

Name Institution Type Deployer StatusGeneSat-1 Ames Triple P-POD Operational

6 17 April 2007 DNEPR Baikonur, Kazakstan EgyptSat

Name Institution Type Deployer StatusCP4 CalPoly Single P-POD Partial operationsAeroCube-2 Aerospace Single P-POD Short contactCSTB-1 Boeing Single P-POD OperationalMAST Tethers Single P-POD Partial operationCP3 CalPoly Single P-POD No contactCAPE-1 U.Lousiana Single P-POD Partial operationLibertad-1 Sergio Arbol. Single P-POD Operational

7 28 Apr 2008 PLSV SDSC, India CartoSat-2A, IMS-1

Name Institution Type Deployer StatusCanX-2 U.Toronto Triple X-POD OperationalCUTE-1.7+APD2 TITECH Double X-POD OperationalDelfi-C3 TUDELFT Triple X-POD OperationalAAUsat-2 AAU Single X-POD OperationalCompass One FH Aachen Single X-POD OperationalSEEDS 2 Nihon Single X-POD Operational

8 3 Aug 2008 Falcon-1 Omelek, Marshall Is. Trailblazer

Name Institution Type Deployer StatusNanoSail-d Ames Triple P-POD Launch failurePREsat Ames Triple P-POD Launch failure

9 23 Jan 2009 H-IIA TNSC, Japan GOSAT, SDS-1

Name Institution Type Deployer StatusKKS-1 JAXA Double T-POD No contactSTARS JAXA Single T-POD No contactPRISM JAXA Single T-POD Operational

10 19 Jan 2009 Minotaur MARS, USA TacSat-3

Name Institution Type Deployer StatusAeroCube-3 Aerospace Single P-POD ContactedHawkSat Hawk Inst. Single P-POD ContactedCP6 CalPoly Single P-POD ContactedPharmaSat Ames Triple P-POD Contacted

11 23 Sep 2009 PLSV SDSC, India OceanSat-2

Name Institution Type Deployer StatusUwe-2 U.Wurzburg Single P-POD ContactedITUpSAT1 ITU Single P-POD ContactedSwissCube EPFL Single P-POD ContactedBEESAT TU Berlin Single P-POD Contacted


A.2. Upcoming launches

Table A.2: CubeSats upcoming launches

Batch # Date (approx) LV Launch Site Prim. Payload

1 TBC-delayed TBC (Space X) TBC TBC

Name Institution Type Deployer StatusInnoSat Malaysia Triple P-POD TBLCubeSat ATSB Triple P-POD TBL

2 23 Jan 2010 Taurus-XL Vandenberg Glory

Name Institution Type Deployer StatusExplorer-1 PRIME Montana Single P-POD TBLKySat-1 U.Kentucky Single P-POD TBLHERMES U.Colorado Single P-POD TBLASTREC 1 (Backup) U.Florida Single P-POD TBL

4 Feb 2010 Minotaur IV Kodiak FASTSAT

Name Institution Type Deployer StatusOREO Ames Triple P-POD TBLRAX U.Michigan, SRI Triple P-POD TBL

3 Oct 2010 VEGA (maiden) Kourou LARES

Name Institution Type Deployer StatusSeissCube-2 EPFL Single P-POD TBLXatcobeo U.Vigo Single P-POD TBLUniCubesat U.Roma Single P-POD TBLRobusta UM2 Single P-POD TBLatmoCube U.Trieste Single P-POD TBLe-st@r U.Torino Single P-POD TBLOUFTI-1 U.Liege Single P-POD TBLGoliat U.Bucharest Single P-POD TBLPW-Sat Pol.Warsaw Single P-POD TBLUWE-3 (Backup) U.Wurzburg Single P-POD TBLHiNCube (backup) NUC Single P-POD TBL

TBC: To be confirmed

TBL: To be launched

A.3. Cubesat participants


Table A.3: List of Cubesat participants. Source [2].

Institution Complete Name Location

TITECH Tokyo Institute of Technology Tokyo, JapanU.Tokyo The University of Tokyo Tokyo, JapanU.Toronto University of Toronto Toronto, CanadaDTU Technical University of Denmark Lyngby, DenmarkAAU Aalborg University Aalborg, DenmarkStanford Stanford University Palo alto, CA, USANTNU Norwegian University of Science and Tech. Trondheim, NorwayU.Wurzburg University of Wurzburg Wurzburg, GermanyU.Illinois University of Illinois Illionois, USAU.Arizona The University of Arizona Tucson, AZ, USAU.Kansas The University of Kansas Lawrence, KS, USACornell Cornell University Ithaca, NY, USANihon Nihon University Tokyo, JapanHankuk Hankuk Aviation University Goyang, KoreaMontana Montana State University Montana, USAAerospace The Aerospace Corporation USACalPoly California Polytechnic State Univesity San Luis Obispo, CA, USAU.Hawaii The University of Hawaii Hawaii, USABoeing The Boeing Company Chicago, II, USATethers Tethers Unlimited Bothell, WA, USAU.Lousiana University of Lousiana Lousiana, USASergio Arbol. Universidad Sergio Arboleda Bogota, ComlobiaTUDELFT Delft University of Technology Delft, The NetherlandsFH Aachen Fachhochschule Aachen Aachen, GermanyAmes NASA Ames Research Center Moffett Field, CA, USAJAXA Japan Aerospace Exploration Agency JapanHawk Inst. Hawk Institute for Space Sciences Pocomoke City, MD, USAMalaysia-USM Universiti Sains Malaysia Pulua Pinang, MalaysiaMalaysia-UTM Universiti Teknologi Malaysia Johor Bahru, MalaysiaMalaysia-UniMAP Universiti Malaysia Perlis Arau Perlis, MalaysiaATSB Astronautic Technology (m) Sdn BHD Shah Alam, MalaysiaU.Kentucky University of Kentucky Lexington, KN, USAU.Colorado University of Colorado Boulder, CO, USAU.Florida University of Florida Gainesville, FL, USAEPFL Ecole Polytechnique Federale de Lausanne Lausanne, SwitzerlandU.Vigo Universidad de Vigo Vigo, SpainU.Roma Universita degli Studi di Roma ”La Sapienza” Roma, ItalyUM2 Universite de Montpellier 2 Montpellier, FranceU.Trieste Universita degli Studi di Trieste Trieste, ItalyU.Torino Universita degli Studi di Torino Torino, ItalyU.Liege Universite de Liege Liege, BelgiumU.Bucharest University of Bucharest Bucharest, Romania

Continued on next page


Table A.3 – continued from previous pageInstitution Complete name Location

Pol. Warsaw Warsaw University of Technology Warsaw, PolandNUC Narvik University College Narvik, NorwayU.Michigan University of Michigan Michigan, USASRI SRI International California, USAISU Istanbul Technical University Istanbul, TurkeyTU Berlin Technical University of Berlin Berlin, Germany

Cubesat launch vehicles 67

Appendix B

CUBESAT LAUNCH VEHICLES

This appendix presents the current launch vehicles that have launched at least one Cube-sat with a short description of its most important characteristics and a final table (Table B)comparing the main characteristics of each one.

Rokot

Rokot is a Russian space launch vehicle that can launch a payload of 1,950 kilograms intoa 200 kilometer orbit with 63 of inclination. It is a derivative of the UR-100N intercontinen-tal ballistic missile (ICBM), supplied and operated by Eurockot Launch Services. The firstlaunches started in the 1990s from Baikonur Cosmodrome out of a silo. Later commerciallaunches commenced from Plesetsk Cosmodrome using a launch ramp specially rebuiltfrom one of the Kosmos-3M rocket. The cost of a commercial launch is about $14 million.

Kosmos-3M

The Kosmos-3M is a Russian space launch vehicle. It is a liquid-fueled two-stage rocket,first launched in 1967 and with over 410 successful launches to its name. It uses nitrogentetroxide as an oxidizer to lift roughly 1400 kg of payload into orbit. PO Polyot has manu-factured these launch vehicles in the Russian town of Omsk for decades, though the latestdigitally controlled rockets are now officially referred to as ’Kosmos 3MU’. It is scheduledto be retired from service in 2011. By the meantime, it is launched from Plesetsk andKapustin Yar Cosmodromes.

Dnepr

Dnepr is a three-stage Ukrainian space launch vehicle named after the Dnieper River. Itis a converted ICBM used for launching artificial satellites into orbit, operated by launchservice provider ISC Kosmotras. The first launch, on April 21, 1999 and can launch up to4500 kilograms into LEO. Its current launch sites are Baikonur and Dombarovsky.

Minotaur I and IV

The Minotaur is a family of American solid fuel rockets derived from converted Minutemanand Peacekeeper intercontinental ballistic missiles. They are built by Orbital Sciences Cor-poration. Minotaur I is an American expendable launch system derived from the Minute-man II missile. It is used to launch small satellites for the US Government. Initially MinotaurI launches were conducted from the Vandenberg Air Force Base. Starting with the launchof TacSat-2 in December 2006, launches have also been conducted from the Mid-AtlanticRegional Spaceport on Wallops Island. The Minotaur IV, also known as Peacekeeper is anAmerican expendable launch system derived from the Peacekeeper missile. It is sched-uled to make its maiden flight in early 2010, with the SBSS satellite for the United States AirForce and some CubeSats. Minotaur IV launches will be conducted from Vandenberg AirForce Base, the Mid-Atlantic Regional Spaceport, and from the Kodiak Launch Complex.


M-V

The M-V rocket was a Japanese solid-fuel rocket designed to launch scientific satellites.The Institute of Space and Astronautical Science (ISAS) began developing the M-V in 1990at a cost of 15 billion yen. It has three stages and it was capable of launching a satelliteweighing 1.8 tons into an orbit as high as 250 km. The final launch was that of the Hinodeon 22 September 2006. It was launched from the Uchinoura Space Center.

H-IIA

The H-IIA is a family of Japanese liquid-fuelled rockets providing an expendable launchsystem for the purpose of launching satellites into geostationary orbit. It is manufactured byMitsubishi Heavy Industries (MHI) for the Japan Aerospace Exploration Agency, or JAXA.Launches occur at the Tanegashima Space Center.

PSLV

The Polar Satellite Launch Vehicle commonly known by its abbreviation PSLV is an Indianexpendable launch system developed and operated by the Indian Space Research Orga-nization (ISRO). It was developed to allow India to launch its Indian Remote Sensing (IRS)satellites into sun synchronous orbits. PSLV can also launch small size satellites into geo-stationary transfer orbit (GTO). The PSLV has launched 41 satellites into a variety of orbitstill date. In April 2008, it successfully launched 10 satellites in one go, breaking a worldrecord previously held by Russia Each launch costs 17 million USD. It is launched form theSatish Dhawan Space Centre.

Falcon 1 and 9

The Falcon 1 and 9 are two rockets developed by Space X, a private American spacetransport company. The Falcon 1 is a partially reusable launch system designed and itis the first successful fully liquid-propelled orbital launch vehicle developed with privatefunding. Falcon 1 achieved orbit on its fourth attempt, on 28 September 2008, with amass simulator as a payload. Its current launch site is in Omelek Island, in the Republicof the Marshall Islands but it would also use the Vandenberg facility Falcon 9 is a reusabletwo-stage-to-orbit, liquid oxygen and rocket-grade kerosene powered launch vehicle. Itis scheduled to have its maiden launch in late 2009. Multiple variants are planned withpayloads of between 10,450 kg and 26,610 kg to low Earth orbit , and between 4,540 kgand 15,010 kg to geostationary transfer orbit. Moreover, the Falcon 9 will be the launchvehicle for the SpaceX Dragon spacecraft. It will be launched from Cape Canaveral andform Omelek.

Vega

Vega (Fig. B.1) is a European expendable launch system being developed for Arianespacejointly by the Italian Space Agency and the European Space Agency. Development beganin 1998 and the first launch, which will take place from the Guiana Space Centre in thelate 2010. Vega is a single-body launcher composed of three solid-propellant stages anda re-startable liquid-propellant fourth stage. It is 30 m high, has a maximum diameter of3 m and weighs 137 tons at lift-off. Vega has three sections: the Lower Composite, theUpper Module and the Payload Composite. The Upper Module, known as the Altitude and

Cubesat launch vehicles 69

Vernier Upper Module (AVUM), is itself composed of a Propulsion Module and an AvionicsModule. The AVUM provides attitude control and axial thrust during the final phases ofVega’s flight to allow the correct orientation and orbit injection of multiple payloads, withfinal de-orbiting of the stage once maneuvers are completed.

Figure B.1: Vega launch vehicle. Source [6].

Table B.1: Launch vehicles comparative. Source [21].

LV. Country Stages Fuel Payload (T.) Launch Site Launch Price*

Rokot Russia 3 Liquid 1’95 LEO Plesetsk 14 million USDKosmos 3-M Russia 2 Liquid 1’5 LEO

0.775 SSOPlesetsk 10 million USD

Dnepr Ukraine 3 Liquid 4’5 LEO BaikonurDom-barovsky

10-13 millionUSD

Minotaur I USA 4/5 Solid 0’58 LEO0’331 SSO

VandebergMARS

12’5 million USD

Minotaur IV USA 4 Solid 1’735 LEO VandebergMARSKodiak

-***

M-V Japan 3 Solid 1’8 LEO Uchinoura 60 million USDH-IIA Japan 2 Sol./Liq. 4’1/6 GTO Tanegashima 190 million USDPSLV India 4 Sol./Liq. 3’25 LEO

1’06 GTOSatishDhawan

30 million USD



Table B.1 – continued from previous pageLV Country Stages Fuel Payload (T.) Launch Site Launch Price*

Falcon 1 Space X 2 Liquid 0’67 LEO0’43 SSO

OmelekVandeberg

7 million USD

Falcon 9** Space X 2 Liquid 10’45 LEO4’54 GTO

CapeCanaveralOmelek

3.365 USD LEO10.000 USD GTO

Vega Europe 4 Sol./Liq. 1.5 LEO Kourou 23.5 million USD

* Launch prices are approximate and depends on the configuration of each launch and its payload.

** Falcon 9 has different configurations. Characteristics are considered for the basic Flacon 9 configuration.

*** No price has been found. No launches have been carried out for this LV yet.

STK modules 71

Appendix C

STK MODULES

STK Basic is free to all users and is also the core module for all other STK modules [9].It allows access calculations to be performed between satellites and fixed points on theEarth’s surface (or between satellites). There is also the ability to import satellites from theNORAD public satellite database (which can be updated online from within STK).

STK Professional adds to the Basic Edition with the following abilities:

• High fidelity trajectories

• Aircraft performance models

• Multi-point and group inter-visibility

• Constrained inter-visibility

• Complex sensor modeling

• Integrated 3D analysis tools

• Custom reports and graphs

STK Expert adds a host of additional modules to what is provided in the STK ProfessionalEdition:

• STK/Integration Module (ability to integrate STK with external tools through Connectand/or through Matlab as well as embed STK into a custom application)

• STK/Terrain, Imagery and Maps Module (high-resolution imagery and terrain of thewhole world)

• STK/Analyzer (perform trade-off studies and what-if analyses)

• STK/Attitude (integrate custom attitude control laws into STK)

• STK/Communications (high-fidelity link budget analysis)

• STK/Coverage (multi-point access calculations and navigation system analysis)

• STK/Radar (ground, space and airborne radar systems simulation)

Each of the above modules can be purchased individually and added to either the STK/BasicEdition or the STK/Professional Edition.

STK Specialized Analysis Modules are modules that can be added to the Basic, Profes-sional or Expert editions:


• STK/Astrogator (interplanetary orbits, orbit maintenance, LEOP simulation)

• STK/Conjunction Analysis Tools (In-orbit collision prediction)

• STK/Missile Modeling Tools (missile simulation)

• STK/PODS (Precision Orbit Determination System - to reconstruct satellite orbitsthrough observational data)

• STK/Scheduler (use scarce resources in the most efficient way)

• STK/Space Environment (radiation dose, debris flux, thermal loading)

Additional theory for mission analysis 73

Appendix D

ADDITIONAL THEORY FOR MISSION ANALYSIS

D.1. The n-body problem

The N-body problem is effectively a class of problem, which can be described as theproblem of taking an initial set of data that gives the positions, masses, and velocities ofsome set of n bodies, for some particular point in time, and then using that set of data todetermine the motions of the n bodies, and to find their positions at other time [11] [10].

In this case, the bodies in Space exert a gravitational force to all the other bodies around.The magnitude of this force, as the equation of gravity shows, would depend on the massesof the bodies and the distance between them. So if we take into consideration an N-bodyproblem we would study the gravitational force that these N bodies exert to one of them.In addition, the gravitational force is not the only one acting in a celestial body. There areother forces such as the non-spherical shape of the planets, the propulsive forces, theatmospheric drag, etc.., which should be considered in the problem.

So for each pair of bodies i and j, we have a force j acting on i (see Eq. D.1 and Eq. D.2).

Fg j = −Gmimj

r2i j

·r ji

r ji(D.1)

r ji = r i − r j (D.2)

If all the n-bodies are applied to the particle i, it is obtained Eq. D.3.

Fg = −Gmi ·n

∑j=1j 6=i

mj

r3ji

· r ji (D.3)

This Fg is the gravitational force of the n-bodies acting on the bodies of study but there arestill others forces to consider that it will be called Fothers, so the total force acting on thebody is Eq. D.4.

Ftotal = Fg + Fothers (D.4)

Newton’s second law of motion (Eq. D.5) is now ready to be applied.

∑F = mr (D.5)


Thus we obtain Eq. D.6.

ddt

(mivi) = Ftotal (D.6)

This time derivative can be expanded to Eq. D.7.

midv i

dt+ vi

dmi

dt= Ftotal (D.7)

So finally it is obtained Eq. D.8.

r i =Ftotal

mi− r i

mi

mi(D.8)

Eq. D.8 is a second order, nonlinear, vector, differential equation of motion which has de-fied solution in its present form. It is here therefore that we have to make some simplifyingassumptions and depart from the realities of nature.

It would be assumed no perturbation forces (Fothers= 0) and no external forces such asthe propellant coming out from the rocket (v i

dmidt = 0). So the only forces that it would be

taken into account are the gravitational ones. Eq. D.8 would be reduced to Eq. D.9.

r i = −G·n

∑j=1j 6=i

mj

r3ji

· r ji (D.9)

To solve Eq. D.9 in an analytical way, 6n 2nd order equations are needed. For example, forthe three-body problem, 18 equations will be needed to solve the problem. The problemrelays that there are only 10 equations: six of center of masses (position and accelerationin the three axes, one of conservation of energy and three for conservation of momen-tum. This is the reason because there is no analytical solution for the three (or more)body problem and it must be performed a numerical simulation to obtain an approximatesolution.

Continuing now with the previous equation, it is of interest the study of the motion of a nearEarth satellite thus the CubeSat will orbit around the Earth at a low altitude. Therefore, letus rewrite the equation in a different form. If m1 is the Earth m2 is the satellite and all theother masses may be different celestial bodies as the Moon, the Sun, or other planets inthe Solar System, then we obtain the following expressions.

r1 = −G·n

∑j=2

mj

r3j1

· r j1 (D.10)

r2 = −G·n

∑j=1j 6=2

mj

r3j2

· r j2 (D.11)


r12 = r2− r1 (D.12)

r12 = r2− r1 (D.13)

So:

r12 = −[Gm1

r312

· r12+Gn

∑j=3

mj

r3j2

· r j2]− [Gm2

r321

· r21+Gn

∑j=3

mj

r3j1

· r j1] (D.14)

r12 =G(m1 +m2)

r312

· r12−n

∑j=3

Gmj(r j2

r3j2

−r j1

r3j1

) (D.15)

The first term of Eq. D.15 is the force acting between the two main bodies (the Earth andthe satellite). The other term is the perturbation of the other bodies affecting the force ofthe two main ones.

In order to determine the force between the Earth and the satellite, the accelerations ofthe other bodies must be calculated. In Table D.1 there is a comparison of the relativeacceleration for a 200 NM Earth satellite.

Table D.1: Relative accelerations form other bodies to a LEO satellite

Earth 0.89Sun 6.0x10-4Mercury 2.6x10-10Venus 1.9x10-8Mars 7.1x10-10Jupiter 3.2x10-8Saturn 2.3x10-9Uranus 8.0x10-11Neptune 3.6x10-11Moon 3.3x10-6Earth oblateness 10-3

From Table D.1, some conclusions can be taken. The acceleration coming from otherbodies different from the Earth is very little. Just the effect of the Sun and the Earthoblateness have a considerable value. It is for this reason that some assumptions can bemade.

The two body restricted problem is a simplification of the n-body problem. The simplifica-tions hypothesis made are the following ones:

• The two bodies are the only ones in Space

• The bodies are spherical and homogenous


• There are not any external or internal force acting to the system

Therefore, using these assumptions and if the mass of the satellite is m and the mass ofthe Earth is M, the equation will result as Eq. D.16.

r =G(M +m)

r3 r (D.16)

The mass of the satellite is very little compared to the mass of the Earth (M ≫ m). If aparameter µ= G(M +m)≈ GM is defined, the equation would result as follows Eq. D.17.

r +µr3 r = 0 (D.17)

µ≡ GM (D.18)

Eq. D.17 is the two-body equation of motion. This equation can be solved analytically, incontrast to the three body problem or higher that can only be solved numerically.

D.2. The trajectory equation

In order to obtain the trajectory equation, the two body equation of motion must be derived.Previously, some useful information regarding the nature of the orbit must be explained.First, a gravitational field is conservative, that is, an object moving under the influenceof gravity alone does not lose or gain mechanical energy but only exchanges one formof energy to another one (kinetic to potential energy). Secondly, the gravitational forceis always directed radially toward the center of the large mass. If it is recalled that ittakes a tangential component of force to change the angular momentum of a system inrotational motion, it is expected that the angular momentum of the satellite about the centerof our reference frame, the center of the Earth, does not change. So the conservation ofmechanical energy and of angular momentum would be the constants of motion neededto derive the two body equation of motion and obtain the trajectory equation [11] [10].

1) Conservation of mechanical energy

Multiply the two body equation of motion by r:

r · r + r ·µr3 r = 0 (D.19)

Since in general a · a = aa, v = r and v = r, then:

v · v +µr3 r · r = 0 (D.20)


So:

vv+µr3r r = 0 (D.21)

Noticing that ddt(

v2

2 ) = vv and ddt(

−µr ) = µ

r2 r :

ddt

(v2

2)+

ddt

(−µr

) = 0 (D.22)

ddt

(v2

2−

µr

+c) = 0 (D.23)

C is an arbitrary constant referring to the origin of the energies. Normally, this constant iso because the origin of the energies is at the infinity.

This expression must be a constant that is called specific mechanical energy (ε). Theexpression means that the sum of the kinetic energy per unit mass and the potential en-ergy per unit mass of a satellite remains constant along its orbit, neither increasing nordecreasing as a result of its motion.

ε =v2

2−

µr

(D.24)

2) Conservation of angular momentum

If r is cross multiplied to the two body equation of motion:

r × r + r ×µr3 r = 0 (D.25)

Since in general a×a = 0:

r × r = 0 (D.26)

Noticing that ddt(r × r) = r × r + r × r:

ddt

(r × r) = 0 orddt

(r × v) = 0 (D.27)

The expression r×v which must be a constant of the motion is simply the vector h, calledspecific angular momentum. Therefore, we have shown that the specific angular momen-tum h of a satellite remains constant along its orbit and that the expression for h is:

h = r × v (D.28)


These equations also tells that the satellite must be confined to a plane which is fixed inspace, or in other words, in the orbital plane. There are some angles in the orbital planethat must be explained before continuing with the explanation of the trajectory equation.

Figure D.1: Orbital plane angles

γ = Zenith angle

φ = Flight-path angle

From the definition of the specific angular momentum:

h = rvsinγ (D.29)

If the expression is expressed in terms of the flight-path angle:

h = rvcosφ (D.30)

Finally, the integration of the two body equation of motion can start. If the original equationis multiplied by h:

r ×h = −µr3(r ×h) (D.31)

The left side of the equation is clearly ddt(r ×h) and the right side of the equation can be

operated as follows:

µr3(r ×h) =

µr3(r × v)× r =

µr3 [v(r · r)− r(r · v)] =

µr

v −µrr2 r (D.32)

Taking into account that µ times the derivative of the unit vector is also µ ddt(

rr ) = µ

r v − µrr2 r

and that r · r = r r , the equation can be rewrite as the following expression:


ddt

(r ×h) = µddt

(r

r) (D.33)

Integrating both sides:

r ×h = µ(r

r)+B (D.34)

Where B is the vector constant of integration. Multiplying this equation by r:

r · r ×h = r ·µ(r

r)+ r ·B (D.35)

Simplifying this equation:

h2 = µr+ rBcosν (D.36)

Where ν is the angle between the constant vector B and the radius vector r. The trajectoryequation is obtained by solving this equation for r.

r =h2/µ

1+(Bµ)cosν

(D.37)

If e= B/µ, we obtain the polar equation of a conic section, that it is mathematical equal inform to the trajectory equation and widely used in the study of orbits:

r =p

1+ecosν(D.38)

Where p is the parameter of the orbit and e is the eccentricity. The eccentricity determinesthe type of conic section that represents the orbit.

D.3. Type of conics

In mathematics, a conic section is a curve obtained by intersecting a cone with a plane.The three types of conics are the hyperbola, ellipse, and parabola (see Fig. D.2). Thecircle can be considered as a fourth type (as it was by Apollonius in the 200 BC) or as akind of ellipse. The circle and the ellipse arise when the intersection of cone and plane isa closed curve. The circle is obtained when the cutting plane is parallel to the plane of thegenerating circle of the cone. If the cutting plane is parallel to exactly one generating lineof the cone, then the conic is unbounded and is called a parabola. In the remaining case,the figure is a hyperbola. In this case, the plane will intersect both halves of the cone,producing two separate unbounded curves, though often one is ignored [11] [10].


Figure D.2: Types of conic sections

All conic sections can be defined in terms of eccentricity (e). The type of conic section isalso related to its semi-major axis (a) and the energy (ε). Table D.2 shows the relationshipbetween eccentricity, semi-major axis energy and type of conic section.

Table D.2: Realationship between the type of conic and e, a and εConic Section Eccentricity (e) Semi-major axis (a) Energy ( ε)

Circle 0 = radius < 0Ellipse 0<e<1 >0 < 0Parabola 1 ∞ 0Hyperbola >1 <0 > 0

The eccentricity of a conic section is thus a measure of how far it deviates from beingcircular.

D.4. Types of orbit

Orbits can be classified in different types depending on some of their nature. These clas-sifications would only describe the type of orbits that are of interest to the project. Notethat may be other orbits not described below.

A first classification can be made regarding which body is one of the focuses of the orbit.

• Heliocentric orbit : An orbit around the Sun. In our Solar System, all planets, comets,and asteroids are in such orbits.

• Geocentric orbit : An orbit around the planet Earth, such as the Moon or artificialsatellites. Currently there are approximately 2,465 artificial satellites orbiting theEarth.


Geocentric orbits can also be classified regarding to the distance to Earth, to its altitudewith respect to Earth.

• Low Earth orbit (LEO): Ranging in altitude from 0-2,000 km.

• Medium Earth orbit (MEO): Ranging in altitude from 2,000 km to just below geosyn-chronous orbit at 35,786 km.

• High Earth orbit (HEO): Above the altitude of geosynchronous orbit 35,786 km.

Orbits can also be classified regarding its inclination. An inclined orbit is an orbit whoseinclination in reference to the equatorial plane is not 0. A special type of these orbits is thepolar orbit.

• Polar orbit : An orbit that passes above or nearly above both poles of the planet oneach revolution. Therefore it has an inclination of approximately 90 degrees.

In contrast, a non-inclined orbit is an orbit whose inclination is equal to zero with respectto some plane of reference. A special type of these orbits is the equatorial orbit.

• Equatorial orbit : A non-inclined orbit with respect to the equator.

There is also a classification regarding its eccentricity.

• Circular orbit: An orbit that has an eccentricity of 0.

• Elliptic orbit: An orbit with an eccentricity greater than 0 and less than 1 whose orbittraces the path of an ellipse.

• Parabolic orbit: An orbit with the eccentricity equal to 1. Such an orbit has a velocityequal to the escape velocity and therefore will escape the gravitational pull of theplanet and travel until its velocity relative to the planet is 0. If the speed of such anorbit is increased it will become a hyperbolic orbit.

• Hyperbolic orbit: An orbit with the eccentricity greater than 1. Such an orbit also hasa velocity greater than the escape velocity and as such, will escape the gravitationalpull of the planet and continue to travel infinitely.

A Synchronous orbit is an orbit where the satellite has an orbital period that is a rationalmultiple of the average rotational period of the body being orbited and in the same directionof rotation as that body. This means the track of the satellite, as seen from the central body,will repeat exactly after a fixed number of orbits. Important types of these orbits are thegeosynchronous and the sun-synchronous orbits.


• Geosynchronous orbit (GEO): An orbit around the Earth with a period equal to onesidereal day, which is Earth’s average rotational period of 23 hours, 56 minutes,4.091 seconds. For a nearly circular orbit, this implies an altitude of approximately35,786 km (22,240 miles). If both the inclination and eccentricity are zero, then thesatellite will appear stationary from the ground. If not, then each day the satellitetraces out an analemma in the sky, as seen from the ground.

• Graveyard orbit : This orbit, also called a super-synchronous orbit, junk orbit or dis-posal orbit, is an orbit significantly above synchronous orbit where spacecraft areintentionally placed at the end of their operational life.

• Sun-synchronous orbit (SSO): Geocentric orbit which combines altitude and inclina-tion in such a way that an object on that orbit ascends or descends over any givenpoint of the Earth’s surface at the same local time. The surface illumination anglewill be nearly the same every time. This consistent lighting is a useful characteristicfor satellites that image the Earth’s surface and for other remote sensing satellites.

Other types of orbits with different characteristics from the above mentioned are the fol-lowing.

• Molniya orbit : Highly elliptical orbit with an inclination of 63.4 degrees and an orbitalperiod of about 12 hours. These orbits are named after a series of Soviet/RussianMolniya (”Lightning” in Russian) communications satellites which have been usingthis type of orbit since the mid 1960s. A satellite placed in a Molniya orbit spendsmost of its time over a designated area of the earth as a result of ’apogee dwell’.

• Geostationary orbit (GSO): A circular geosynchronous orbit with an inclination ofzero. To an observer on the ground this satellite appears as a fixed point in the sky.

• Escape orbit (EO): A high-speed parabolic orbit where the object has escape velocityand is moving away from the planet.

• Capture orbit : A high-speed parabolic orbit where the object has escape velocityand is moving toward the planet.

• Retrograde orbit : An orbit with an inclination of more than 90. In other words, anorbit counter to the direction of rotation of the planet.

• Hohmann transfer orbit : An orbital maneuver that moves a spacecraft from onecircular orbit to another using two engine impulses.

• Halo orbits and Lissajous orbits: These are orbits around a Lagrangian point. Orbitsnear these points allow a spacecraft to stay in constant relative position with verylittle use of fuel. Orbits around these points are used by spacecraft that want aconstant view of the Sun or by missions that always want both the Earth and Sunbehind them.


D.5. Perturbation study

There are four main factors that perturb the orbit.

• Third-bodies

• Non-spherical Earth

• Atmospheric drag

• Solar radiation pressure

In this section we will study how this factor perturbs the orbit by analyzing the changesthey induce to the orbital elements. These changes can be classified as:

• Secular

• Large-Periodic

• Short-Periodic

Secular are non-periodic changes that monotonously vary in time. The large-periodic andshort periodic changes are terms which its variation is repeated with a large period (greaterthan the orbital period) and short period (same order than the orbital period) respectively[19].

Although it is true that the periodic changes can have interest, in general, the most impor-tant ones are the secular changes.

Figure D.3: Orbital element perturbation changes. Source [19].

In Fig. D.3 it can be appreciated the three different types of orbital element changes. Thestraight line shows the secular effects. The large oscillating line shows the secular pluslong-periodic effects and the small oscillatory line, which combines all three, shows theshort-periodic effects.


The four main perturbation forces affecting a satellite orbiting the Earth are presented witha description of the changes each one creates to the orbital elements [11] [10].

a) Third-body perturbation

Gravitational forces of other celestial bodies different from the Earth cause important peri-odic variations in all of the orbital elements. The most important accelerations from otherbodies are those from the Sun and the Moon, thus these two bodies would be the onesthat would cause a major change to the satellite orbiting around the Earth. A brief table ispresented below to illustrate the fact that the Sun and the Moon are the main bodies thatwould affect a satellite orbiting around Earth at an altitude of 200 NM (see Table D.3). Amore complete table can be found in the appendix.

Table D.3: Most important accelerations form other bodies to a LEO satellite

Body Acceleration

Earth 0.89Sun 6.0x10-4Venus 1.9x10-8Mars 7.1x10-10Moon 3.3x10-6

Secular variations are only experienced by the right ascension of the ascending node,the argument of perigee and the mean anomaly. These secular variations in the meananomaly are much smaller than the mean motion and have little effect on the orbit; how-ever, the secular variations in the right ascension of the ascending node and the argumentof perigee are important, especially for high-altitude orbits.

The equations for the secular rates of change of an Earth-centered satellite orbit resultingfrom the Sun and the Moon are presented below (Eq. D.39, D.40, D.41 and D.42).

ΩMoon = −0.00338cosin

(D.39)

ΩSun= −0.00154cosin

(D.40)

ωMoon = 0.001694−5sin2i

n(D.41)

ωSun= 0.000774−5sin2i

n(D.42)

Where i is the orbital inclination, n is the number of orbit revolutions per day and Ω and ωare in deg/day. These equations are only approximate, they neglect the variation causedby the orbital plane’s changing orientation with respect to the Moon’s orbital plane and theecliptic plane.


b) Non-spherical Earth perturbation

When developing the two-body equation of motion, the Earth is assumed to be a spheri-cally symmetrical, homogenous mass. In fact, the Earth is neither homogenous nor spher-ical. The most dominant features are a bulge at the equator, a slight pear shape anda flattening at the poles. For a potential function of the Earth, a satellite’s accelerationcan be found by taking the gradient of the potential function. A widely used from of thegeopotential function is shown in Eq. D.43.

φ =µr[1−

∞

∑j=1

Jj(RE

r) jPj sin( jL)] (D.43)

Where RE is the Earth equatorial radius in km, Pj the Legendre polinomials, L the geocen-tric latitude in degrees and Jj the dimensionless geopotential coefficients or harmonics, ofwhich the most important are:

J2 = 1.083·10−3

J3 = −2.534·10−6

J4 = −1.620·10−6

The first term of the geopotential function represents the sphere, while the other onesrepresent the deviation from the spherical model. This form of the geopotential functiondepends on latitude, and its coefficients (Jj ) are called zonal coefficients. Other, more gen-eral expressions for the geopotential include sectoral and tesseral terms in the expansion.The sectoral terms divide the Earth into slices and depend only on longitude. The tesseralterms depend on both longitude and latitude and divide the Earth into a checkboard patternof regions that alternately add to and subtract from the two-body potential.

The potential generated by the non-spherical Earth causes periodic variations in all orbitalelements. However, the secular variations are the dominant ones, precisely in the rightascension of the ascending node and in the argument of perigee because of the Earthoblateness, represented by the J2 term. The rates of change of Ω and ω due to J2 are thefollowing ones in Eq. D.44 and Eq. D.45 respectively.

ΩJ2 = −1.5nJ2(RE

a)2(

cosi(1−e2)2) (D.44)

ωJ2 = 0.75nJ2(RE

a)2(

4−5sin2i(1−e2)2 ) (D.45)

The first phenomena it is known as nodal regression (Fig. D.4) while the second one iscalled apsidal rotation (Fig. D.5). In the nodal regression, the perturbation manifest itselfthrough a change in the angular momentum vector, and the node regress much like aprecessing top. It changes the orbital plane continuously. The apsidal rotation modifiesthe geographic location of the line of apsides (apogee and perigee).


Figure D.4: Nodal regression. Source [19]. Figure D.5: Apsidal rotation. Source [19].

The J3 coefficient produces long period periodic effects and the J4 accounts also for sec-ular variations in the orbit elements due to Earth oblateness. Secular variations of J4 are100 times smaller than those coming from J2.

c) Atmospheric drag

When the orbit perigee height is below 1000 km, the atmospheric drag effect becomesincreasingly important. Drag, unlike other perturbations forces, is a non conservative forceand will continuously take energy away from the orbit. Thus, the orbit semi-major axis andthe period are gradually decreasing because of the effect of the drag.

Since drag is greatest at perigee, where the velocity and atmospheric density are greater,the energy drain is also greater at this point. Under this dominant negative impulse atperigee, the orbit would become more circular in each revolution. Moreover, decreasingenergy causes the orbit to shrink, leading to further increases in drag. Eventually the orbit’saltitude becomes so small that the satellite reenters the atmosphere. The atmosphericdrag acceleration can be modeled with Eq. D.46.

aD = −12

ρ(CDA

m)v2 (D.46)

Where ρ is the tmospheric density in kg/m3, CD is the drag coefficient (2-3), A is thesatellite cross sectional area in m2, m is the satellite mass in kg and v is the satellite’svelocity with respect to the atmosphere in m/s.

Density depends on the altitude and it is very difficult to model. For the same altitude,different values fluctuate between a maximum and a minimum. There exist different atmo-spheric density models, each one taken into account different considerations with differentaccuracies. A list of existing atmospheric density models is presented in the appendix.

Moreover, this perturbation induces important secular variations to the semi-major axis andthe eccentricity. It also produces secular changes to the inclination and periodic changesto all of them.


The changes in semi-major axis and eccentricity per revolution can be approximate by Eq.D.47 and Eq. D.48 respectively, obtained from the Bessel functions.

∆arev = −2πCDA

m)a2ρpe−c[I0+2eI1] (D.47)

∆erev = −2πCDA

m)aρpe−c[I1+

e2(I0+I2)] (D.48)

Where ρp is the atmospheric density at perigee in kg/m3, c is ae/H, H the density scaleheight in meters and Ii the Modified Bessel Functions of order i and argument c

This effect is typically for low altitudes the one responsible of the lifetime of the satellite.This lifetime can also be roughly estimate by the Eq. D.49.

L =−H∆erev

(D.49)

Fig. D.6 shows the lifetime of a satellite. It can be seen how the apogee and the perigeealtitude decay with time. For a circular 300 km orbit, the average lifetime is less than 35days.

Figure D.6: Typical dacay of a satellite for a 300 km circular orbit

d) Solar radiation pressure

Solar radiation pressure effects induce periodic variations in all orbital elements, evenexceeding the effects of atmospheric drag at altitudes above 900 km. Let’s see how thiseffect works.

Solar radiation pressure is the mechanical effect produced by the incidence of solar flux(photons) in a surface. In the Earth, the average solar radiation flux is typically I =1358W/m2. Then, the mechanical pressure is computed by Eq. D.50, where c is thespeed of light in vacuum.


p = I/c = 4.5·10−6N/m2 (D.50)

Moreover, the force in a flat panel will be F = pA(1+ ε)cosϕ where A is the area, ε is thecoefficient of reflectivity and ϕ the angle of incidence of the solar flux. Then, the perturbforce can be approximate by Eq. D.51 where m is the satellite mass in kg.

aR ≈−4.5·10−6

m(1+ ε) ·cosϕ (D.51)

The albedo of the Earth (reflection of the solar flux in the Earth) should be also taken intoaccount in the calculation along with the direct radiation coming from the Earth.

The solar radiation pressure is complex to treat analytically but it can be demonstrated thatthere are only secular variations in Ω and ω while there are periodic variations in all theorbital elements with a period of one year. The induced changes in perigee height canhave significant effects on the satellite’s lifetime, but the typical radiation pressure effect onsatellite orbits is the long-term sinusoidal variations on eccentricity. For a typical satelliteat geosynchronous orbits, the eccentricity may vary from 0.001 to 0.004 in six months asa result of this effect. Its effect is strongest in satellites with low ballistic coefficient.

Finally, it is important to mention that the solar radiation pressure must only be taken intoaccount when the satellite is facing the Sun. In other words, when the satellite is in eclipseor umbra (shadow of the Earth) this force must not be taken into account.

D.6. HPOP force models

The available force models that can be used in the HPOP are presented in the table below[9].

Table D.4: Force models available in the HPOP

Force model Types

EGM-96 (70x70)GEM-T1 (36x36)JGM-2 (70X70)JGM-3 (70x70)

Gravity WGS-84 (70x70)WGS-84/EGM-96 (70x70)WGS-84 old (WGS-84 version 1) (12x12)GGM01C (90x90)GGM02C (90x90)WGS72 ZonalsToJ4 (4x0)



Table D.4 – continued from previous pageForce model Types

1976 Standard: A table look-up model based on the satellite’saltitude, with a valid range of 86km - 1000 km.Harris-Priester: Takes into account a 10.7 cm solar flux level anddiurnal bulge. Valid range of 0 - 1000 km.Jacchia 1970: The predecessor to the Jacchia 1971 model. Validrange is 90 km - 2500 km.

Atmosphericdensity model

Jacchia 1971: Computes atmospheric density based on the com-position of the atmosphere, which depends on the satellite’s alti-tude as well as a divisional and seasonal variation. Valid range is100km - 2500 km.Jacchia-Roberts: Similar to Jacchia 1971 but uses analyticalmethods to improve performance.CIRA 1972: Empirical model of atmospheric temperature anddensities as recommended by the Committee on Space Research(COSPAR). Similar to the Jacchia 1971 model but uses numericintegration rather than interpolating polynomials for some quanti-ties.Jacchia 1960: An earlier model by Jacchia that uses the solarcycle to predict a value for the F10.7 cm flux and accounts for theeffects of the dirunal bulge.

RK 4: Runge-Kutta integration method of 4th order with no errorcontrol for the integration step size.RKF 7(8): Runge-Kutta-Fehlberg integration method of 7th orderwith 8th order error control for the integration step size.

Integrationmethod

Bulirsch-Stoer: Integration method based on Richardson extrap-olation with automatic step size control.Gauss-Jackson: 12th order Gauss-Jackson integration methodfor second order ODEs. There is currently no error control imple-mented for this method meaning that a fixed step size is used.

VOP: Uses a special interpolator that deals well with ephemerisproduced at a large step size, which happens frequently when us-ing the VOP formulation. The interpolator itself uses a VOP formu-lation. The VOP mu value is the gravitational parameter used bythe formulation. You can also specify the interpolation order.

Interpolation Lagrange: Uses the standard Lagrange interpolation scheme, in-terpolating position and velocity separately. You can also specifythe interpolation order.Hermitian: Uses the standard Hermitian interpolation scheme,which uses the position and velocity ephemeris to interpolate po-sition and velocity together (i.e., using a polynomial and its deriva-tive). You can also specify the interpolation order.

STK user’s guide 91

Appendix E

STK USER’S GUIDE

In order to understand how the simulations have been performed in the STK, a brief user’sguide explaining the steps to complete a basic simulation is presented. At the end of thissection, you would be able to make basic simulations in STK and also to understand whathas been done in the results section of the main body report.

For this simulation, we have performed the simulations for access, lighting and lifetime withjust the UPC ground station using the HPOP propagator and an elliptic 1200x350 km orbit.

Step 1) Create the scenario

In STK, the files are known as scenarios. The scenario is the highest-level object in STK.It includes the 2D and 3D Graphics windows and contains all other STK objects (e.g.,satellites, facilities, etc.).

So we create a new scenario in the STK by clicking the corresponding icon.

Figure E.1: STK window with main commands

Highlight the scenario in the Object Browser (see Fig. E.1), and click the Properties buttonon the toolbar to display its Properties Browser. In the scenario properties page, we shouldselect the time period of our simulations, this is the interval of time we want the satellite tosimulate (see Fig. E.2). We have introduced some future values for it, because the UPCCubesat would fly at some time in the future. So the values entered are the following.

• Start: 1 July 2010 at 00:00h.


• Stop: 1 July 2011 at 00:00h.

• Epoch time: 1 July 2010 at 00:00h.

Figure E.2: Period

Step 2) Creating the ground station

The first thing to introduce in our simulation should be the objects necessary to performit, the satellite and the ground station. In order to do it, we need to use the object catalogicon. In that icon, we can specify which object we want to introduce. First, we will introducethe ground station, so we will create a new facility that we can rename for instance UPC. Inthe facility properties page we will introduce the geographical characteristics of our facility,this is, the latitude and the longitude of the ground station (see Fig. E.3). In our case, forBarcelona we have introduced:

• Latitude: 41.53o

• Longitude: 2.17o

Figure E.3: Satellite geographic coordinates

There exist a different way of defining facilities. You can insert facilities from the STKdatabase with no need of setting the geographical characteristics. You just specify thename of the city and the STK will perform a search in its database. In order to do it, youmust select insert from the main toolbar and then city from database.

Moreover, we will specify the constraint we will apply in our simulations. Our simulationswill be computed with an elevation constraint of 15o. So we open the basic constraints


Figure E.4: Facility constraints

label in the properties page and we specify a minimum elevation constraint of 15o (seeFig. E.4).

Step 3) Create the Satellite

The next object to introduce will be the satellite that we will rename as UPCSat. We use theObject Catalog and select satellite. In the satellite properties page, we will specify whichpropagator we want to use and the necessary terms to carry out the simulation. As wehave said before, we will use the HPOP propagator so in the propagator menu we selectHPOP (see Fig. E.5). Then, we should introduce the values needed for the simulationwhich are resumed below.

• Apogee altitude: 1200 km

• Perigee altitude: 350 km

• Inclination 71o

• Argument of perigee: 0o

• RAAN: 45o

• Mean anomaly: 30o

Leave the other values as default.

Then, the force models should be specified (see Fig. E.6). If we open the Force modelspage, it would appear all the perturbations the HPOP can handle. Our satellite will beaffected by the atmospheric drag, the solar radiation pressure and the gravities of the Sunand the Moon. So, we will select all these forces in the force models page with the followingvalues for each one. Leave the other default values as they appear.

• Cd: 2.2


• Area/Mass ratio: 0.01 m2/kg

• Atm. Density model: Jachia-Roberts

• Cr: 1.5

• Shadow model: Dual cone

Figure E.5: Propagator page

Figure E.6: Force models page

In the integrator page inside the one of the propagator, we will select the Gauss-Jacksonmethod with the default values.


Note that by changing all these values, different results will be obtained. These valueshave been selected taking into account all the characteristics of the satellite and all thetheory explained in this project.

Step 4) Obtaining results

Returning to the main propagator properties page and selecting apply, the simulationwould be computed. Note that it may take several seconds, so do not attempt to obtainresults until the computation has finished.

Then, you may run the simulation with the play button in the 2-D or in the 3-D graphicswindow. There, you would be able to see how the satellite is orbiting around the Earth withthe specified orbital elements.

Results can be obtained either with a report or a graphic. These two options can be ob-tained dynamically (dynamic display and strip chart) or in steady-state (report and graph).

So highlight the ground station and display the facility menu form the main toolbar. There,you can select which option you want to compute. First, we will calculate the access to oursatellite from the UPC ground station. You must select access in the facility menu and anew window will appear (see Fig. E.7).

Figure E.7: Access page

In order to obtain the access, you should select the element to which you want to calculatethe access, in our case, the UPCSat and then select compute. Then we will select Accessin the reports menu to obtain the list of accesses to our satellite during a year. A newwindow will appear with the list of accesses and at the bottom of it, global statistics of thesimulation such as the maximum time of one single access, the minimum time or the meantime in seconds (see Fig. E.8).


Figure E.8: Access report example

We can see that there are 1352 accesses during a year with a total duration of 618909seconds. These values are exactly the same as the ones obtained during the simulationsof this project.

There are other results that are independent of the ground station and that we are goingto compute now. First of all, the lighting of the satellite will be computed. This is thetime the satellite spends facing directly to the Sun, in umbra or in penumbra. To performthis calculation we must highlight the satellite in the Objects Browser and then display thesatellite menu in the main toolbar. There, you must select reports.

Different types of reports can be obtained depending on the property you want to study.For our case, we will study the lighting of the satellite, so you must select lighting times inthe report type and then create. A list similar to the one of access will appear with all theintervals the satellite is in lighting first, penumbra, and umbra at the end (see Fig. E.9).

Figure E.9: Lighting report example

The global statistics of each property appear at the end of the intervals of each one.For lighting, penumbra and umbra we obtain a total duration of 23.587.878, 123.049 and7.827.523 seconds respectively.


Finally, we are going to compute the lifetime of our satellite. In satellite menu, there is anoption that is called lifetime. We must go there. Several terms must be introduced beforecomputing the lifetime (see Fig. E.10).

Figure E.10: Lifetime page

The drag coefficient and the reflection coefficients will be left as in the propagator options.The drag area and the area exposed to the Sun are set to 0.01 m2 because we assumethat there is only one face facing the Sun.

A = 10cm·10cm= 0.01m2 (E.1)

Finally, the atmospheric density model is set to the Jacchia-Roberts, the same as in thepropagator computation. Then, by clicking compute, a new window appears telling you thelifetime of your satellite, in our case, this is 6.2 years. If you want a more visual descriptionof the lifetime, you can select the graph option in the same page and a graphic with theevolution of the apogee and perigee altitudes and the eccentricity over time will appear(see Fig. E.11).


Figure E.11: Lifetime graphic

Simulation tables of the mission analysis 99

Appendix F

SIMULATION TABLES OF THE MISSIONANALYSIS

F.1. Individual access analysis

Table F.1: Complete list of the individual access analysis forall ground stations

GS # AY # AD TDY (sec) MDA (sec) DD (sec)

Aachen 934 2.558 177562 190.109 486.470Aalborg 1181 3.235 225548 190.981 617.939Arizona 618 1.693 118728 192.116 325.281Auburn 645 1.767 120922 187.475 331.292Beirut 645 1.767 122788 190.369 336.404

Berlin Tech 986 2.701 187795 190.462 514.507Boston 760 2.082 141995 186.835 389.026

Bucharest 786 2.153 149340 190.000 409.151Buenos Aires 667 1.827 128929 193.297 353.231

Cal Poly 647 1.772 123609 191.05 338.654Carleton 804 2.202 152679 189.899 418.000

Chen Kung 559 1.531 107318 191.983 294.022Chicago 729 1.997 139575 191.461 382.397Colorado 717 1.964 136116 189.841 372.921Cornell 753 2.063 142225 188.878 389.658

Delft 968 2.652 184628 190.732 505.830Dnipropetrovsk 870 2.383 165187 189.871 452.568

DTU 1116 3.057 212995 190.856 583.549Embry-Riddle 612 1.676 115288 188.38 315.858

George Washington 703 1.926 133060 189.274 364.547Goyang 689 1.887 129584 188.075 355.024Hawaii 564 1.545 105891 187.749 290.111

Illionois 721 1.975 136724 189.631 374.586Imperial College 950 2.602 181844 191.415 498.202

Iowa State 761 2.084 141285 185.657 387.082Istambul 741 2.030 138593 187.035 379.706Kansas 698 1.912 132507 189.838 363.033

Laussane 816 2.235 156573 191.879 428.967Lousiana 619 1.695 116298 187.88 318.624Malaysia 528 1.446 97863 185.346 268.117

Michigan Tech 837 2.293 159674 190.769 437.462Continued on next page


Table F.1 – continued from previous pageGS # AY # AD TDY (sec) MDA (sec) DD (sec)

Montana 800 2.191 153944 192.431 421.765NC State 671 1.838 126810 188.987 347.425New Delh i 601 1.646 114185 189.991 312.834NM State 631 1.728 119339 189.126 326.954

North Dakota 871 2.386 163898 188.172 449.035NTNU 2130 5.835 376957 176.975 1032.759

Oklahoma 643 1.761 123045 191.361 337.109Porto 743 2.035 138447 186.335 379.306

Purdue 729 1.997 137084 188.044 375.572Roma 742 2.032 140784 189.736 385.709

Sergio Arboleda 530 1.452 98823 186.459 270.749Sherbrooke 807 2.210 152836 189.388 418.729

Siegen 934 2.558 177821 190.386 487.180Stanford 682 1.868 129636 190.083 355.168

Stellenbosch 668 1.830 128045 191.684 350.808SUPSI 813 2.227 155165 190.854 425.108Sydney 678 1.857 129150 190.487 353.836Taylor 729 1.997 136965 187.881 375.246Texas 626 1.715 116568 186.211 319.363

Texas AaM 617 1.690 116712 189.161 319.759Texas Christian 635 1.739 119829 188.707 328.299

Tokyo 661 1.810 125361 189.653 343.454Toronto 775 2.123 146835 189.465 402.288Trieste 806 2.208 153308 190.208 420.020

Tsinghua 724 1.983 136750 188.881 374.657UNOPAR 602 1.649 112229 186.428 307.477

UPC 732 2.005 140095 191.387 383.823Utah State 737 2.019 140647 190.837 385.333

Warsaw 969 2.654 185708 191.65 508.790Was-StLouis 694 1.901 132179 190.459 362.133Washingto n 849 2.326 161246 189.924 441.768Wurzburg 907 2.484 172110 189.758 471.534

Mean Values 767.6 2.103 145169 189.369 397.723

GS: Ground Station

AY: Access/year

AD: Access/day



DD: Duration/day


F.2. Orbit shape comparative

1) Accessibility

Table F.2: Accessibility analysis vs. orbit shape for UPC ground station

UPC Analysis

Orbit Shape # AY # AD TDY (sec) MDA (sec) DD (sec)350x350 732 2.005 140095 191.387 383.823

1200x350 1250 3.424 544962 435.969 1493.045

AY: Access/year

AD: Access/day



DD: Duration/day

Table F.3: Accessibility analysis vs. orbit shape for NTNU ground station

NTNU Analysis

Orbit Shape # AY # AD TDY (sec) MDA (sec) DD (sec)350x350 2130 5.835 376957 176.975 1032.759

1200x350 2397 6.567 1074035 448.075 2942.561

Table F.4: Accessibility analysis vs. orbit shape for Malaysia ground station

Malaysia Analysis

Orbit Shape # AY # AD TDY (sec) MDA (sec) DD (sec)350x350 528 1.446 97863 185.346 268.1171200x350 901 2.468 401865 446.022 1101.001

2) Lighting


Table F.5: Lighting analysis vs. orbit shape

Orbit Shape MaxD (sec) MinD (sec) MeanD (sec) TD (sec) MDA (sec)

350x350Lighting 9.730 6.390 64.491 20949334 15.943

Penumbra 40.837 0.130 0.237 153750 0.117Umbra 36.394 0.442 32.230 10434988 7.941

1200x350Lighting 17.359 2.264 88.196 23437346 17.836

Penumbra 40.499 0.122 0.268 142178 0.108Umbra 36.593 1.612 30.156 7957779 6.056

MaxD: Maximum Duration

MinD: Minimum Duration

MeanD: Mean Duration

TD: Total duration

MDA: Mean duration/day

F.3. Propagator comparative

1) Accessibility

Table F.6: Accessibility analysis vs. propagator for UPC ground station

UPC Analysis

Propagator # AY # AD TDY (sec) MDA (sec) DD (min)SGP4 732 2.005 140095 191.387 6.397

J4 828 2.268 179922 217.297 8.215J2 826 2.263 179919 217.820 8.215

TwoBody 829 2.271 180117 217.270 8.224

AY: Access/year

AD: Access/day



DD: Duration/day

Table F.7: Accessibility analysis vs. propagator for NTNU ground station

NTNU Analysis


J4 2233 6.117 494232 221.331 22.567J2 2231 6.112 494205 221.517 22.566

TwoBody 2230 6.109 494846 221.904 22.595


Table F.8: Accessibility analysis vs. propagator for Malaysia ground station

Malaysia Analysis


J4 574 1.572 122894 214.101 5.611J2 576 1.578 122892 213.354 5.611

TwoBody 578 1.583 122730 212.335 5.604

2) Lighting

Table F.9: Lighting analysis vs. propagator

Propagator MaxD (sec) MinD (sec) MeanD (sec) TD (sec) MDA (sec)

SGP4Lighting 840701.59 383.45 3869.47 20949334 57395.43

Penumbra 2450.22 7.84 14.22 153750 421.23Umbra 2183.67 26.57 1933.83 10434987 28589.00

J4Lighting 893306.21 2017.94 4237.05 21740323 59562.53

Penumbra 1546.78 7.97 14.85 152144 416.83Umbra 2161.15 43.13 1888.1 9646607 26429.06

J2Lighting 898726.98 2017.94 4239.65 21745174 59575.82

Penumbra 1556.65 7.97 14.88 152402 417.54Umbra 2161.14 33.53 1887.17 9641552 26415.21

Two-BodyLighting 3787.92 62.29 3497.44 20089343 55039.29

Penumbra 1315.66 7.99 11.83 135906 372.34Umbra 2158.41 1672.41 1970.63 11313401 30995.62




TD: Total duration



F.4. Elevation angle comparative

Table F.10: Elevation angle accessibility analysis for UPC ground station

UPC Analysis

Angle # AY # AD TDY (sec) MDA (sec) DD (min) % Dif15o 732 2.005 140095 191.387 6.3975o 1251 3.427 396008 316.554 18.082 282.60o 1687 4.621 709455 420.543 32.395 506.4

AY: Access/year

AD: Access/day



DD: Duration/day

Dif: Difference

Table F.11: Elevation angle accessibility analysis for NTNU ground station

NTNU Analysis


Table F.12: Elevation angle accessibility analysis for Malaysia ground station

Malaysia Analysis


F.5. HPOP vs. SGP4 comparative

1) Accessibility


Table F.13: HPOP and SGP4 accessibility analysis for UPC ground station

UPC Analysis

Propagator # AY # AD TDY (sec) MDA (sec) DD (min)SGP4 1250 3.424 544961 435.969 24.884HPOP 1336 3.660 608790 455.682 27.798

AY: Access/year

AD: Access/day



DD: Duration/day

Table F.14: HPOP and SGP4 accessibility analysis for NTNU ground station

NTNU Analysis


Table F.15: HPOP and SGP4 accessibility analysis for Malaysia ground station

Malaysia Analysis


2) Lighting

Table F.16: HPOP and SGP4 Lighting comparative

Propagator MaxD (sec) MinD (sec) MeanD (sec) TD (sec) MDA (sec)

SGP4Lighting 17.359 2.264 88.196 23437346 17.836

Penumbra 40.499 0.122 0.268 142178 0.108Umbra 36.593 1.612 30.156 7957779 6.056

HPOPLighting 16.095 2.695 89.327 23480637 17.869

Penumbra 20.732 0.122 0.232 121845 0.092Umbra 36.497 2.015 30.348 7935623 6.039




TD: Total duration


Thermal analysis information 107

Appendix G

THERMAL ANALYSIS INFORMATION

G.1. UPCSat Information

In order to determine the thermal balance of the UPCSat, the characteristics of the Cube-sat must be known and studied. Moreover, it is important to know the values of emissivityand absorptivity for each material related to the Cubesat.

If the Cubesat is launched through a P-POD, the use of Aluminum 7075 is suggested forthe main structure [22]. If other materials are used, the thermal expansion must be similarto that of the P-POD (Aluminum 7075-T73). However, the Cubesat kit is composed bydifferent types of materials. The base plate, chassis and cover plate are made from 5052-H32 aluminum. The two plates are made from 0.060” material, the chassis from 0.050”.The chassis is hard anodized and alodyned in a manner that leaves the rail surfaces hardanodized, and the rest of the structure alodyned, so that it remains conductive and there-fore gives you a Faraday cage. If it were completely hard anodized, it would be an electricalinsulator, which is undesirable in this application. Panels use the 7175 aluminum alloy, andare alodyned as said before The CubeSat Kit’s feet are machined from 6061-T6 aluminum,and are also hard anodized. This alloy has roughly the same coefficient of thermal expan-sion as the 5000-series material used in the structure. Finally, all fasteners (screws andcaptive fasteners) are stainless steel.

Although these are the initial inputs, the structure can be completed with other materials inorder to change the values of emissivity/absorptivity or to enhance the power subsystemwith for example solar cells, which is the case of the UPCSat. Moreover, the use of Kaptonfoil is typical for insulation purposes between the solar cells and the panels.

Typical values of emissivity and absorptivity for the different parts of the structure and thethermal characteristics of the two types of aluminum alloys are presented in Table G.1 andTable G.2 respecitvely [23].

Table G.1: Emissivity and absorptivity of different parts of the Cubesat

Part Material Thermal finish α εAluminum frame 5052 Al alloy Alodine 0.08 0.15Aluminum framerails

5052 Al alloy Hard anodized 0.88 0.88

Aluminum panels 7075 Al alloy Alodine 1200 0.1 0.1Aluminum panels(outside)

7075 Al alloy Kapton foil on Alodine1200

0.87 0.81

Solar panels GaAs cells Anti reflective coating 0.91 0.81


Table G.2: Material properties

Alloy ρ(kg/m3) c(J/KgK) k(W/mK)

5052 2672-2698 963-1002 140-1527075 2770-2830 913-979 131-137

G.2. Thermal analysis methodology

Several simplifications have been made in chapter 3 to obtain a first approximation of thesolution. These are:

• Cubesat is a sphere with radius r

• No internal dissipation is observed

• There is no thermal inertia

Treating the Cubesat as a sphere reduces the computations for the angle of incidenceof the heat flux by making the angle constants because of the same area of incidence.Values of emissivity and absorptivity will change due to this factor which must be takeninto account.

Moreover, thermal inertia as explained in chapter 3 must be also studied because thedifference in temperature evolution. To do it, transient analysis must be performed.

Finally, an accurate calculation of temperatures of all internal parts is needed in order toobtain the internal dissipation of the satellite. However, this is extremely complex so theproblem is again simplified to a thermal mathematical model (TMM) which assumes thatthe spacecraft is a set of blocks represented by nodes, and each block has no thermalgradient (isothermal). Results obtained from STK were through node analysis and tookinto account the internal dissipation of the satellite. However, it was just a single nodeanalysis which it is not the most realistic one.

Radiation and conduction in a complex structure of various materials should be studied[20]. The heat flow between any pair of nodes i and j is presented in Eq. G.1 where h isthe thermal conductance.

Qci j = hi j (Ti −Tj) (G.1)

So, a TMM is a mathematical model that forms this network of nodes and calculates allthe heat fluxes numerically to reach a steady state. Radiation heat flow has a similarsituation as the environmental thermal balance taking into account that emission betweentwo surfaces reflects each other [20].

Qr i j = AiFi j εi j σ(T4i −T4

j ) (G.2)


εi j =εiε j

εi + ε j − εiε j(G.3)

So the goal of the thermal design is to keep the critical systems within its operating limitsand not to achieve a specific temperature. To do it, the worst-case conditions shouldbe used and a network of TMM nodes should be defined. Then, the thermal balancetemperature limits are obtained and they must be compared to the operating limits (seeFig. G.1) in order to apply or not a control method to bring temperatures back inside thelimits.

Figure G.1: Typical operational limits of components of a satellite. Source [23].

TMM calculation is a quite complex calculation so available software is used to performthis part of the thermal analysis. Equations can be introduced by the user in software lan-guages as Matlab which will give accurate results depending on the inputs introduced. Inaddition, there exists commercial software that performs this type of analysis also. Exam-ples of software are ESATAN, ESARAD and ANSYS that are presented in the next sectionof the appendix.

G.3. Software available

ESATAN [24] is a software package for the prediction of temperature and heat flows usinga thermal lumped parameter network. It is the standard European thermal analysis toolused to support the design and verification of space thermal control systems. It providesthe following capabilities.

• Steady state and transient analysis.


• One, two and three dimensional models.

• Conduction, convection and radiation heat transfer.

• Condensation and boiling heat transfer.

• Facilities to allow the user to model phase change phenomena.

ESARAD [24] is a thermal-radiative analysis and pre/post-processing tool that providesthe following functionality:

• Define and visualize a 3D external surface model of a space-craft with thermo-opticaland thermo-physical properties.

• Compute view factors, radiative exchange factors and couplings.

• Define space-craft trajectories (orbits), attitude and pointing.

• Optionally add articulation (rigid body kinematics).

• Compute solar and planetary heat fluxes for a selected set of positions along aspace-craft trajectory.

Moreover, it is a pre and post process for ESATAN. It produces the thermal-radiative partof an ESATAN lumped parameter thermal network model, and can be used to visualize theresults of an ESATAN run on the geometric model.

ANSYS is an engineering simulation software provider [25] [26]. It develops general-purpose finite element analysis and computational fluid dynamics software. While ANSYShas developed a range of computer-aided engineering (CAE) products, it is perhaps bestknown for its ANSYS Mechanical and ANSYS Multiphysics products.

ANSYS Mechanical and ANSYS Multiphysics software are non exportable analysis toolsincorporating pre-processing (geometry creation, meshing), solver and post-processingmodules in a graphical user interface. These are general-purpose finite element modelingpackages for numerically solving mechanical problems, including static/dynamic structuralanalysis (both linear and non-linear), heat transfer and fluid problems, as well as acousticand electro-magnetic problems. ANSYS software can also be used in civil engineering,electrical engineering, physics and chemistry.

There exist other software but this three are the most common used in thermal analysis.However, there are some differences between them. While ESATAN and ESARAD aresoftwares that can be downloaded for evaluation, ANSYS is a software that must be boughtand then paid for being able to use it. Functionality of each of them is quite different also.ESATAN and ESARAD are software developed for the thermal analysis purposes uniquelywhile ANSYS is an engineering software that provides thermal analysis among a widerange of other uses. This capability of ANSYS makes it more complete than the otherones because you can perform other analysis and coupled analysis to your satellite but onthe other hand it is more complex to use because there are a lot of parameters to take intoaccount.


In conclusion, there are many programs that can be used for thermal analysis, each ofthem with its own characteristics but that at the end they must give similar results.

master thesis mission and thermal analysis of the upc …the cubesat that is planning to launch the...

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