Journal of Control Engineering and Technology JCET

JCET Vol. 5 Iss. 1 Jan 2015 PP. 1-8 DOI: 10.14511/jcet.issue.050101 © American V-King Scientific Publish 1

TIGRISAT Orbital MotionSimulation and Analysis Mohammed Chessab Mahdi*1

*1Faculty of Engineering University of Kufa– Iraq *1mchessab@yahoo.com

Abstract- Satellite orbit simulation and analysis based on data collected from NASA/ North American Defense Command (NORAD) as a Two Line Elements (TLE) files is presented. General Mission Analysis Tool (GMAT) is used to simulate the orbital motion of TIGRISAT. The analysis includes orbit determination and prediction of satellite’s position and velocity, satellite tracking, and command summary. Orbital path of the TIGRISAT projected onto a two-dimensional world map over some time for one and two revolution of the satellite is plotted.

Keywords- Orbit Determination; Mission Planning; NORAD; TLE; SGP4; TIGRISAT; GMAT; KufaSat; Satellite Tracking

I. INTRODUCTION

Most satellite missions planning required tracking and orbit determination. To track satellite through space it is needed to determine the position and velocity of the satellite in the orbit now and later.Satellite orbit determination estimates the position and velocity of an orbiting object from discrete observations which includes external and internal measurements, external measurements from terrestrial radar and electro-optical sensors and internal measurements from sensors and devices which are installed on the satellite itself. Finding the spacecraft position at any time is a requirement for a satellite mission planning. There are two commonly proposed solutions for finding orbital position,the first is, position estimated from a Two-Line Element (TLE) set using Simplified General Perturbations (SGP4) propagator. TLE are two lines of text data that are frequently issued to the public free of charge, and contain the latest orbital parameters of a satellite. SGP4 model predicts the effect of perturbations caused by the Earth’s shape, drag, radiation, and gravitation effects from other bodies such as the sun and moon. It is mathematical model used to calculate orbital state vectors of satellites relative to the Earth-centered inertial coordinate system. The SGP4 model takes TLE as the input for the orbit prediction. The second is, Global Positioning System (GPS).In spite ofhigh power consumption of GPS receiver [1] the use of this receiver to obtain position, velocity, and time solution should therefore likely satisfy the orbital knowledge requirements for virtually any Low Earth Orbit (LEO)satellite. Accurate position determination is accomplished using a low-cost commercial GPS receiver that has been modified to work in low Earth orbit [2]. The combination of both solutions leads to a rising accuracy and reliability because if one solution fails, it can still use the information of the other system to complete the mission. The purposes of this work are, first,simulation and analysis TIGRISAT’sorbitbased on data collected from NASA/ NORAD TLE files. TIGRISAT is an Iraqi 3U CubeSat built by Iraqi students at the La Sapienza University of Rome with a mission to detect dust storms over Iraq. TIGRISATLaunched in June 19, 2014. It transmits images to two ground stations, one located in Rome and another in Baghdad [3].

Secondusing the results of simulation and analysis TIGRISAT’s orbitin KufaSat mission planning. Kufasat is an Iraqi student satellite project sponsored by the University of Kufa. The main tasks for Kufasat will be to imaging purposes. It is 1U cubesat with 1.5 m long gravity gradient boom, which will be used for passive attitude stabilization and will be flying in Low Earth Orbit(LEO)with 600 km altitude [4].

II. BACKGROUND

Orbits are defined by a set of six elements which aremathematical parameters used to completely describe the motion of a satellite within an orbit andenable us to accurately describe orbit’s shape, orbit’s size, orbit’s orientation, and spacecraft’s location. These elements are also called Keplerian Elements. Knowingthese elements allow satellite tracking programs to calculate a satellite's position in space at a specific time.These elements are [5]:

Eccentricity (e): This element defines the shape of the orbit the value of eccentricity ranges from 0 when the orbit is a perfect circle to 1 when the orbit is very flat.

Semi major axis (a): This defines the size of the orbit.It is the distance between apogee and perigee divided by two.

Inclination angle (i): This element defines the orientation of the orbit with respect to the Earth’s equator.This element tells you what the angle is between the equator and the orbit when looking from the center of the Earth. If the orbit went exactly around the equator from left to right, then the inclination would be 0. The inclination ranges from 0 to 180 degrees.

Right Ascension of Ascending Node (Ω) : This is probably one of the most difficult of the elements to describe .It defines the location of the ascending and descending orbit locations with respect to the Earth's equatorial plane. The ascending node is the place where the satellite crosses the equator while going from the Southern Hemisphere to the Northern Hemisphere.

Journal of Control Engineering and Technology JCET

JCET Vol. 5 Iss. 1 Jan 2015 PP. 1-8 DOI: 10.14511/jcet.issue.050101 © American V-King Scientific Publish 2

Argument of Perigee (ω): Since an orbit usually has an elliptical shape, the satellite will be closer to the Earth at one point than at another. The point where the satellite is the closest to the Earth is called the perigee and the furthest from the Earth is called the apogee. Argument of perigee defines where the low point, perigee, of the orbit is with respect to the Earth's surface.

True mean anomaly (v):The mean anomaly tells you where the satellite is in its orbital path. The mean anomaly ranges from 0 to 360 degrees. The mean anomaly is referenced to the perigee. If the satellite were at the perigee, the mean anomaly would be 0.

The Keplerian orbitis ideal since it assumes that the earth is a uniform spherical mass. Actually the Earth is not a sphere but rather an oblate spheroid in which the radius at the equator is about 21km greater than at the poles. Earth’s asymmetrical mass causes a non-central gravitational pull. Satellites orbiting in near-Earth are subject to a lot of disturbing forces. These forces can be divided into three categories: the gravitational forces, the non-gravitational forces, and empirical forces.The equation of motion of a near-Earth satellite can be described in an inertial reference frame as follows [6]:

r a a a (1)

Where:

ris the position vector of the center of mass of the satellite,a is the sum of the gravitational forces acting on the satellite including Earth’s geopotential, solid earth tides, ocean tides, planetary third-body perturbations, and relativistic accelerations,a is the sum of the non-gravitational forces acting on the surfaces of the satellite including drag, solar radiation pressure, earth radiation pressure, and thermal radiation acceleration, anda is the unmodeled forces which act on the satellite due to either a functionally incorrect orincomplete description of the various forces acting on the spacecraft or inaccurate values for the constant parameters which appear in the force model.Another way to determine the orbit is the orbital state vectors which are Cartesian vectors of position (r) and velocity (v) that together with their epoch time (t) uniquely determine the trajectory of the orbiting body in space. The position vector describes the position of the body in the specific frame of reference, while the velocity vector describes its velocity in the same frame at the same time.

III. TWO-LINE ELEMENT

A two-line element (TLE) is a special form of mean classical orbital elements that describe the orbit of an earth satellite. TLEs are generated with an orbit determination process based on observations by the United States Space Surveillance Network (SSN), which comprises a number of radar and electro-optical sensors [7]. These elements are periodically updated so as to maintain a reasonable prediction capability on all space objects. The TLE is in a format specified by North American Aerospace Defense Command (NORAD) and used by NORAD and NASA. The TLE can be used directly by all Simplified perturbations models (SGP, SGP4, SDP4, SGP8 and SDP8) which used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system. Orbital elements are determined for many thousands of space objects by NORAD and are freely distributed on the Internet in the form of TLEs.Data for each satellite consists of three lines in the format shown in Figure (1)

Fig. 1TIGRISAT Two Line Element

Line 0 is a twenty-four character name (to be consistent with the name length in the NORAD Satellite Catalog SATCAT). Lines 1 and 2 are the standard Two-Line Orbital Element Set Format identical to that used by NORAD and NASA. The format description is as shown in Figure (2).

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JCET Vol. 5 Iss. 1 Jan 2015 PP. 1-8 DOI: 10.14511/jcet.issue.050101 © American V-King Scientific Publish 8

future, using the parameters of KufaSat instead of TIGRISAT gives ability to observe the effects on shape and position of the orbit which lets a better understanding of the KufaSat orbit.

REFERENCES

[1] Mechael .R .Greene, Robert E. Zee ”Increasing Accuracy of Orbital Position Information from NORAD SGP4 Using Intermittent GPS Readings”, 23rd Annual AIAA/USU Conference on Small Satellite.

[2] Mohammed Chessab Mahdi et al,“Attitude Determination and Control System design of KufaSat” International Journal of Current Engineering and Technology, Vol.4, No.4 (Aug 2014)

[3] REAL TIME SATELLITE TRACKING AND PREDICTIONS http://www.n2yo.com/satellite/?s=40043 [4] Mohammed Chessab Mahdi et al, “Direct Fuzzy Logic Controller for Nano-Satellite” Journal of Control Engineering and Technology, Vol.4, No.3 (July,

2014) [5] Wikipedia Orbital elements. http://en.wikipedia.org/wiki/Orbital_elements [6] H. J. Rim, B. E. Schutz, “PRECISION ORBIT DETERMINATION (POD)”, Center for Space Research The University of Texas at Austin, October

2002. [7] James MASON, “Development of a MATLAB/STK TLE Accuracy Assessment Tool, in Support of the NASA Ames Space Traffic Management

Project”, Master Thesis, International Space University, August, 2009. [8] Hujsak, R.S. and Hoots, F.R. (1982), “Deep Space Perturbations Ephemeris Generation”, Aerospace Defense Command, Peterson AFB, CO. [9] GMAT, General Mission Analysis Tool. http://gmat.gsfc.nasa.gov/

BIOGRAPHY

Mohammed Chessab Mahdireceived his B.Sc. degree in control & systems engineering from University of Technology –Baghdad in 1984 and received his M.Sc. Degree in space technology from University of Kufa in 2013. He is full time lecture in Technical Institute of Kufa Al-Furat Al-Awsat Technical University – Iraq and member of KufaSat team - Space Researchs Unit-Faculty of Engineering University of Kufa. He has good skills in the design and modeling of attitude determination and control systems using Matlab program. He has been published more than 9 researches.