Design of a Surface Albedo Modification Payload for Near Earth Asteroid (NEA) Mitigation

Scientific Preparatory Academy for Cosmic ExplorersShen Ge, Hyerim Kim, Darkhan Alimzhanov, Neha Satak

Shen Ge, sge@spaceacad.org; Hyerim Kim, hk@spacecad.org; Darkhan Alimzhanov, da@spaceacad.org; Neha Satak, ns@spaceacad.org

2

Outline

• IntroductionSATS Overview

• Ground Experiment• Simulations

• Distinguishing team and individual work:– All slides with contributions primarily done by

Shen Ge will have a yellow title.

3

Introduction to NEOs and PHAs• Near-Earth object (NEO) is a

solar system object whose orbit intersects with that of Earth.

• All NEOs have a perihelion distance less than 1.3 AU

• Potentially hazardous objects (PHAs) are NEOs that can be less than 0.05 AU from Earth and is at least 150 m

• Many studies have gone into deflection of such bodies away from Earth

Flyby of asteroid 2004 FH, closest miss ever noticed

4

Introduction to Mitigation Strategy• Short-term and long-term mitigation payload

in addition to exploration mission• Reference mission to asteroid 99942 Apophis

is the proof of concept for this process

Ground Experiments and Simulations

LEO Flight Experiments

Apophis Exploration and Mitigation Platform

5

Apophis 99942 Background• LL-chondrite composition• Orbital period 323.6 days

– 7:8 Earth-Apophis orbit resonance• Rotational period of 30.6 h• Keyhole Event – April 13, 2029

– Results in resonant return and possible impact in April 2036

• Current impact probability: – 1 in 250000

• 400 MT impact energy would yield regional destruction

– Largest bomb ever detonated was Tsar-Bomb (25 MT)

Sources: “Apophis Risk Summary”, JPL NEO ProgramChesley, Milani, Vokrouhlicky, Icarus 148, 118–138 (2000)

Physical Characteristics

Diameter 270 m

Mass 2.78E+10 kg

Vinf 5.87 km/s

Energy 400 MT

Orbital Characteristics

Eccentricity 0.1911

Inclination 3.331°

Aphelion 1.099 AU

Perihelion 0.746 AU

Period 323.6 days

6

Why consider Apophis?

• Apophis appears somewhat representative of the mid-range (~20 billion kg) of hazardous NEAs capable of causing regional destruction

• Apophis is relatively easy to get to in the not-too-distant future– There are favorable, low energy launch windows every ~7yrs – coinciding with

Apophis’ close approaches to Earth– We’ve missed the 2012-2014 window, but can still try for 2020-2022

• Although Apophis closely approaches Earth (esp. in 2029 and then in 2036) it is very unlikely to impact Earth– The Apophis mission is intended to be a “dress rehearsal,” not the “real

thing.” – The aim is to flight-validate an archetypal exploration/mitigation operation

• The 2021 – 2023 mission allows us to measurably change the orbit, verifying the technologies without producing significantly harmful orbit perturbations.

– Once our technologies are proven, we can be ready for the real thing

7

AEMP: Mission Profile

•Launch – Feb 2021

•Cruise

•Rendezvous – Sep 2021

•Preliminary Exploration

•Long Term Mitigation – May 2023 •Short Term Mitigation – Apr 2022

•Post Mitigation Investigation

•Preliminary Analysis

•Intermediate Analysis

•End of Mission – Nov 2023

8

Long-Term Mitigation Technique: Altering Yarkovsky Effect

Sola

r Rad

iatio

nCooler “dawn” side

hotter “dusk” side

Excess radiationCarries away momentum Pphoton per photon

Net force

D. Vokrouhlicky, A. Milani, and S. R. Chesley. “Yarkovsky Effect on Small Near-Earth Asteroids: Mathematical Formulation and Examples”, Icarus 148, 118-138 (2000).

sJxh

hchPphoton

3410626.6

9

Yarkovsky Effect

-Yarkovsky effect is the result of anisotropic heating of a celestial object.-As the sunlit side of the asteroid rotates away from the sun, the warmer dusk side radiates more energy than on the cooler dawn side. -The resulting net force acts in a direction that is determined by the asteroid’s spin axis, rotation rate, and orbital period.

10

How to Modify the Yarkovsky Effect• Yarkovsky Effect is due to non-uniform thermal

distribution of surface temperatures of asteroid.

Modify diurnal thermal wave directly by depositing material on surface a depth of O(1 cm)

Modify diurnal thermal wave indirectly by changing the albedo, the diffuse reflectivity, of the surface, which changes how many thermal photons are absorbed or reflected. Maximum O(.01 cm) is needed for opacity

Option 1: Dump dirt Option 2: Change color

11

Apophis Trajectory Change from 2/14/2018 to

2/14/2036 Due to Changes in Energy Reflection,

Absorption and Emission

Case:Spin state

Absorption, Mass

Trajectory change in earth Radii due to a 4% change in

(1-A)

Orbit deflection sensitivity

x/A(Earth radii)

ProgradeMin. Absorp., Max.

mass

8.0 200

ProgradeMax. Absorp., Min

mass

18.0 450

In-planeMin. Absorp., Max.

mass

9.0 225

In-planeMax. Absorp., Min

mass

20.0 500

RetrogradeMin. Absorp., Max.

mass

27.0 675

RetrogradeMax. Absorp., Min

mass

58.0 1450

• Two materials must be carried (light and dark) to account for orbit sensitivities due to spin axis orientation

Efficacy of Albedo Change

Giorgini, Benner, Ostro, Nolan, and Busch. Icarus 193 (2008) 1-19

12

AEMP: Surface Albedo Treatment System (SATS)

• SATS raises or lowers the average albedo to produce a three-Earth-radii orbit deflection by 2036.

• On the sun-facing side, the surface has a net positive charge.

• The SATS nozzle is designed to impart a negative charge to the ACPs and dispensing is performed solely on the sun lit side.

• This effect further ensures that the particles will be quickly bound to the surface and will not rebound or levitate into an escape condition.

P. Lee, “Dust Levitation on Asteroids”, Icarus 124, 181-194 (1996)

2023MAY

2023NOV

13

AEMP: ACP Mass Calculation

VARIABLE QUANTITY DESCRIPTIONRadius of Apophis R 105 – 165 mDensity of Apophis ρp 1.78 g/cm3

Surface Thickness W 50 μmDistance from Orbital Track by 2036 ||Δx||2036 3REarth

Bond Albedo of Treated Surface αT 0.0461-0.4149Bond Albedo of Untreated Surface α0 0.1383-0.1613Orbit Sensitivity Factor Γ 200-1450

2

2036

0 1A T

TT

R w xM

R

SCENARIO WHITE ACP MASS(kg) BLACK ACP MASS (kg) TOTAL MASS (kg)Largest Mass (165 m),

Least Reflective (0.1613)

1.35 2.98 4.33

Nominal mass (135 m), Nom. Reflective

(0.1521)

3.58 8.86 12.4

Smallest Mass (105 m), Most Reflective

(0.1383)

21.4 64.2 85.6

2023MAY

2023NOV

14

Conservative Mass Calculation• Actually, only

requires 0.5% of the surface to be modified.

J. Giorgini, et al. “Predicting the Earth Encounters of (99942) Apophis”, Icarus 193: 1-19 (2008).

15

AEMP SATS Schematic

Pressurized Inert Gas

Albedo Change Particles

Fluidization stream

ACP Chamber

Mixing Chamber

Tribo ionization tube

A secondary flow is released into the

outer portion of the selected ACP

chamber

The ACP storage chamber is double-walled; the ACPs being contained within the inner wall. The inner wall is perforated by many

small holes.

The gas flows through the holes in the inner wall, both

“fluidizing” the ACP mass (mixing up the ACPs so that the dry powder behaves like

a liquid) and expelling a steady stream of ACPs into

the mixing chamber.

The main flow out of the gas supply leads directly to

the mixing chamber.

Once mixed, the ACPs plus gas is forced through the narrow

tribo ionization tube

2023MAY

2023NOV

16

SATS Design

• Tribo Ionization Tube• ACP Chamber (hopper system)• Valve Controller• Pressure Channels

17

Triboionization Tube

• Static friction charging with particles gaining charge while traveling through a long tube of material with opposite electronegativity.

• Requires pressurized gas to propel particles through tube.

• Tribodispensers must be designed to optimize certain requirements.

18

Advantages of Tribo over CoronaDISADVANTAGES OF TRIBO DISADVANTAGES OF CORONA

Cleaning required periodically. In industry, every 15 minutes. For mission, will

depend on material composition of tube and powders.*

More complicated components makes it more likely to fail. Single point of failure

with the electrodes.

Transfer efficiency is low. Best first pass transfer efficiency (FPTE) is 50%.*

Electrodes at end of tube require more power.

Wears out fast but actual lifetime for mission will depend on frequency of

usage, mass flow rate, and abrasiveness of powder. For ~50 kg of powder spray,

there is no lifetime issue.**

Works by ionizing air molecules at end of electrode and then letting particles pick up charge as it goes through this ionized plasma. In a vacuum, we have no dense

gas mixture to ionize outside of the spacecraft. Of course, we can have a little

gas chamber inside the spacecraft but that makes it more complicated and

introduces issues like spacecraft charging.

19

Tribodispenser Schematic

*Based off Nordson Tribomatic 500

Modify hopper system

Modify tribo tube

20

Tribo Tube: Component Changes

EXPERIMENT COMPONENT CHANGES*

Optimize length of tube. #4, 5

Optimize radius of tube #4, 5, 6, 7, 8

Optimize material of tube #4, 5

Optimize mass flow rate. NONE

Optimize nozzle design. #6, 7, 8

Optimize angular tilt of tube. #4, 5, 6, 7, 8

*Based off Nordson Tribomatic 500

21

Tribo Tube: Model Choice• Ultimately, we chose Tribomatic 500

manufactured by Nordson because of – “Best” retrofitability – Lowest mass– Technical support personnel ability and willingness

to help– Rigorous and detailed technical manuals– Proximity to Powder Coating Research Group

22

Electron Donor (+)Nylon 6/6Cellulose

Cellulose acetatePolymethyl methacrylate

PolyacetalPolyethylene terephthalate

PolyacrylonitrilePolyvinyl chloride

Polybisphenol carbonatePolychloroether

Polyvinylidene chloridePolystyrenePolythylene

PolypropylenePolytetrafluoroethylene (PTFE or teflon)

Electron Acceptor; Most electronegative (-)

Triboelectric Series

23

SATS Pressure Channels

Dascalescu, Lucian. “Virtual Instrument for Statistic Control of Powder Tribo-charging Processes. “ Journal of Electrostatics Vol. 63: 565-570, 2005.

24

LEO Flight Experiments (LFE)

• The Apophis Mitigation Technology LEO Flight Experiments (LFE) will demonstrate feasibility of an albedo changing prototype on a target surface in a controlled environment

• Static Preliminary Albedo Demonstration Experiment (SPADE) design is a cube-shaped spacecraft 40x40x40 cm

• Static, flat SATS test surface is part of satellite and exposed to LEO environment

2012DEC

2013FEB

25

LFE: SPADE Design Powder Canister

Pressurant Gas CanisterTorque Rod (3)

Tribodispenser Tube

SunSensor (4)

Antenna

Camera

Electronics Bay

Batteries

Test Surface

26

Ground Experiments (GE)• Ground tests to determine optimal parameters for design of

tribodispenser through repeated experiments with combinations of varying inputs.

• Outputs to be maximized:– Charge-mass ratio (Q/M). This is immediately out of tube. will not be

the same for each particle but we want the charge to be +/- 10-6 Coulombs (C) within 1 standard dev (σ).

– Albedo Change (AC). Difference between albedo after treatment with albedo before treatment. This will mostly depend on the pigmentation of the powder.

– Coverage area-mass ratio (A/M). – First pass transfer efficiency (FPTE). Mass of powder on surface over

total mass after one trial.

2012

2010

27

Experimental Parameters COMPONENT Q/M AC A/M FPTE

Tube length X X X

Tube material X

Tube radius X X X

Gas Pressures (injection,

dilution, vortex)

X X X X

Particle/Gas Ratio X X X X

Surface albedo X

Nozzle choice X X X X

Comment: This chart only shows direct correlation. Obviously there’s indirect correlations as well. For instance, particles that have greater charge/mass ratio (Q/M) are more likely to “stick” to the surface and hence produce a larger albedo (AC).

ASSUMED CONSTANTS:1. Powder (developed by PCRG for our application)2. Surface temperature (400K)3. Surface roughness (distributed according to asteroid)4. Surface material (LL Chondrite mod)5. Surface charge (5 V)

Secondary variables affecting the experiment are not shown!

28

Objective Hierarchy Q/M AC A/M FPTE

Q/M 1 ½ 3 2

AC 2 1 4 3

A/M 1/3 ¼ 1 ½

FPTE ½ 1/3 2 1

Q/M AC A/M FPTE

.2771 .4658 .0960 .1611

Weights:

AHM:

Albedo change is the most important objective criteria. Coverage area-mass ratio is the least important.

Note: All row entries are the number of times more important than column entries

29

Optimization of Design

1. Conduct multiple runs of experiments with varying input parameters.

2. Obtain average and standard deviation of runs.3. Give a measure of “goodness” to each output result

(Q/M, AC, A/M, and FPTE) of each set of input parameters.

4. Multiply each “goodness” by the weights defined in objective hierarchy and sum them to obtain one number for each setup. The setup with the maximum number is the one to use.

30

Minimizing Experiment Runs

• A full factorial experiment assuming two levels of factors, 2n runs are necessary where n is the number of independent parameters.

• Using Taguchi methodology, this can be cut to 2(n+1) runs depending on number of considered interactions.

• Orthogonal array/Taguchi Method assumes interactions between variables are negligible unless otherwise stated.

31

List of Parameters for MethodSymbol Parameter Secondary

VariablesOption 1

(-)Option 2

(+)

L Length of tube Charge on particle

521 mm (default)

1000 mm

r Radius of tube Mass flow rate through tribogun

~35 mm diameter (default)

~15 mm diameter

ηm Tube material Charge on particle

Teflon Nylon

ηn Tube nozzle Particle distribution

Straight Fan-shaped

φ Particle-gas ratio

Charge on particle

TBD TBD

ρinj Pressure – injection

Mass flow rate through tribogun

140 kPa ? TBD

Ρdil Pressure – Dilution

Particle concentration

in gas

110 kPa ? TBD

ρvor Pressure – Vortex

Turbulence of motion in gas

80 kPa ? TBD

32

Experimental TrialsC

F

L

ηnΦ

ρinj ρdil

ηmr

ρvo

r

A

D E

B

G H

T A C AC D AD B BD E F G FG H GH AG e

1 - - - - - - - - - - - - - - -

2 - - - - - - - + + + + + + + +

3 - - - + + + + - - - - + + + +

4 - - - + + + + + + + + - - - -

5 - + + - - + + - - + + - - + +

6 - + + - - + + + + - - + + - -

7 - + + + + - - - - + + + + - -

8 - + + + + - - + + - - - - + +

9 + - + - + - + - + - + - + - +

10 + - + - + - + + - + - + - + -

11 + - + + - + - - + - + + - + -

12 + - + + - + - + - + - - + - +

13 + + - - + + - - + + - - + + -

14 + + - - + + - + - - + + - - +

15 + + - + - - + - + + - + - - +

16 + + - + - - + + - - + - + + -

NOTE:For experiments not requiring all 8 factors here, simply ignore respective column in chart.

Comment:e may be useful for error estimation

33

Determining Interrelationships

• To find the optimal configuration, an equation can be written,

16/

16/0

6

1,

8

10

kiki

k

jjiji

iiik

yxa

ya

xxaxaay

where yk = kth trial result of output (can be Q/M, albedo, FPTE, A/M)a = coefficients to be determined. Note that ai also applies to double coefficientsxi = 1 (for maximum input value) or -1 (for minimum input value)

Note:This is assuming a linear and quadratic term is sufficient for modeling.

34

Experimental Trials

• In addition to the 16 trials necessary, 3 repeated trials of conditions at the midpoint of the high and low levels for all 8 factors need to be conducted to find the errors

• If errors are greater than data variation, more experiments have to be conducted and a more sophisticated equation model used

35

Equipment RequiredSYSTEM COMPONENTS

Surface Albedo Treatment System

(SATS)

- Tribogun- Powder- Hopper (will contain powder)- Control electronics- Valves- Pipes- Pressurant Tank (will contain neutral gas)- Neutral gas

Heat/Light Source + Heat Detector

- Modified projector lamp(simulates solar radiation)- Infrared heater (continually heats the surface with IR)- Thermistors

Surface - 0.22 m2 Aluminum plate with varying albedo and roughness (or multiple plates with differing albedo/roughness)

Charge Detector (CD) - Faraday Cup Electrometer (connected to DAQ)

Mass Measurer (MM) -Scale

Cameras - High speed to Look at flow and curing- Webcam to look at surface after treatment

Environment - Vacuum chamber (eliminates charge interaction with air)

36

Experimental Schematic

Gas Tank

SATS Triboiontube of SATS

Faraday cages

Electrometers

Aluminum plate

Lamp

Nozzle

Faraday cage

Electrometer

Vacuum Chamber

Not shown:- DAQ + Computers- Scale (to measure mass of SATS before and after each run as well as mass of plate before and after each run)- Cameras (to take photos of plate before and after each run for albedo and coverage area analysis AND flow)-Thermistors (measure temperature of plate)

Infrared heater

37

Mounting Schematic

Wedge MountHoleProjector

Tribodispenser Tube

Charged Surface

Top SurfaceSide panel with slots for top surface to be placed on

Pipe Anchor

Note: Actual setup needs to be vertical to simulate the condition of spraying onto an asteroid.

38

Environment Simulator

• Vacuum chamber pressure is maintained at ultra-high vacuum of < O(10-5) Torr to simulate LEO environment (200 km altitude)

• Solar lamp with wavelengths 300-4000 nm simulates solar radiation

• Simulations in future will simulate degradation of ACPs through chemical reaction with atomic oxygen

39

Detector: Albedo Change

• Nikon SLR camera has a wide depth of field to see all of surface area

• Use Lambertian reflectance model knowing projector wavelength and intensity to predict reflected radiation.

• Processed photons-> electrons -> voltage-> Gray scale intensity

40

Detector: Q/M Ratio• Optimal length for

the tribo tube to pick up maximum charge

• Multiple Faraday cages connected to electrometers along length of tube

41

Detector: FPTE and A/M

• First pass transfer efficiency (FPTE) is ratio of powder deposited on coating target to amount of powder ejected from powder spray dispenser

• Coverage area over mass (A/M) is found through two scale measurements of mass of surface (before and after deposition) and a camera/imaging algorithm to detect area

42

Surface• 0.22 m2 aluminum plate.• Necessary to confirm performance of simulation

results of powder deposition. • Actual flight experiment has only one plate with

roughness that varies along x-axis and albedo that varies along y-axis of plate.

• Parameters to vary:• Roughness (ranging from perfectly smooth to very

bumpy) • Albedo (ranging from pure white to pure black).• Charge

• Other parameters (non-varying):• Temperature

43

Surface – 2D Test Bed• Eventually, Al surface will be replaced with

surrogate asteroid surface.

44

Surface - 3D Design

• A 3D model will be designed and constructed. Two routes:– Design 3D model in CAD and use CNC machine to

construct model. Affix minerals afterwards.– Design and build wooden framework, wrap and

staple flexible quarter inch wire around, and then apply plaster to wire for base surface. Affix minerals afterwards.

45

Powders: Requirements1. Photoinitiators for curing to occur because energy is from

radiation and not conduction. This is necessary for non-thermoset powders.*

2. Pigmentation for black and white powders. The right materials must be found to be compatible with photoinitiators. Will affect IR absorption (heat up) and albedo effect.

3. Rheology requirements. The powders must after melting, flow and harden.

4. Charge for powder is negative. Amount of charge also depends on several other factors aside from powder composition and size. There is a minimum charge required. Currently doing simulations.

5. Size of powder must be larger than a certain size, possibly 100 microns diameter**. Currently doing simulations.

46

Powder InteractionThermal

Conduction Absorber

IR Radiation Absorber

Melts

UV radiation Absorber

Cures Hardens

Powder will have multiple materials that can perform different functions in the melting and curing process.

47

Powders: UV Curing

• Material that can cure under UV radiation already exists. To formulate powder which can do so should not be a great technological leap.

• A provisional patent can be filed within a week.• Choose materials based on solar UV radiation at

LEO, solar IR radiation at LEO, and IR conduction of the surface.

PARAMETER AT 1 AU VALUE ACCEPTABLE?

UV (7.5e14 to 3e16 Hz)

178 J/s/m2 ?

IR (.003 to 4e14 Hz) 576 J/s/m2 ?

Surface Temperature 394 K (121 C)* >90-100 C is fine

* Assuming black body with emissivity 1.

48

Powders: Pigments

• Those materials that absorb or reflect too much radiation in the same bandwidth as photoinitiators will not allow photoinitiators to absorb enough energy.

• Choose pigments for optimal IR absorption to heat powder and affect flow-out.

49

Pigmentation: Degradation

• Primary causes of degradation on Earth– Water (moisture in air)– Oxygen (in air)– UV radiation (from sun)

• Primary cause of degradation in space is just UV radiation.

• With these materials, we can last for a while:– Black: Use calceine metal oxide. Can last ~20 years.– White: Titanium oxide encapsulated in an inert

material. Last for >5 years.

50

Powders: Thickness Requirements

• Enough thickness is necessary for opaqueness. An opaque coating completely covers a surface with color.

• To achieve opaqueness, we require– Combination of an engineering of delivery device

(Tribodispenser) and an optimal particle size distribution.*

– A combination of large and small particles may be necessary for optimal packing.

51

Powder: Sample Particle Size Distribution (Kynar ADX)

52

Powder: First Steps• As the first step we are using commercial industrial powder so we can get started with some basic testing.• We are using Kynar ADX 111 which melts at a higher temperature than we want and may not have the best charging characteristics but at least have everything else!

53

Kynar ADX 111 Powder CharacteristicsPowder Spraying-80 V to -100 V typical

Melting- Melts at 167 C.

Fusion-10-15 minutes at 240-270 C depending on thickness and materialNOTE: This is substantially higher than the expected 127 C at 1 AU.

Coating Thickness-80-120 microns

Specific Density1.78 g/cm3

Colors-Natural or green-For other colors, please add the right proportion of pigments from another company

54

Simulator: Particle Deposition

• Particle deposition simulator simulates particle dynamics from spacecraft to surface

• Inputs are design parameters such as tribodispenser length, particle size, spacecraft hovering height, etc

• Outputs are particle trajectories, charge-mass ratio, albedo change, etc

• Works concurrently with ground experiments to optimize design

55

Simulation Outline

• Nine sections, split into two groups• Sections 1-4 focus on gas-particle flow where

pressurized gas forces dominate• Sections 5-9 focus on interspatial and asteroid

based forces where these forces dominate

56

Sim: Far Field I (FF1)O

utputs

Spacecraft Height

Asteroid Size and Shape

Position

Asteroid Mass Density

Forces (acceleration)

Inputs

Asteroid Surface Charge

Density

ACP Charge

ACP Density

ACP Radius

ACP Position

ACP Velocity

ACP Acceleration

ACP Position

ACP Velocity

ACP Acceleration

From outputs of near-field

ACP Charge

Numerical integration of force equations propagated

Note: All variable constants are outlined in red.

57

FF1: EquationsGravitational Force (Fg)G – gravitational constantM – mass of Apophism – mass of ACPr – distance between mass centers of Apophis and ACP

Electrostatic Force (FE)q – charge of ACPσ – surface charge density of ApophisA – incremental surface area

Solar Radiation Force (Fr)S – solar fluxA – surface area of Apophisc – speed of lightv – velocity of ACPQpr – radiation pressure coefficient

Burns, Joseph A. “Radiation Forces on Smal l Particles in the Solar System.” Icarus Vol. 40: pp. 1-48. 1979.

58

FF1: Algorithm

1. Starting at t=0, n powders are ejected from spacecraft at an altitude h with some velocity and acceleration. Eject more n powders every tint seconds.

2. Velocity and position is propagated forward in time using Newton-Euler equations and Runge-Kutta integration with time step Δt.

3. Detect when powders are ~1 meter above the surface and pass the simulation of Far-Field 1 to Far-Field 2.

59

Sim: Far Field II (FF2)

Plasma Sheath Thickness

Position

Solar Wind Mach Number

Forces (acceleration)

Inputs

Plasma Sheath Potential

ACP Charge

ACP Density

ACP Radius

Outputs

ACP Position

ACP Velocity

ACP Acceleration

ACP Position

ACP Velocity

ACP Acceleration

From outputs of Far-Field 1

ACP Charge

Numerical integration of force equations propagated

60

FF2: Ending Scenarios• A plasma sheath of negatively charged

particles floats right above the surface and screens out the positive charges on the surface.

• The powder particles must be able to penetrate through this Debye layer.

• Once the ACP enters the sheath, its ultimate fate can only be one of three possibilities:1. It falls to the surface. GOOD2. It gets deflected and totally escapes.

NOT GOOD3. It becomes suspended in the sheath.

NOT GOODAsteroid

Powder Paths

Layer of charged electrons

61

FF2: Debye Length• Solid body in a plasma will be surrounded by a

plasma sheath.• Debye length is the minimum distance scale over

which the particles may be considered in its collective behavior. Any smaller than this distance will have to consider interactions between individual particles.

• Two Debye length:– Solar wind– Photoelectron layer (from photoelectric effect)

Lee, Pascal. “Dust Levitation on Asteroids.” Icarus 124, 181-194, 1996.

62

FF2: Comparisons of Debye Lengths

• The spatial scale at which solar wind interacts at 1 AU: 12 m.

• Spatial scale at which the near-surface electron cloud interacts at 1 AU: 0.1 m

• The more significant Debye length is the shorter one.

Lee, Pascal. “Dust Levitation on Asteroids.” Icarus 124, 181-194, 1996.

63

FF2: ForcesCharged dust particle in sheath will be subjected to

electric and gravitational forces.

Constantsm = mass of particleg = gravitational constant (assume radius of asteroid is much larger than Debye length)λd= Debye length (assume much smaller than radius of asteroid)a = particle radius (assume much smaller than Debye length)n0 = ion density far from surfaceε0 = permittivity constant in vacuume = electron chargek = Boltzmann constantTe = electron temperatureNon-dimensional variables:z = x/ λd (normalized z-position)Yd = eU/kTe (normalized relative potential of ACP surface) Y = eV/kTe (normalized electric potential of plasma sheath)

mgdzdYY

ekTena

dtzdm d

ed

2/3

002

2

4

Nitter, Tore and Havnes, Ove. “Dynamics of Dust in a Plasma Sheath and Injection of Dust into the Plasma Sheath above Moon and Asteroidal Surfaces.” Earth, Moon, and Planets Vol. 56: 7-34, 1992.

64

FF2: Secondary Equation

Besides the force equation, the other key differential equation to solve to find z is the net current equation. This is the total current that runs through the particle:

whereQ = charge of particleIe = electron currentIi = ion current

ie IIdtdQ

Nitter, Tore and Havnes, Ove. “Dynamics of Dust in a Plasma Sheath and Injection of Dust into the Plasma Sheath above Moon and Asteroidal Surfaces.” Earth, Moon, and Planets Vol. 56: 7-34, 1992.

65

FF2: Electron Current Equation

Assuming a Maxwellian distribution of electrons having gone through potential V,

0),1exp(exp8

0),exp(exp8

2/12

0

2/12

0

UYkTeV

mkTaenI

UYkTeV

mkTaenI

dee

ee

dee

ee

66

FF2: Ion Current Equation

Similarly,

M is Mach number in relation to ion drift velocity in the Debye sheath

e

e

i

ei kTeVM

kTeUmkTMaenI

/2/21 2

2/12

0

Nitter, Tore and Havnes, Ove. “Dynamics of Dust in a Plasma Sheath and Injection of Dust into the Plasma Sheath above Moon and Asteroidal Surfaces.” Earth, Moon, and Planets Vol. 56: 7-34, 1992.

i

e

dri

mkTv

M ,

67

FF2 Equations

• Solve two pairs of equations:

mgdzdYY

ekT

enadt

zdm de

d

2/3

002

2

4

ie IIdtdQ

0),1exp(exp8

0),exp(exp8

2/12

0

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Force

Current

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FF2 Outline

1. Take position, velocity, and acceleration of particles from FF1.

2. Propagate positions and velocities of particles through FF2 forces.

3. Relay outputs to FF3 as inputs after undergoing a certain plasma sheath thickness.

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FF2 Results: 150 m Spacecraft Altitude

8 9 10 11 12 13 14 150

10

20

30

40

50

60

70

ACP Dispersal Locations for 165 m Asteroid

0 Degrees30 Degrees

Dispensing Velocity (cm/s)

Disp

lace

men

t fro

m S

pace

craft

Nad

ir

Dispensing Velocity Angle

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FF2 Results: 150 m Spacecraft Altitude

14 150

102030405060708090

ACP Dispersal Locations for 135 m Asteroid

0 Degrees30 Degrees

Dispensing Velocity (cm/s)

Disp

lace

men

t fro

m S

pace

craft

Nad

ir

Dispensing Velocity Angle

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FF2 Results: 150 m Spacecraft Altitude

9 10 11 12 13 14 150

20

40

60

80

100

120

ACP Dispersal Locations for 105 m Asteroid

0 Degrees30 Degrees

Dispensing Velocity (cm/s)

Disp

lace

men

t fro

m S

pace

craft

Nad

ir

Dispensing Velocity Angle

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FF2 Insights

• Negligible impact of Mach number variation (M = 0.95-5) or normalized sheath potential variation (-0.5 to -4.1)

• For nominal case examined (150 m spacecraft altitude), to go through sheath and to land on surface, the optimal dispensing speeds are – 11-15 cm/s for 105 m asteroid– 14-15 cm/s for 135 m asteroid– 8-15 cm/s for 165 m asteroid

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Sim: Far Field III (FF3)

• After passing through the sheath, the particles will hit the ground.

• But will the ground be – Shadowed (negatively charged) or sunlit (positively

charged)? (Will the particle be repelled or attracted at certain places?)

– Hilly or flat? (Will the particle bounce upon impact? How will this affect coverage area?)

– Rocky or soft? (Will the particle bounce upon impact?)– Light or dark? (Will the particle create much albedo

change?)

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FF3: Algorithm• Current simulation efforts take into account a distribution of

albedo and heights on surface generated by:1. Create a realistic needle map n(i, j) of the surface where (i, j) is a

particular pixel in the MxN image matrix. A needle map is just a matrix of normal vectors to the surface.

2. Assume a solar position relative to the surface. This determines the direction of the lighting.

3. Create an intensity map of an asteroid dependent on the needle map.

4. Find the geometric albedo at every pixel by assuming a Lambertian model.

5. Apply ACP positions from outputs of FF2 for both colors. Find the amount of albedo change detected for either case.Smith, William. and Hancock, Edwin R. “Single Image Estimation of

Facial Albedo Maps.” Brain, Vision, and Artificial Intelligence 517-526, 2005.

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FF3: Relation to FF2 • Due to extent of time needed to run

comprehensive dispenser velocity magnitudes and angular directions, a simplified approach was used here to approximate landing positions of particles.

• Found particle landing probability of ~60% for the collection of particles in ranges 6 cm/s – 15 cm/s with angular distributions of 0, 30, 45, and 60 degrees.

• Used a normal distribution of 500 ACP areas (each ACP area = 1 m2) centered at center of 135 m asteroid with similar approximate landing probability.

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Sim: Far Field III

• Assuming 500 m2 coverage, i.e. 1.4% area coverage for the smallest possible sizeSCENARIO ALBEDO BEFORE (AVG) ALBEDO AFTER (WHITE) ALBEDO AFTER (DARK) Light 0.6947 0.7862 0.5795Mid 0.4228 0.5682 0.3617Dark 0.2205 0.4276 0.2451

More significant change

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Future Work Sim: Particle Dispenser• Overall need to actually conduct simulations

assuming a comprehensive range of dispensing velocity variations to plot out the distribution of ACPs on the surface

• FF3: Take existing asteroid images and model the terrain’s albedo and altitude variations based on that

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Simulator: Optimal Area• Assuming a polyhedron model for an asteroid,

develop a method to find the most effective areas to change the asteroid’s albedo (to paint).

• Assumptions:– Constant temperature– Lambertian surface– Constant solar direction

• Note: Modeling Yarkovsky Effect will require full temperature profile which this code does not do here. This code simply identifies surfaces or area neighborhoods where a change in thermal emission will produce the greatest change in force and torque.

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Assumed ParametersParameter Value

Asteroid Length (x-axis) ~165 m

Asteroid Length (y-axis) ~105 m

Asteroid Length (z-axis) ~105 m

Sunlit Side Temperature* 400 K

Dark Side Temperature 250 K (150 K lower than daytime)

Solar Vector (Rs) to C.O.M [1 0 0]

Rotational Angular Velocity 5*10-3 rev/s

Tilt Angle (relative to z-axis)** 30°

* Except for temperature variation simulation runs.** Except for tilt angle variation simulation runs.

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Algorithm: Part 11. Generate a polyhedron

model of asteroid of radius 135 m, nominal radius of Apophis.

2. Acquire the three vectors that describes the x-y-z positions of the ith triangular surface and find its centroid.

3. Find the normal vector N and the normalized force vector f of the ith triangular surface.

N

r

c = speed of lightFs = solar intensityσ = Stefan-Boltzmann constantT = temperature (assume constant 400 K for parts exposed to the sun)

Rubincam, David Parry. “Radiative Spin-up and Spin-Down of Smal l Asteroids.” Icarus Vol 148: 2-11. 2000.

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Algorithm: Part 24. Find the area vector dA of the ith triangular surface.

Considering that the area to be covered is a constant circle while the triangular surfaces are of varying sizes, a method was used to find the intersection area of the circle and the triangle.

5. Knowing the normal vector, normalized force vector, and the area vector, find the forces, torques and normalized torques of the ith triangular surface.

6. Repeat steps 2-4 for all surfaces to account for all surfaces. For each surface, there is a different radius vector, normal vector N, and area vector dA. Rubincam, David Parry. “Radiative Spin-up and

Spin-Down of Smal l Asteroids.” Icarus Vol 148: 2-11. 2000.

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Algorithm: Part 3

7. Repeat steps 2-5 for all time steps in one orbit. Sum up the forces, torques, and normalized torques.

Principal axis of rotation

Asteroid is tilted at an angle to z-axis

x y

z

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Last Step

8. Find the combinations of surfaces that give the area required to be covered and produce the maximum forces, torques and normalized torques in x, y, and z direction.

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Max Force Changes: Temperature

85

Max Force Changes: Tilt Angle

86

Max Torque Changes: Temperature

87

Max Torque Changes: Tilt Angle

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Optimal Area: Result Analysis

• Higher temperature results in greater torque. The numbers also match nicely with the quartic rise calculated by the formula, i.e. the torque at 450K is approximately (450/350)4 = 2.7326 times greater than that of the torque at 350K.

• Torque and force generated at 90 degrees should be smallest since the surface area exposed to the sun over one rotation remains mostly uniform there. This is exactly as observed and O(106) ratio in torque difference is observed between maximum torque at 0 degrees and minimum torque at 90 degrees.

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Distribution of Effective Areas• For this model, a

collection of smaller surfaces with same area as one large surface were found to be less effective.

• Body-fixed hovering will be preferable over inertial hovering.

…

VersusØ 35.2 m

90

Future Work: Sim Optimal Area

• Optimize the altitude for the thrust• Use Dr. Hyland’s rubble pile model for the

asteroid geometry• Include orbital parameter changes• More realistic model for asteroid

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Conclusion• Envisioned original concept of using terrestrial industrial

electrostatic powder dispenser system to modify surface albedo for asteroids

• Designed ground experiment from scratch including– Identifying the criteria which needs to be optimized– Formulating the experimental method to reduce number of experiments– Doing lit reviews and outlining necessary components for space

environmental emulations and detectors– Negotiating contracts with companies for collaboration– Conducting trade studies and ordered experimental parts with help of Dr.

Hyland’s undergrad students• Developed first-level simulations including

– Demonstrating some preliminary boundaries on ejection velocities and spacecraft hovering altitudes

– Modeling effect of white or black powder on a pseudo-asteroid– Showing optimal positions for asteroid painting to occur

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Questions?

93

EXTRA SLIDES

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Body-fixed Hovering

• For this model, body-fixed hovering is more advantageous since the distribution of effective areas is concentrated.

Thrust required to maintain spacecraft position relative to the body.

Minimize the thrust by choosing the optimal height for the spacecraft to hover.

Equations of motion for system in uniformly rotating, small-body Cartesian coordinate frame

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Composition of 99942 Apophis

• Composition according to Binzel, et. al in Spectral properties and composition of potentially hazardous Asteroid (99942) Apophis– Olivine (65 - 75%)– Ortho-Pyroxene (17 - 27%)– Clino-Pyroxene (3 - 13%)

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Surface Design

• Surface is the top plate of a parallel plate capacitor in order to simulate charged surface of asteroid

• Equilibrium surface potential according to Lee needs to be +5 V

• These surfaces will be painted and difficult to clean up which means that we need to have at least 20 surfaces.

• Initially using simple setup with Al surfaces.• Size: 50 cm x 44 cm

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Surface - Charging

• As shown in the equation below, the capacitance of a flat plate capacitor depends on the area A, the number of plates (n), and the relative permittivity (εr), also known as dielectric constant, of the medium between the plates.

dnACVQC

r /)1(/

0

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Surface - Q-Panels

• Q-Panel provides consistent and uniform test aluminum surfaces.

• For maximum convenience, Q-Panel substrates are supplied pre-cleaned, with a 1/4" (6 mm) hole.

• Thousands of labs use millions of our paint test panels each user for color development, weathering exposures, salt spray and corrosion tests.

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Powder Development Questions

1. Will the UV and IR photoinitiators be chemically compatible with the pigmentation and IR conduction material? YES.

2. How difficult is it to incorporate physically in the processing plant? Tricky but can be done.

3. Will there be handling issues. Must store in a dark room before experimentation. Precaution should help.