Multi-tired Implementation for
Near-Earth Asteroid Mitigation
Scientific Preparatory Academy for Cosmic Explorers
Shen 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
NEO Mitigation Strategy
• Detailed three-tiered layer for exploring and
mitigating Near Earth Asteroids (NEAs)
• Reference mission to asteroid 99942 Apophis
is the proof of concept for this process
Apophis Exploration
and Mitigation Platform
LEO Flight Experiments
Ground Experiments
and Simulations
2
2023
NOV
Apophis Exploration and Mitigation
Platform (AEMP)
• Exploration and mitigation platform to Apophis.
2021
Scheduled Objectives:
FEB
1.
2.
3.
4.
5.
1. Begin a mission with precision tracking, “tagging” the asteroid
with the spacecraft, and combine this with science
measurements of the gravity field, material composition, and
thermal properties. [2021]
2. Cross-correlate the tracking data found in the initial
exploration phase with SDM predictions and resolve the
modeling and parameter uncertainties. [2021 – 2022]
4. Perform an initial mitigation technique that depends on the
least data (mass distribution, total mass, center-of-mass location,
geometric envelope, spin state). [2022]
5. Combine the initial mitigation phase with continued
observation to map the albedo, model the thermal properties,
model solar pressure, and the Yarkovsky effect. [2022-2023]
6. Finally, apply some permanent mitigation technique that can
eventually retire the threat completely. [2023]
3
AEMP: Mission Profile
•Intermediate Analysis
•Long Term Mitigation – May 2023
•Short Term Mitigation – Apr 2022
•Preliminary Analysis
•Preliminary Exploration
•Rendezvous – Sep 2021
•Cruise
•Launch – Feb 2021
•Post Mitigation Investigation
•End of Mission – Nov 2023
4
AEMP: Orbital Transfer
2021
SEP
•
2021 •
FEB
•
•
Simple 2-impulse orbit transfer
Direct launch-to-transfer orbit using a Falcon-9 vehicle
Solid kick motor provides majority of rendezvous ΔV
Upon insertion into the proximate heliocentric orbit near
Apophis, the spacecraft is to take up a 2 to 3 km stand-off
position to begin exploration
• Proximity maneuvers performed by mono-propellant
Hydrazine main engine and attitude control thrusters
Launch date:
Feb 19-2021
Rendezvous Date:
Sep 14 2021
Time of flight:
208 days
C3
4.3 km2/s2
ΔVf
3 km/s
5
Why is Exploration Needed Before Mitigation?
(J. D. Giorgini, L. A. M. Benner, S. J. Ostro, M. C. Nolan, and M. W. Busch. “Predicting the Earth
encounters of (99942) Apophis”, Icarus 193 (2008) 1-19.)
•Errors in the Standard Dynamical
Model (SDM) can produce tens of
Earth radii positional errors over
the period 2029 - 2036
•Uncertainties in Apophis’ thermal
emission parameters (e.g. bond albedo)
can produce tens of Earth radii errors
over the period 2018-2036
6
2022
APR
2021
SEP
AEMP: Initial Exploration Phase
The first actions to be performed are designed to
achieve the following science objectives:
1) Determine the trajectory of Apophis 99942 with
sufficient accuracy to establish the minimum
trajectory change that can guarantee no Earth impact
through the close approach of 2036
2) Study physical characteristics
a) to refine the orbit propagation models.
•
•
Spin state
Asteroid mass, etc.
b) to refine intervention procedures.
•
•
Surface mapping of geometric albedo
Gravity model valid ~100m from surface
7
Determine Absolute Position of Spacecraft
Determine SC to Apophis relative position
Determine mass of Apophis
Map surface geometry
Determine bulk volume and density
Model the gravity field
Map the albedo of the Apophis
Determine average bond albedo
Map surface temperature
Determine spin axis
Micro-Bolometer
Star Tracker
Inertial Measurement Unit
Optical Navigation Camera
Laser Range Finder
Radio Science
Inertial Measurement Unit
Star Tracker
Micro-bolometer
Radio Science
•
•
•
•
•
•
Laser Range Finder
2021
SEP
AEMP: Instrumentation/Science Mapping
Optical Navigation Camera
2022
APR
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
8
Tracking and Mitigation Pose Conflicting Requirements
Suppose we launch early
(2012), and acquire
tracking data over the
following year.
Make tracking measurements
and incorporate data into
trajectory model
Then as we propagate forward over a long time period using the
dynamical model, the uncertainty (tube width) might grow so large
that an unambiguous prediction is impossible by 2036.
Nominal trajectory
Whereas, if we launch and do tracking
just before a close approach, our
uncertainty will be smaller but there will
be no time for mitigation.
Tracking
measurements
9
9
AEMP: Tracking Error vs. Deflection Effectiveness
Tracking begins
1/10 Earth Radius
3 Earth Radii
April, 2029 close
approach
10
2023
MAY
AEMP: Gravity Tractor
2022
APR•
The gravity tractor is well-known and can be applied early in mission since
detailed knowledge of the physical properties of the NEO is not required.
• The thrusters used are xenon Hall Effect thrusters canted Φ = 38˚off the
thrust axis and providing a net tractor force of Fhover = 4 mN.
• By maintaining a position d = 270m from C.O.M. of Apophis for 1 year
(prior to the 2029 close approach), 3 Earth radii of deflection will be
achieved by 2036.
Tractoring
period
Average Mass
Distance from
CM
Force imparted
1 year
560 kg
270 m
0.014 N
11
Yarkovsky Effect
Solar Radiation
Cooler “dawn” side
Net
force
hotter “dusk” side
h h

c

h  6.626 x10 34 J  s
Pphoton 
Excess radiation
Carries away momentum Pphoton per photon
D. Vokrouhlicky, A. Milani, and S. R. Chesley. “Yarkovsky Effect on Small
Near-Earth Asteroids: Mathematical Formulation and Examples”, Icarus
148, 118-138 (2000).
12
2023
NOV
2023
MAY
AEMP: Surface Albedo Treatment
System (SATS)
• SATS raises or lowers the average
albedo to produce a three-Earthradii 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)
13
2023
NOV
2023
MAY
AEMP: Surface Albedo Treatment
System (SATS)
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.
Fluidization
stream
ACP Chamber
Albedo Change
Particles
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.
Pressurized Inert
Gas
Mixing
Chamber
The main flow out of the
gas supply leads directly to
the mixing chamber.
Tribo ionization tube
Once mixed, the ACPs plus gas
is forced through the narrow
tribo ionization tube
14
2023
NOV
2023
MAY
AEMP: ACP Mass Calculation
MT 
VARIABLE
Radius of Apophis
Density of Apophis
Surface Thickness
Distance from Orbital Track by 2036
Bond Albedo of Treated Surface
Bond Albedo of Untreated Surface
Orbit Sensitivity Factor
SCENARIO
Largest Mass (165 m),
Least Reflective
(0.1613)
Nominal mass (135
m), Nom. Reflective
(0.1521)
Smallest Mass (105
m), Most Reflective
(0.1383)
 RA2 wT x  2036
 T  0  1 R
QUANTITY
R
ρp
W
||Δx||2036
αT
α0
Γ
DESCRIPTION
105 – 165 m
1.78 g/cm3
50 μm
3REarth
0.0461-0.4149
0.1383-0.1613
200-1450
WHITE ACP MASS(kg)
1.35
BLACK ACP MASS (kg)
2.98
TOTAL MASS (kg)
4.33
3.58
8.86
12.4
21.4
64.2
85.6
15
AEMP: Spacecraft Design
•
•
•
•
•
•
Mass:
•
Launch mass to Earth escape = 1100 kg
•
Wet mass = 570 kg
•
Dry mass = 415 kg
Power:
•
Solar arrays
•
Li-Ion battery packs
•
Max power mode = Grav Tractor ~ 1kW
Attitude control system provides 3-axis
stabilization
•
Reaction wheels
•
Attitude thrusters provide minor
translational capability
Propulsion
•
Solid kick motor for rendezvous ΔV
•
Hydrazine monopropellant system for
proximity operations
•
2 Xenon propellant Hall’s effect thrusters
Semi-autonomous command structure
Communications
•
1 m parabolic high gain antenna
•
2 omni directional low gain antenna
Development time: ~5yrs
Total cost: ~ $350 M
•
Sensor suite
•
Star tracker
•
Inertial measurement unit
•
Optical navigation cameras
•
Sun sensors
•
Laser range finder
•
Micro-bolometer
16
AEMP: Cost Justification
Payload
Price
(US Dollars,
millions)
Element
Amount in 2009 (US
Dollars, millions)
Dawn Framing Camera
25.4
PM/SE/MA
24.5
NEAR Laser Range Finder
10.1
Payload
60.9
Microbolometer
15.2
Spacecraft
102.5
Albedo Change
10.2
Hardware total
163.5
Total
60.9
MOS.GDS
18.0
Development Cost, No Reserves
206.0
Development reserves
61.8
Total Development costs
267.8
Phase E&F costs
28.0
Phase E&F Reserves
8.4
Total mission costs, no launch
Vehicle
304.2
Launch Vehicle/services
50.0
Total mission
354.2
 Costing exercise was done at
Ames Mission Design Center in
April 2009
 Spacecraft and payload cost
estimated using parametric cost
estimation models
 Other costs modeled as
percentage warp-factors
 Phase E/F costs based on
historic Discovery class missions
17
LEO Flight Experiments (LFE)
• The Apophis Mitigation Technology LEO Flight
Experiments (LFE) will demonstrate feasibility
2013
of an albedo changing prototype on a target
FEB
surface in a controlled environment
• Static Preliminary Albedo Demonstration
2012
Experiment (SPADE) design is a cube-shaped
DEC
spacecraft 40x40x40 cm
• Static, flat SATS test surface is part of satellite
and exposed to LEO environment
18
LFE: SPADE Design
Powder Canister
Sun
Sensor (4)
Pressurant Gas Canister
Torque Rod (3)
Tribodispenser
Tube
Electronics Bay
Batteries
Antenna
Camera
Test Surface
19
LFE: Mission Profile
V∞
1. Orient spacecraft
2. Charge test surface
then remove power
supply
3. Initiate tribodispenser and
spray test surface
20
LFE: Mission Profile (Part 2)
4. Allow particles time
to cure
5. Observe, record, and
transmit data
Data
21
LFE: Orbital and Attitude
Requirements
• Orient so that panel is facing sun when on sun side
of earth to allow particles to cure in sunlight
• Orient so main body of the craft shields the panel
while moving through LEO atmosphere
• Main body in ‘ram’ direction, panel in ‘plasma wake’
Parameter
Value
Altitude*
350 km
Inclination**
46o
Ballistic Coefficient
58 – 82 kg/m2
Orbit Lifetime
30 – 200 days
* To avoid excess radiation, altitude < 700 km but for 30-day mission
timeline, altitude > 300 km
** Communications with College Station, TX ground station requires > 31o
22
LFE: Surface Design
• Surface simulated by
charged aluminum
plates of varying
roughness
• Surface charge from
parallel plate capacitor
• Required electric field
based on expected
asteroid charge density
E
Plate Area
0.217 m2
Assumed Resistivity
2.82 × 10-8 Ω·m
Dielectric Constant
9.15
Distance between Plates 0.01 m
Potential Difference
0.1 V
Capacitance
1.76 x 10-9 F
Charge on top plate
1.76 x 10-10 C
23
LFE: Mass Budget
GUMSTIX
Computer
Total Mass Budget
[kg]
Albedo Change Demo
5.9
Telecommunications and
Instrumentations
1.0
Propulsion and Attitude Control
2.8
Structure, Thermal, and Power
32.2
Total
41.9
Total (with 30% safety factor)
54.5
EELV
Secondary
Payload
Adapter
Camera (Cosmos-1
adapted)
Magnetometer
Sunsensors (x4)
Magnetorquer (x3)
24
LFE: Cost Budget
Cost Component
1 Payload
2 Spacecraft
2.1 Structure
2.2 Thermal
2.3 Electrical Power System (EPS)
2.4a Telemetry Tracking & Command (TT&C)
2.4b Command & Data Handling (C&DH)
2.5 Attitude Determination & Control Sys. (ADCS)
2.6 Propulsion
3 Integration, Assembly & Test (IA&T)
4 Program Level
Parameter X (Unit)
Parameter Value
1st Unit Cost
SubTotal Cost
Spacecraft Total Cost
Satellite bus dry wt. (kg)
Structures wt. (kg)
Thermal control wt. (kg)
Average power (W)
Power system wt.
Battery capacity (A-hr)
1.68 x
3.57 x 10
1.99 x 10
1.00
1.50
1.48 x 10
2.27 x 10
$4.00
$0.00
$1.05
$0.20
$0.01
$1.50
$4.50
$2.70
$0.00
$0.45
$0.20
$0.01
$0.90
$2.75
$6.70
$0.00
$1.50
$3.25
$0.02
$2.40
$7.25
BOL Power (W)
EOL Power (W)
TT&C / DH (W)
Downlink data rate (Kbps)
1.80 x 102
1.00
3.00
5.60 x 10
$3.50
$3.00
***
***
$2.10
$1.70
$0.20
$0.92
$5.50
$4.40
$0.20
$9.15
TT&C + DH wt. (kg)
9.00 x 10-1
$0.50
$0.20
$7.00
Data Storage Capacity (MB)
1.40 x 102
$3.00
$1.25
$4.30
ADCS dry wt. (kg)
Pointing accuracy (deg.)
Pointing knowledge (deg.)
Satellite Bus dry wt. (kg)
1.50
1.00
1.00
3.57 x 10
***
***
***
***
$1.15
$2.45
$2.20
$0.00
$1.15
$3.45
$2.20
$0.00
Satellite volume (m^3)
9.87 x 10-2
***
$0.00
Total:
$0.00
$23.5 M
Spacecraft total cost
1.68 x 104
$0.00
$3.00
$3.00
Spacecraft total cost
1.68 x
104
$2.50
$2.50
$5.00
104
***
$1.50
$1.50
***
$1.35
$1.35
Satellite Cost:
$34 M
5 Ground Support Equipment (GSE)
Spacecraft total cost
1.68 x
6 Launch & Orbital Operations Support (LOOS)
Spacecraft total cost
1.68 x 104
Inflation Factor
RDT&E Cost
104
1.30
Total
25
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:
2012
2010
– 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.
26
GE: Experimental Parameters
COMPONENT
Q/M
Tube length
X
Tube material
X
Tube radius
X
Gas Pressures
(injection,
dilution, vortex)
X
Particle/Gas Ratio
X
Surface albedo
Nozzle choice
AC
A/M
FPTE
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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!
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).
27
GE: Objective Hierarchy
AHM:
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
Weights:
Q/M
AC
A/M
FPTE
.2771
.4658
.0960
.1611
Albedo change is the most important objective criteria. Coverage
area-mass ratio is the least important.
28
GE: 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.
29
GE: 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.
30
GE: Experimental Schematic
Lamp
Faraday cage
SATS
Infrared
heater
Triboiontube of SATS
Nozzle
Faraday
cages
Gas
Tank
Vacuum
Chamber
Aluminum
plate
Electrometer
Electrometers
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)
31
Simulation Outline
• 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
32
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
33
Sim: Near Field
Input Parameters
Materials
- Average particle size and density,
particle volume fraction, particle
velocity
Configuration
- Length and Diameter of the tube
Pressurant application
- Injection pressure, dilution
pressure, vortex pressure
Output Parameters
• Mass flow rate
•ACP charge
• Gas Pressure
• Particle Positions,
Velocities, Accelerations
-> Distribution
34
Sim: Near Field
Design procedure
1) Models for Tribocharging Tube
2) Models for Dispensing
a) ACP/Gas flow (+ turbulence)
a) Solid particle motion
b) Electrostatic Charging
b) Electrostatic Field
1. a) ACP/Gas Flow
- Governing Equations:
1) Mass conservation eqn.
2) Momentum Conservation eqn.
Turbulent air flow
- The standard κ-ε model
35
Sim: Near Field
1. b) Electrostatic Charging
- Rate of particle collisions with tube walls
For Charge per mass:
 g Dielectric constant of gas - usually close to vacuum constant
 q

 mp
3 gVc

 p D p z0
 
 Du
max 1  3 m g
4  p Dp v
Vc Effective contact potential (Volta potential)
 p Mass density of particle material
 g Mass density of gas
D Diameter of tribotube
D p Diameter of powder particles
z0
Seperation distance, a few angstroms according to paper
u
Axial gas velocity
v
m
Mean axial particle velocity
Gas/Particle mass flow ratio

W
2
4
 D gu
W Powder mass flow rate
36
Sim: Near Field
2. a) Solid particle motion
- Lagrangian Approach
the equation of motion for the particles
-> predicts the trajectories of the
particles
-> stepwise integration over discrete
time steps
-> solved in each coordinate direction
to predict the velocity and position
of the particle at given time.
2. b) Electrostatic Field
-Consider the space charge from nozzle to near field, and
interactions between particle - particle.
Laplace equation
37
Sim: Near Field
First Tribo dispenser Model (Solidworks)
38
Sim: Near Field
Tribo dispenser Model (Gambit)
Volume Meshes
Set Boundary conditions
39
Sim: Far Field I
Inputs
Spacecraft
Height
Asteroid Size
and Shape
From
outputs of
near-field
Asteroid Mass
Density
Position
Forces
(acceleration)
ACP Position
ACP Velocity
ACP Velocity
ACP Density
ACP
Acceleration
ACP
Acceleration
ACP Radius
ACP Charge
ACP Position
ACP Charge
Note: All variable constants
are outlined in red.
Numerical integration of
force equations
propagated
Outputs
Asteroid
Surface Charge
Density
40
Sim: Far Field I
Gravitational Force (Fg)
G – gravitational constant
M – mass of Apophis
m – mass of ACP
r – distance between mass centers of
Apophis and ACP
Electrostatic Force (FE)
q – charge of ACP
σ – surface charge density of Apophis
A – incremental surface area
Solar Radiation Force (Fr)
S – solar flux
A – surface area of Apophis
c – speed of light
v – velocity of ACP
Qpr – radiation pressure coefficient
41
Sim: Far Field I
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 RungeKutta 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.
42
Sim: Far Field II
Position
Inputs
Plasma Sheath
Thickness
From
outputs of
Far-Field 1
Forces
(acceleration)
ACP Position
Plasma Sheath
Potential
ACP Velocity
ACP Velocity
ACP Density
ACP
Acceleration
ACP
Acceleration
ACP Radius
ACP Charge
ACP Position
ACP Charge
Numerical integration of
force equations
propagated
Outputs
Solar Wind
Mach Number
43
Sim: Far Field II
• 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 “punch” through this cloud.
• Once the ACP enters the sheath, its
ultimate fate can only be one of
three possibilities:
1. It falls to the surface. GOOD
2. It gets deflected and totally
escapes. NOT GOOD
3. It becomes suspended in the
sheath. NOT GOOD
Powder
Paths
Layer of
charged
electrons
Asteroid
44
Sim: Far Field II
• Solve two pairs of equations:
d z
 kTe 
md 2  4a  0 n0 e 

dt
 e 
2
Force
Current
3/ 2
dY
Yd
 mg
dz
dQ
 Ie  Ii
dt
1/ 2
 eV
exp 
 kTe

 exp( Yd ), U  0

1/ 2
 eV
exp 
 kTe

 exp(1  Yd ), U  0

 8kTe
I e   n0 ea 2 
 me



 8kTe
I e   n0 ea 2 
 me



1/ 2
 kTe 
2

I i  n0 ea M 
 mi 

2eU / kTe 
1  2

 M  2eV / kTe 
45
Sim: Far Field II
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.
46
Sim: Far Field III
• 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?)
47
Sim: Far Field III
• Current simulation efforts take into account a distribution of albedo
and heights on surface generated by:
1.
2.
3.
4.
5.
•
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.
Assume a solar position relative to the surface. This determines the
direction of the lighting.
Create an intensity map of an asteroid dependent on the needle
map.
Find the geometric albedo at every pixel by assuming a Lambertian
model.
Apply ACP positions from outputs of FF2 for both colors. Find the
amount of albedo change detected for either case.
Currently just using a rough probability of landed particles for
generating the normal distribution of ACP landings for particles.
48
Sim: Far Field III
• Assuming 500 m2 coverage, i.e. 1.4% area
coverage for the smallest possible size
SCENARIO ALBEDO BEFORE (AVG)
ALBEDO AFTER (WHITE)
ALBEDO AFTER (DARK)
Light
Mid
Dark
0.7862
0.5682
0.4276
0.5795
0.3617
0.2451
0.6947
0.4228
0.2205
49
Conclusion
• Three-tiered design process of AEMP mission,
LEO test flight satellite mission, and ground
experiments with simulations is progressing
concurrently providing insight on all three
layers of design
• Continued collaboration between the three
design layers will culminate in the launch of a
fully functioning spacecraft to the near earth
asteroid Apophis early 2022
50
Questions?
51
EXTRA SLIDES
52
 EELV Secondary Payload Adapter (ESPA)
 Small Launch scaled version
 38.8” primary interface diameter
 Sized for:
 Minotaur IV
 Falcon 1e
 Taurus
 Delta II
 Fits CubeSats up to 180 kg
 Flight validation costs are low
 Use existing test facilities
53
List of Parameters for Method
Symbol
Parameter
Secondary
Variables
Option 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
D
L
Experimental Trials
E
r
C
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
+
+
-
+
-
-
+
+
-
-
+
-
+
+
-
ηm
B
A
Φ
ηn
F
ρinj
G
ρdil
Hρ
vo
r
NOTE:
For experiments not
requiring all 8
factors here, simply
ignore respective
column in chart.
Comment:
e may be useful for
error estimation
Determining Interrelationships
• To find the optimal configuration, an equation
8
6
can be written,
yk  a0   ai xi   ai , j xi x j
i 1
j 1
a0   yk / 16
ai   xik yk / 16
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
coefficients
xi = 1 (for maximum input value) or -1 (for minimum input value)
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 determine the validity of
the measurements.
Equipment Required
SYSTEM COMPONENTS
Surface Albedo - Tribogun
Treatment System - Powder
(SATS) - Hopper (will contain powder)
- Control electronics
- Valves
- Pipes
- Pressurant Tank (will contain neutral gas)
- Neutral gas
Heat/Light Source + - Modified projector lamp(simulates solar radiation)
Heat Detector - 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)
Debye Length
• Solid body in a plasma will be surrounded by a
plasma sheath.
• Minimum distance scale over which the particles
may be considered in its collective behavior. Any
smaller than this and the interactions between
individual particles have to be considered.
• Two Debye length:
– Solar wind
– Photoelectron layer (from photoelectric effect)
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.
Forces
 Charged dust particle in sheath will be subjected to
electric and gravitational forces.
3/ 2
d z
dY
 kTe 
md 2  4a  0 n0 e 
 mg
 Yd
Constants
dt
dz
 e 
m = mass of particle
2
g = 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 surface
ε0 = permittivity constant in vacuum
e = electron charge
k = Boltzmann constant
Te = electron temperature
Non-dimensional variables:
z = x/ λd
Y = eV/kTe
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:
where
Q = charge of particle
Ie = electron current
Ii = ion current
dQ
 Ie  Ii
dt
Electron Current Equation
 Assuming a Maxwellian distribution of
electrons having gone through potential V,
1/ 2
 eV 
 exp(Yd ), U  0
exp 
 kTe 
1/ 2
 eV 
 exp(1  Yd ), U  0
exp 
 kTe 
 8kTe 

I e   n0 ea 
 me 
2
 8kTe 

I e   n0 ea 
 me 
2
Ion Current equation
 Similarly,
1/ 2
 kTe 

I i  n0 ea M 
 mi 
2

2eU / kTe 
1  2

 M  2eV / kTe 
Solidworks Model
65
Fluent Simulation: velocity, mass flow rates
Future Work
Develop User Defiened
Function to allow Fluent
to account for Charges
of particle
66