Kepler Dust Cover Ejection Event
Design and Optimization
Chris Zeller and David Acton
Ball Aerospace & Technologies Corp.
czeller@ball.com
dacton@ball.com
Outline
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Kepler mission overview
Summary of problem
How and why project used AGI software
Optimizing dust cover release attitude
Key risk reductions from using AGI software
2
Kepler mission overview
 NASA mission launched March 2009
Planet transit
 Search for Earth-size planets
– In/near habitable zone of solar-like stars
 Highly sensitive photometer
 Continuously and simultaneously
measures brightness of >100k stars
Variation in star brightness
indicates planet transit
 Flight segment design and fabrication at
Ball Aerospace & Technologies Corp.
 Scientific Operations Center at NASA
Ames Research Center
 Mission Operations Center at LASP –
University of Colorado
3
Summary of problem
 Ensure ejected photometer dust cover (DC) does not
return to strike flight segment (FS)
 Determine release attitude to maximize FS-to-DC
distance over mission duration
– Must meet power, telecom, and sun-avoidance constraints
 Ensure validity of solution considering uncertainties
– DC ejection direction and velocity
– DC surface properties
– DC release date
4
Kepler trajectory description
 Helio-centric Earth-trailing
orbit avoids obscurations
Projection of
photometer
axis onto
the ecliptic
View from the
ecliptic North Pole
Autumnal
Equinox
Kepler’s
orbit
Fall
roll period
– ~0.5 AU range from Earth
after 4 years
 No traditional V
maneuvers required
Earth’s
orbit
Winter
roll period
Winter
Solstice
Summer
Solstice
Sun
 Periodic reaction wheel
desaturations
– Via RCS thruster pulses
– Small but measurable
effects on trajectory
– STK excellent modeling fit
Summer
roll period
Orbital
direction
Kepler 4 years later
Kepler 1 year later
Earth on March 6th
Spring
roll period
Launch
Vernal
Equinox
Earth’s orbit
Kepler’s orbit
Kepler’s position on
March 6th of each year
Earth at launch
Roll period
5
Dust cover design and release
Dust cover

Protects photometer
– Contamination prior to, and during launch
– Stray/direct sunlight during launch and early commissioning
Photometer

Deployment mechanism
– Single latch, single fly-away hinge, and pre-loaded screws
Spacecraft

Dust cover
> 14 kg
1.7 x 1.3 m
Hinge
Nominal release
– Along vector ~ 8º from sunshade
normal, towards hinge side
– Relative velocity ~0.5 m/sec
– Variations must be considered
Pre-load
fittings (x4)
Latch
Photometer
field-of-view
(~100 deg2)

t = 2.9 sec
t = 3.3 sec
t = 3.9 sec
t = 4.2 sec
Constraints on release attitude
– Power
– Telecom
– Photometer Sun-Avoidance
Sunshade
normal
Sunline
Cover position at
t = 2.4 sec after
release
Sunshade
assembly
6
STK allowed efficient and accurate
analysis for important Kepler issues
 STK as standard trajectory modeling and analysis tool
– Chosen early in the project
– Ease of use, flexibility, visualization, accuracy, and familiarity to analysts
 Used for a variety of analyses
–
–
–
–
–
–
Power estimates, telecom range and angles for duration of mission
Initial Acquisition timing and angles
Deep Space Network station view periods
Optimization of quarterly roll windows
Verification of commissioning attitudes
Dust Cover Ejection event (this presentation)
 Allowed validation of similar customer analyses
 This analysis – STK Professional, Astrogator, Chains, and Analyzer
– Astrogator provided unique features to tailor deep space analysis
7
Baseline trajectory model

Trajectory modeled using Astrogator
–
–
–
–
–
Initial conditions at launch vehicle separation
Near-Earth perturbations with Earth-moon gravity model
Dust cover separation reaction modeled as a maneuver
Desaturation burns (every 3 days) using sequence loops
Deep Space propagation (6 years)
Kepler-Earth
body-body
rotating
reference frame
8
Validation of the STK Kepler model

Validated model with JPL Navigation Team’s MONTE Tool
– Tailored Astrogator propagator to determine which physics to model
– Updated STK to latest planetary ephemeris to match JPL inputs
Final result – highly accurate STK trajectory model
Range Difference Between JPL and STK Solutions
30000
Selected Propagator:
• Earth J2 with Moon + Sun 3rd bodies
• Heliocentric + all 9 planets after
9.25E+5 km from Earth
25000
Relativity On
Standard HPOP, Helio
HPOP No Moon
Standard STK HPOP
HPOP CIS Lunar Helio No Rel
CIS Lunar Helio No HPOP
Cis Lunar Helio Rel
J2 Helio
HPOP Lite Helio
J2 Moon Sun Helio
JDM3 HPOP Helio
J2 8x8 JDM3
J2 2x0 JDM3
20000
Range (km)

15000
Alternate Selection:
• Earth HPOP +
Sun/moon 3rd bodies
• Heliocentric + all 9
planets after 9.25E+5
km from Earth
10000
5000
0
0
500
1000
1500
2000
2500
3000
Days After Release
Validation was essential to provide customer confidence in solution
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Features of the dust cover ejection model

Coordinate system selected for
fixed attitude with respect to Sun
– Provided fixed constraints for
photometer sun-avoidance & power
– STK Vector Geometry Tool validated
antenna, star tracker, photometer
FOV constraints

Target pointing attitude selection
used to determine release attitude
VNC(Sun) = Velocity, Normal, Co-Normal, centered on Sun

Baseline DC trajectory returned
towards FS several times
– Oscillatory behavior
– Suggested we perform optimization
and sensitivity analyses
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Analyzer Carpet Plot was generated to
optimize release directions
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Appropriate Figure-of-Merit was crucial
– Oscillatory behavior of DC motion required careful FoM choice
– FoM chosen as minimum range after initial “drift-away” period
Note: Not all
options were
good ones
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Optimum release direction
Optimal release direction
maximized minimum range
– But did not meet Earth and Sun
constraints
– Selected next best option
– Nominal minimum range after
drift away is 40,820 km
Kepler Dust Cover - FS Relative Range
600,000
500,000
Actual 0 Az,35 El
Optimum 0 Az, 0 El
400,000
Range (km)

300,000
200,000
100,000

Desaturation impulses help
– Tend to push FS away from
DC over time

0
Mar-2009
Mar-2010
Mar-2011
Mar-2012
Mar-2013
Mar-2014
Mar-2015
Date
Attitude computation
– Target Pointing attitude and
custom reports used to
compute VNC-Body
quaternion
12
Sensitivity analysis using Analyzer
Distribution of Dust Cover Minimum Range for Variation in
Release Direction, Magnitude and SRP
– Release angle, release
velocity, and DC reflectivity
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30
Monte Carlo tool to investigate
variations in parameters
Verified large minimum range
met under even 3 conditions
Reduced risk that inaccuracy
in any one parameter could
throw us “off the cliff”
-3 34,327 Km
Mean 40,814 Km
+3 47,302 Km
25
Frequency

20
15
10
5
0
34,090 35,511 36,932 38,354 39,775 41,196 42,618 44,039 45,461 46,882
Min Range (km)
13
Sensitivity analysis for DC release date
 Reduce impact of commissioning schedule changes
 Necessary to run manually
– Analyzer could not handle variations in epoch dates
 Determined release date variations acceptable
– Within range of dates considered
DC-FS Range With Varying Release Date Vs. March 28th 2009
10,000
29-Mar-09
30-Mar-09
5,000
Range Difference (km)
31-Mar-09
1-Apr-09
0
2-Apr-09
3-Apr-09
-5,000
4-Apr-09
5-Apr-09
6-Apr-09
-10,000
Dust cover
successfully
released on
April 8, 2009
7-Apr-09
Worst Case DC-FS range > 40,000 km
-15,000
8-Apr-09
9-Apr-09
10-Apr-09
-20,000
0
500
1000
1500
2000
Days After Release
14
STK provided key risk reduction for dust
cover ejection
 STK allowed efficient analyses of complex problem
– Reduced cost and time to address important Mission Design concern
 Ability to fine-tune trajectory estimates during independent
validation with customer solutions lowered risk of errors
 Cost-benefit of Analyzer was important
– Significantly reduced time for optimization and Monte Carlo analyses
 3D visualization provided simple visual verification of all results
– Lowered risk of violating flight rules
– Easy to communicate results across program and to stakeholders
15
Acknowledgements
 AGI Tech Support
– For their helpful dedication and long hours helping sort
out the best way to approach the problem
 Jeff Baxter
 Dana Oberg
 Luis Montano
 Ball Aerospace colleagues
– For their insightful consultation
 Scott Mitchell
 Adam Harvey
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Contact information
 Chris Zeller
– Senior Systems Engineer
– Ball Aerospace & Technologies Corp.
– Boulder, Colorado
– czeller@ball.com
– 303-939-4636
 David Acton
– Senior Systems Engineer
– Ball Aerospace & Technologies Corp.
– Boulder, Colorado
– dacton@ball.com
– 303-939-4775
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