1. Kepler Dust Cover Ejection Event Design and Optimization
Based in Boulder, Colorado, Ball Aerospace & Technologies Corp. is a subsidiary of Ball Corporation. Ball Aerospace is a leader in design, development and manufacture of innovative aerospace systems. We produce spacecraft, instruments and sensors, RF and microwave technologies, data exploitation solutions and a variety of advanced aerospace technologies and products that enable exciting missions.
Ball Aerospace is the prime contractor for NASA’s Kepler Mission to search for rocky, Earth-sized planets around other stars. Ball Aerospace built the photometer and spacecraft, and managed the system integration and testing for the Discovery Class mission. Ball Aerospace employed its instrument expertise from successes such as Hubble Space Telescope in the photometer for Kepler and the spacecraft design used in Deep Impact for providing power, communications and telescope pointing.
Chris Zeller and David Acton
Ball Aerospace & Technologies Corp.

2. Outline 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
Kepler mission overview
Summary of problem
Trajectory description
Dust cover description
How and why Kepler project used AGI software
Model description, including validation
Optimizing dust cover release attitude
Sensitivity analysis using Analyzer Monte Carlo
Sensitivity analysis for launch date
Key risk reductions from using AGI software

3. Kepler mission overview
Planet transit
NASA mission launched March 2009
Search for Earth-size planets
In/near habitable zone of solar-like stars
Highly sensitive photometer
Continuously and simultaneously measures brightness of >100k stars
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
Variation in star brightness
indicates planet transit
NASA Discovery class mission launched in March 2009
Designed to search for Earth-size planets in or near habitable zone of solar-like stars
Uses highly sensitive photometer to continuously and simultaneously measure variation in brightness of over 100,000 stars
Detects planet when it crosses in front of star – called a “transit”
Only a single star field in Cygnus-Lyra region, near galactic plane, is monitored
Mission life is 3.5 years nominal, extendable to at least 6 years
Scientific Operations Center at NASA Ames Research Center
Mission Operations Center at Laboratory for Atmospheric and Space Physics (LASP) – University of Colorado
Flight segment design and fabrication at Ball Aerospace & Technologies Corp.

4. 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
Note that the concern is long-term return, not short term

5. Kepler trajectory description
Helio-centric Earth-trailing orbit avoids obscurations
~0.5 AU range from Earth after 4 years
No traditional V maneuvers required
Periodic reaction wheel desaturations
Via RCS thruster pulses
Small but measurable effects on trajectory
STK excellent modeling fit
Kepler launched into helio-centric Earth-trailing orbit to avoid obscurations
Science target above ecliptic plane to avoid bright solar system objects
Flight segment reaches approx. 0.5 AU range from Earth after 4 years
No traditional V maneuvers required
Periodic reaction wheel desaturations, via RCS thruster pulses, have small but measurable effect on trajectory
STK excellent for modeling effects of small forces

6. Dust cover design and release
Protects photometer
Contamination prior to, and during launch
Stray/direct sunlight during launch and early commissioning
Deployment mechanism
Single latch, single fly-away hinge, and pre-loaded screws
Nominal release
Along vector ~ 8º from sunshade normal, towards hinge side
Relative velocity ~0.5 m/sec
Variations must be considered
Constraints on release attitude
Power
Telecom
Photometer Sun-Avoidance
Note that the dust cover is ejected, not retained with the flight segment. That is why re-contact after the initial drift-away is being analyzed.
Dust cover is not small or light. If it were to impact the flight segment, severe damage would result.
Protects photometer from contamination prior to, and during launch
Protects photometer from stray or direct sunlight during launch and early commissioning
Deployment mechanism uses single latch, single fly-away hinge, and pre-loaded screws to store deployment energy
Cover is nominally released along vector approx 8º from sunshade normal, towards hinge side, at relative velocity of approx 0.5 m/sec
Variation in these values must be taken into account
Constraints on release attitude
Power (minimum angle to solar array normal)
Telecom (minimum angle to low-gain antenna boresight)
Photometer Sun-Avoidance (no sun within hemisphere around sunshade normal)

7. 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
STK chosen early as standard trajectory modeling and analysis tool for Kepler
Factors included ease of use, flexibility, visualization capabilities, accuracy, and familiarity to analysts
Used for a variety of analyses including
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)
Provided means to validate similar analyses performed by customer
This analysis made use of STK Pro, Astrogator, Chains, and Analyzer
Astrogator provided unique features to tailor the deep space analysis
Propagator selection, math models, bodies, and planetary ephemeris
Transitions between spheres of influence
Modeling reaction wheel desaturation events as a loop
Solar radiation pressure

8. 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

9. 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
Selected Propagator:
Earth J2 with Moon + Sun 3rd bodies
Heliocentric + all 9 planets after
9.25E+5 km from Earth
Range (km)
Alternate Selection:
Earth HPOP +
Sun/moon 3rd bodies
Heliocentric + all 9
planets after 9.25E+5
km from Earth
Validated model with JPL Navigation Team’s MONTE Tool
Tailoring of Astrogator propagator very helpful in determining which physics to model
Updated STK to latest planetary ephemeris to match JPL inputs
Final result was a highly accurate STK trajectory model
Days After Release
Validation was essential to provide customer confidence in solution

10. 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
Baseline DC trajectory returned towards FS several times
Oscillatory behavior
Suggested we perform optimization and sensitivity analyses
VNC(Sun) = Velocity, Normal, Co-Normal, centered on Sun
Coordinate system selected to provide fixed attitude with respect to Sun
VNC(Sun) coordinates provided fixed constraints for photometer sun-avoidance and power
STK Vector Geometry tool used to validate antenna, star tracker and photometer FOV constraints
Target pointing attitude selection used to determine release attitude
Baseline DC trajectory was oscillatory, returning towards flight segment several times
This behavior suggested we perform optimization and sensitivity analyses

11. Analyzer Carpet Plot was generated to optimize release directions
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

12. 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
Desaturation impulses help
Tend to push FS away from DC over time
Attitude computation
Target Pointing attitude and custom reports used to compute VNC-Body quaternion
Optimal release direction found to maximize minimum range
Optimum direction did not meet Earth and Sun constraints
Selected direction was the next best option
Nominal minimum range after drift away is 40,820 km
Desaturation impulses tend to push FS away from DC over time
Attitude computation
Target Pointing attitude and custom reports used to compute VNC-Body quaternion

13. Sensitivity analysis using Analyzer
Monte Carlo tool to investigate variations in parameters
Release angle, release velocity, and DC reflectivity
Verified large minimum range met under even 3 conditions
Reduced risk that inaccuracy in any one parameter could throw us “off the cliff”
Monte Carlo tool used to investigate sensitivity of DC-FS range to variations in parameters
Release angle, release velocity, and DC reflectivity
Verified that large minimum range could be met under even 3 conditions
Reduced risk that inaccuracy in any one parameter could throw us “off the cliff”

14. 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
Dust cover successfully released on
April 8, 2009
Sensitivity to DC release date was examined to reduce impact due to risk of commissioning schedule changes
Necessary to run manually
Analyzer could not handle variations in epoch dates
Determined that variations in DC release date were acceptable within range of dates considered
NOTE: It is important to note that the plot does not show the actual DC-FS range for the particular release date. Rather it shows the difference between the DC-FS range over time resulting from the given release date, versus the range over time resulting from the baseline release data of March 28, 2009.
Worst Case DC-FS range > 40,000 km

15. 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
STK tools allowed efficient analyses of this complex problem
Saved cost and reduced time to address an 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, versus manual execution of all cases
3D visualization provided simple visual verification of all results
Lowered risk of violating flight rules
Easy to communicate results across program and to stakeholders

16. Acknowledgements AGI Tech Support Ball Aerospace colleagues
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

17. Contact information
Chris Zeller
Senior Systems Engineer
Ball Aerospace & Technologies Corp.
Boulder, Colorado
David Acton