Simulations of Altering Yarkovsky Effect on Apophis via Powder Deposition

1. Simulations of Altering Yarkovsky Effect on Apophis via Powder Deposition Shen Ge, Graduate Student, Texas A&M University Dr. David Hyland, Engineering, College of Engineering, Professor of Physics, College of Science, Texas A&M University -----------------------------------------------------------------------------AIAA Region IV Student Conference Houston, TX April 2, 2010

2. Overview Simulation Studies Payload Development Powder Deposition Surface Reflectivity of Apophis Optimal Mission Parameters Spacecraft Attitude Yarkovsky Effect Saves the planet! Trajectory of Apophis

3. Outline Science Overview Mission Overview Simulation Setup Simulation Results Conclusion et al.

4. Near Earth Asteroids (NEAs) • Repeated bombardment in the past have shown their dangerous nature. • 500-1000 NEAs over 1 km in diameter are estimated to cross Earth. • The potentially hazardous asteroid 99942 Apophis is of particular focus.

5. Apophis 99942 Background • Discovered on June 19th, 2004 by R. A. Tucker, D. J. Tholen and F. Bernardi at Kitt Peak • Orbital models have identified several close Earth approaches, occurring roughly every 7 years. • When Apophis passes by on April 13, 2029, it could pass through a gravitational keyhole which could can swing Apophis in a collision with Earth in 2036

6. Why Consider Apophis? • Apophis is • representative of mid-range (~20 billion kg) hazardous NEAs capable of causing regional destruction. • Relatively easy to reach in the near future since there are favorable low energy launch windows coinciding with the 7-year cyclic close approach. • Though impact is unlikely, the 2021-2023 mission allows technology verification.

9. Yarkovsky Effect • Anisotropic heating of a celestial object induces a thermal gradient. • Warmer dusk side radiates more energy than cooler side which results in a net force.

10. Surface Change Required for Trajectory Change Courtesy of Giorgini et al., JPL2

11. Mission Layout

12. Surface Albedo Treatment System (SATS)

13. sun Spacecraft points the SATS directly toward the sun-lit side of Apophis. Negatively charged ACPs are directed with cone angle and dispensing speed. Negative charge on ACPs ensures they will be attracted to the positively charged sun lit portions of the surface and repelled by the shadowed areas. ACPs melt and bond with the surface, forming a thin, opaque coating. Apophis

14. Simulation Assumptions

15. Simulation Forces 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

16. Simulation Algorithm: In space • Starting at t=0, n powders are ejected from spacecraft at an altitude h with a random velocity within the range from vmin to vmax at a random ‘downward’ angle towards the asteroid. Eject more n powders every tint seconds. • Velocity and position is propagated forward in time using Newton-Euler equations and Runge-Kutta integration with time step Δt. • Detect when powders contact the surface and end the simulation for each powder respectively. • Stop simulation after a set time tf.

17. Analysis After landing • Split asteroid surface into different concentric circular zones depending on the distance from the point directly below spacecraft. • Find the number of particles and area covered in each zone modeling curing effects as sphere to randomized flat cylinder with same volume. • Calculate total area coverage. • Repeat runs 10 times for every maximum velocity, spacecraft height, and ACP charge parameter setup. • Plot histograms for each zone. Find standard deviation and mean.

18. Initial Parameter Variables • Spacecraft Height Variation (60 m – 100 m) • ACP Charge Variation (-1 μC to -2 mC) • ACP Initial Velocity Ranges (2 cm/s – 7 m/s)

19. Results • A test run: final ACP positions for 200 ACPs.

20. Results: Variations in Height • Range varies from 0-55 m from z-axis for 60 m altitude deposition to 0-75 m from z-axis for 100 m altitude deposition. Greater height is better! • Standard deviation of the particle count/region shows a small drop as the altitude is increased. No such variation in coverage area/region implies curing has a major effect.

21. Results: Variations in ACP Charge • Electrostatic force is predominant only at short-range. Negligible otherwise. • Will be important if gravity is weaker which may be case if asteroid is modeled non-spherically.

22. Results: Variations in Ejection Velocity • High velocity means high chance of missing asteroid entirely. • Use lower velocity but not too low. 12 cm/s works. Sufficient density and coverage area.

23. Conclusion • Increasing or decreasing the Yarkovsky Effect through surface color modification is an innovative way of altering the potentially Earth-collision trajectory of a NEA. • This simulation gave some preliminary estimates on the design of such a payload on a spacecraft designed for NEA mitigation.

24. Future Work • Look at coverage efficiency, i.e. amount of overlap. • Greater range of initial parameters must be accounted for. • Remains to be done: • Non-spherical geometry of asteroid. Will change mainly gravitational forces. • Electrical double layer (EDL) on asteroid surface. Will predict significant effect of electrostatic forces near surface. • Asteroid terrain and shadowed regions. Will change coverage area analysis and electrostatic forces. • ACP elasticity. Possible bouncing on impact.

25. References 1D.C. Hyland, H.A. Altwaijry, R. Margulieux, S. Ge, J. Doyle, J. Sandberg, B. Young, X. Bai, J. Lopez, N. Satak., “A Permanently-Acting NEA Mitigation Technique via the Yarkovsky Effect,” International Symposium on Near-Earth Hazardous Asteroids, Valletta, Malta, 12-16 October 2009. 2J. 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, pp. 1-19. 3Binzel, Richard P., et al., “Spectral Properties and Composition of Potentially Hazardous Asteroid 99942 Apophis,” Icarus 200, 2009, pp. 480-485. 4Knobbe, Alan J., “Powder Spray Guns,” Report. Nordson Corporation, Amherst, Ohio. 5P. Lee., “Dust Levitation on Asteroids,” Icarus 124, 1996, pp. 181-194. 6D.C. Hyland, B. Young, J. Sandberg, S. Ge, R. Margulieux, H. Kim, J. Doyle., “Apophis Mitigation Technology Demonstration Proposal For Expected Space Flight on KACST Satellite,” Proposal to Dr. Turki Al-Saud, King Abdulaziz City for Science and Technology (KACST), Saudi Arabia, December 2009. 7Burns, Joseph A., “Radiation Forces on Small Particles in the Solar System,” Icarus 40, 1979, pp. 1-48.