Maksim Shirobokov Sergey Trofimov Mikhail Ovchinnikov (speaker)

1. 68th International Astronautical CongressAdelaide, Australia, September 25-29, 2017IAC-17.C1.7.4Station-Keepingof Sun-Venus L2 Libration Point Orbits for a Prospective Space Observatory Mission Maksim Shirobokov Sergey Trofimov Mikhail Ovchinnikov (speaker) Keldysh Institute of Applied Mathematics

2. Contents • Motivation • Dynamics inthe vicinity of L2 • Station-keeping simulation algorithm • Results • Conclusions

3. Missions to libration point orbits and station-keeping characteristics

4. Advantages of using the Sun-Venus L2 libration point orbits • Good location for telescopes that observe the hazardous asteroids with the low aphelion • Flexible shadow conditions and absence of Venus in the camera’s field of view • Low station-keeping costs NEO Survey spacecraft Credit: Ball Aerospace & Technologies Corporation

5. Solar eclipse geometry

6. Rotating reference frame Mass parameter Non-dimensional units: The Sun-Venus system

7. Equations of motion in the CR3BP In the rotating frame where Equilibrium points meet conditions and are called the libration points

8. Lissajous orbit 3,400 x 10,842 x 1,900 km

9. Mean, minimum and maximum illumination coefficients for different Lissajous orbits

10. Halo orbit with the y-amplitude of 489,290 km

11. Family of halo orbits

12. Evolution of the Floquet diagrams along the family of halo orbits

13. The station-keeping simulation algorithm • Design the reference orbit in the high-fidelity model of motion and specify the target points at the times , respectively • Simulate the orbit insertion errors where

14. Two types of the control • The x-axis control: find such that after applying , the objective is minimized • The 3-axis control: find such that after applying the objective is minimized

15. Navigation errors • Simulate the navigational errors before applying the impulse where

16. Impulse execution errors • Simulate the impulse execution errors where and the rotational matrix perform a random rotation with the normally distributed cone angle and the uniformly distributed clock angle • If , then the impulse is skipped

17. Levels of uncertainties • Orbit insetion errors: • Navigation errors: • Impulse execution errors: • Minimum : • Number of points downstream:

18. Mean annual station-keeping cost, its standard deviation and the maximum deviation from the reference orbit x-axis control 3-axis control

19. Approximate bounds of the central manifold (CR3BP)

20. Approximate bounds of the central manifold (Full)

21. Conclusion • The station-keeping cost for Lissajous orbits with a different mean illumination degree is approximately the same and equals 1.14 m/s • The station-keeping cost for halo orbits is slighly less than for Lissajous orbits and decreases as the amplitude increases • The station-keeping costs for the 3-axis control are by 6-10% larger than for the x-axis control • Required navigational accuracies when targeting the xz-plane are estimated for stable halo orbits

22. Thank you for your attention! This work is fully supported by the Russian Science Foundation grant 14-11-00621.

23. Backup

24. Literature review • D. W. Dunham and A. L. Genova. Using Venus for locating space observatories to discover potentially hazardous asteroids. Cosmic Research, 48(5):424-429, 2010. • K.G. Raikunov. Structure and design of the orbital segment of the Earth's asteroid information system. Ph.D. Thesis, Bauman Moscow State Technical University, 2016 (in Russian). • Yu. S. Bodrova and K.G. Raikunov. Rational variants for deployment of space telescopes for concurrent detection of asteroids. In XLI Academic Readings on Cosmonautics, Moscow, 2017. • R. E. Gold. SHIELD - A Comprehensive Earth Protection System. A Phase I Report to the NASA Institute for Advanced Concepts, 1999. • R. Arentz et al. NEO Survey: An Ecient Search for NearEarth Objects by an IR Observatory in a Venuslike Orbit. In AIP Conference Proceedings, volume 1208, pages 418-429. AIP, 2010. • National Research Council. Defending Planet Earth: Near-Earth-Object Surveys and Hazard Mitigation Strategies. The National Academies Press, Washington, DC, 2010. • R.Z. Akhmetshin. Space based Optical Barrier in the Problem of Asteroid Hazard. Keldysh Institute Preprints, (29):1-32, 2012. • R. Z. Akhmetshin. Space patrol: Variants of the optical barrier scheme. Cosmic Research, 51(4):241-253, 2013. • E. T. Lu, H. Reitsema, J. Troeltzsch, and S. Hubbard. The B612 Foundation Sentinel Space Telescope. New Space, 1(1):42-45, 2013. • D. W. Dunham et al. A Concept for Providing Warning of Earth Impacts by Small Asteroids Solar System Research, 47(4):315-324, 2013.

25. Equations of motion in the high-fidelity model

26. Sources of pertubrations

27. Mean illumination coefficients for different Lissajous orbits

28. Histogram of the annual station-keeping costs for the 6,050x3,400 km Lissajous orbit; the x-axis control.

29. Mean annual station-keeping cost, its standard deviation, and the maximum deviation from the reference orbit for different levels of the orbit insertion and navigational uncertainties; the x-axis contol