1. JIMO Team MeetingJune 17, 2004 Europa Orbiter Study Update Rodney L. Anderson Martin W. Lo

2. Rodney.Anderson@colorado.edu June 17, 20042 Overview The Planar Europa Orbiter Trajectory Resonant Orbits  Transition Between Resonances  Energy Changes (  Vs) Europa Approach  5:6 Unstable Orbit (Compared at Different Energies)  Stable Manifold of L 2 Lyapunov Orbit

3. Rodney.Anderson@colorado.edu June 17, 20043 Planar Europa Orbiter Trajectory Europa Orbiter  Low Thrust Initially Too Difficult  Impulsive Case More Easily Understood  Focus on Understanding Resonance Transfers & Capture Planar Restricted Problem  Theoretically Simpler  More Tools Available Achieved Using LTool Differential Corrector

4. Rodney.Anderson@colorado.edu June 17, 20044 Resonant Capture Sequence 3:4|  V | 3:4 | Eu | 5:6 |  V | 5:6 | L2 Lyap | Cap  V Ci Cm Cf C4 Change Energy, C, at  V V V 3:4 5:6 L2L2 V V Ci Cm Cf C4 V V 3:4

5. Rodney.Anderson@colorado.edu June 17, 20045 Planar Europa Orbiter (PEO) Trajectory

6. Rodney.Anderson@colorado.edu June 17, 20046 Planar Europa Orbiter (PEO) Trajectory

7. Rodney.Anderson@colorado.edu June 17, 20047 Normalized Two-Body Period SectionJacobi Constant InitialC i = 2.98460661333 MiddleC m = 2.99742497175 FinalC f = 3.00245952365 Initial Section C i Middle Section C m Final Section C f

8. Rodney.Anderson@colorado.edu June 17, 20048 3:4 Resonant Orbit for Middle Segment C = C m

9. Rodney.Anderson@colorado.edu June 17, 20049 5:6 Resonant Orbit for Middle Segment C = C m

10. Rodney.Anderson@colorado.edu June 17, 200410 Poincaré Section at C m w/ Resonant Orbits

11. Rodney.Anderson@colorado.edu June 17, 200411 Poincaré Section at C m w/ Resonant Orbits

12. Rodney.Anderson@colorado.edu June 17, 200412 Poincaré Section at C f w/ Resonant Orbits

13. Rodney.Anderson@colorado.edu June 17, 200413 Poincaré Section at C f w/ Resonant Orbits

14. Rodney.Anderson@colorado.edu June 17, 200414 5:6 to Lyapunov Orbit

15. Rodney.Anderson@colorado.edu June 17, 200415 ~2:3 Resonance – Note Lobes

16. Rodney.Anderson@colorado.edu June 17, 200416

17. Rodney.Anderson@colorado.edu June 17, 200417 END Homoclinic Tangle Around Neptune 2:3 MMR 2:3 MMR

18. Rodney.Anderson@colorado.edu June 17, 200418 ~9:10 Resonance

19. Rodney.Anderson@colorado.edu June 17, 200419

20. JIMO Team MeetingJune 17, 2004 Stable Region of ~9:10 Resonance

21. Rodney.Anderson@colorado.edu June 17, 200421 5:6 Resonant Orbit for Final Segment C = C f

22. Rodney.Anderson@colorado.edu June 17, 200422 The PEO Follows the Invariant Manifolds

23. Rodney.Anderson@colorado.edu June 17, 200423 The PEO Follows the Unstable Manifold of the 5:6 Resonant Orbit

24. Rodney.Anderson@colorado.edu June 17, 200424 Current Tasks Understand Resonant Orbit Transfers Find Transition in Manifolds at Changes in Energy Levels (  Vs) Put Together Sample Trajectories for Input into Mystic

25. Rodney.Anderson@colorado.edu June 17, 200425 Poincaré Section at C f w/ Resonant Orbits Stable Manifold of L 2 Lyapunov Orbit 5:6 Resonant Orbit with Stable & Unstable Manifolds 3:4 Resonant Orbit & Unstable Manifold

26. Rodney.Anderson@colorado.edu June 17, 200426 5:6 Resonant Orbit for C f (Inertial Frame) C = C f

27. Rodney.Anderson@colorado.edu June 17, 200427 3:4 Resonant Orbit for Final Segment C = C f