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Europa Orbiter Study Update. Rodney L. Anderson Martin W. Lo. 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.
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Europa Orbiter Study Update Rodney L. Anderson Martin W. Lo June 17, 2004
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 L2 Lyapunov Orbit June 17, 2004
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 June 17, 2004
Ci Cm Cf C4 DV DV 5:6 L2 DV Resonant Capture Sequence 3:4| DV | 3:4 | Eu | 5:6 | DV | 5:6 | L2 Lyap | Cap DV Ci Cm Cf C4 Change Energy, C, at DV 3:4 3:4 5:6 3:4 June 17, 2004
Planar Europa Orbiter (PEO) Trajectory June 17, 2004
Planar Europa Orbiter (PEO) Trajectory June 17, 2004
Normalized Two-Body Period Initial Section Ci Final Section Cf Middle Section Cm June 17, 2004
3:4 Resonant Orbit for Middle Segment C = Cm June 17, 2004
5:6 Resonant Orbit for Middle Segment C = Cm June 17, 2004
Poincaré Section at Cm w/ Resonant Orbits June 17, 2004
Poincaré Section at Cm w/ Resonant Orbits June 17, 2004
Poincaré Section at Cf w/ Resonant Orbits June 17, 2004
Poincaré Section at Cf w/ Resonant Orbits June 17, 2004
5:6 to Lyapunov Orbit June 17, 2004
~2:3 Resonance – Note Lobes June 17, 2004
Homoclinic Tangle Around Neptune 2:3 MMR 2:3 MMR END END June 17, 2004
~9:10 Resonance June 17, 2004
Stable Region of ~9:10 Resonance June 17, 2004
5:6 Resonant Orbit for Final Segment C = Cf June 17, 2004
The PEO Follows the Invariant Manifolds June 17, 2004
The PEO Follows the Unstable Manifold of the 5:6 Resonant Orbit June 17, 2004
Current Tasks • Understand Resonant Orbit Transfers • Find Transition in Manifolds at Changes in Energy Levels (DVs) • Put Together Sample Trajectories for Input into Mystic June 17, 2004
Poincaré Section at Cf w/ Resonant Orbits Stable Manifold of L2 Lyapunov Orbit 3:4 Resonant Orbit & Unstable Manifold 5:6 Resonant Orbit with Stable & Unstable Manifolds June 17, 2004
5:6 Resonant Orbit for Cf (Inertial Frame) C = Cf June 17, 2004
3:4 Resonant Orbit for Final Segment C = Cf June 17, 2004