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

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Presentation transcript:

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

June 17, 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

June 17, 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, 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

June 17, Planar Europa Orbiter (PEO) Trajectory

June 17, Planar Europa Orbiter (PEO) Trajectory

June 17, Normalized Two-Body Period SectionJacobi Constant InitialC i = MiddleC m = FinalC f = Initial Section C i Middle Section C m Final Section C f

June 17, :4 Resonant Orbit for Middle Segment C = C m

June 17, :6 Resonant Orbit for Middle Segment C = C m

June 17, Poincaré Section at C m w/ Resonant Orbits

June 17, Poincaré Section at C m w/ Resonant Orbits

June 17, Poincaré Section at C f w/ Resonant Orbits

June 17, Poincaré Section at C f w/ Resonant Orbits

June 17, :6 to Lyapunov Orbit

June 17, ~2:3 Resonance – Note Lobes

June 17,

June 17, END Homoclinic Tangle Around Neptune 2:3 MMR 2:3 MMR

June 17, ~9:10 Resonance

June 17,

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

June 17, :6 Resonant Orbit for Final Segment C = C f

June 17, The PEO Follows the Invariant Manifolds

June 17, The PEO Follows the Unstable Manifold of the 5:6 Resonant Orbit

June 17, Current Tasks Understand Resonant Orbit Transfers Find Transition in Manifolds at Changes in Energy Levels (  Vs) Put Together Sample Trajectories for Input into Mystic

June 17, 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

June 17, :6 Resonant Orbit for C f (Inertial Frame) C = C f

June 17, :4 Resonant Orbit for Final Segment C = C f