JIMO Team Meeting June 17, 2004

Europa Orbiter Study Update

Rodney L. Anderson

Martin W. Lo

Rodney.Anderson@colorado.edu June 17, 2004 2

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

Rodney.Anderson@colorado.edu June 17, 2004 3

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

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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

V3:4

3:45:6

5:6 L2

V

Ci

Cm

Cf

C4

V3:4

Rodney.Anderson@colorado.edu June 17, 2004 5

Planar Europa Orbiter (PEO) Trajectory

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Planar Europa Orbiter (PEO) Trajectory

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Normalized Two-Body Period

Section Jacobi Constant

Initial Ci = 2.98460661333

Middle Cm = 2.99742497175

Final Cf = 3.00245952365

InitialSection

Ci

MiddleSection

Cm

FinalSection

Cf

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3:4 Resonant Orbit for Middle Segment

C = Cm

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5:6 Resonant Orbit for Middle Segment

C = Cm

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Poincaré Section at Cm w/ Resonant Orbits

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Poincaré Section at Cm w/ Resonant Orbits

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Poincaré Section at Cf w/ Resonant Orbits

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Poincaré Section at Cf w/ Resonant Orbits

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5:6 to Lyapunov Orbit

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~2:3 Resonance – Note Lobes

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Rodney.Anderson@colorado.edu June 17, 2004 17

ENDEND

Homoclinic Tangle Around Neptune 2:3 MMR

2:3 MMR

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~9:10 Resonance

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JIMO Team Meeting June 17, 2004

Stable Region of ~9:10 Resonance

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5:6 Resonant Orbit for Final Segment

C = Cf

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The PEO Follows the Invariant Manifolds

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The PEO Follows the Unstable Manifold of the 5:6 Resonant

Orbit

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Current Tasks Understand Resonant Orbit Transfers

Find Transition in Manifolds at Changes in Energy Levels (Vs)

Put Together Sample Trajectories for Input into Mystic

Rodney.Anderson@colorado.edu June 17, 2004 25

Poincaré Section at Cf w/ Resonant OrbitsStable Manifold of L2 Lyapunov Orbit

5:6 Resonant Orbit with Stable & Unstable Manifolds

3:4 Resonant Orbit & Unstable Manifold

Rodney.Anderson@colorado.edu June 17, 2004 26

5:6 Resonant Orbit for Cf (Inertial Frame)

C = Cf

Rodney.Anderson@colorado.edu June 17, 2004 27

3:4 Resonant Orbit for Final Segment

C = Cf