Europa Orbiter Study Update
Rodney L. Anderson
Martin W. Lo
JIMO Team Meeting
June 17, 2004
Overview
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
The Planar Europa Orbiter Trajectory
Resonant Orbits
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Transition Between Resonances
Energy Changes (Vs)
Europa Approach
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
5:6 Unstable Orbit (Compared at Different Energies)
Stable Manifold of L2 Lyapunov Orbit
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June 17, 2004
2
Planar Europa Orbiter Trajectory

Europa Orbiter

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Planar Restricted Problem
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Low Thrust Initially Too Difficult
Impulsive Case More Easily Understood
Focus on Understanding Resonance Transfers & Capture
Theoretically Simpler
More Tools Available
Achieved Using LTool Differential Corrector
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June 17, 2004
3
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
3:4
Ci
V
3:4
5:6
3:4
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Cm
V
5:6
L2
Cf
V
C4
June 17, 2004
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Planar Europa Orbiter (PEO) Trajectory
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June 17, 2004
5
Planar Europa Orbiter (PEO) Trajectory
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June 17, 2004
6
Normalized Two-Body Period
Initial
Section
Ci
Middle
Section
Cm
Final
Section
Cf
Section
Jacobi Constant
Initial
Ci = 2.98460661333
Middle
Cm = 2.99742497175
Final
Cf = 3.00245952365
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June 17, 2004
7
3:4 Resonant Orbit for Middle Segment
C = Cm
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June 17, 2004
8
5:6 Resonant Orbit for Middle Segment
C = Cm
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June 17, 2004
9
Poincaré Section at Cm w/ Resonant Orbits
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June 17, 2004
10
Poincaré Section at Cm w/ Resonant Orbits
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June 17, 2004
11
Poincaré Section at Cf w/ Resonant Orbits
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June 17, 2004
12
Poincaré Section at Cf w/ Resonant Orbits
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June 17, 2004
13
5:6 to Lyapunov Orbit
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June 17, 2004
14
~2:3 Resonance – Note Lobes
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June 17, 2004
15
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June 17, 2004
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END
Homoclinic Tangle Around
Neptune 2:3 MMR
END
2:3 MMR
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June 17, 2004
17
~9:10 Resonance
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June 17, 2004
18
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June 17, 2004
19
Stable Region of ~9:10 Resonance
JIMO Team Meeting
June 17, 2004
5:6 Resonant Orbit for Final Segment
C = Cf
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June 17, 2004
21
The PEO Follows the Invariant Manifolds
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June 17, 2004
22
The PEO Follows the Unstable Manifold
of the 5:6 Resonant Orbit
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June 17, 2004
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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
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June 17, 2004
24
Poincaré Section at Cf w/ Resonant Orbits
Stable Manifold of
L2 Lyapunov Orbit
5:6 Resonant Orbit
with Stable &
Unstable Manifolds
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3:4 Resonant Orbit
& Unstable Manifold
June 17, 2004
25
5:6 Resonant Orbit for Cf (Inertial Frame)
C = Cf
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June 17, 2004
26
3:4 Resonant Orbit for Final Segment
C = Cf
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June 17, 2004
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