1. Lunar Sample Return via the Interplanetary Supherhighway
EL1
Moon
Earth
LL2
Lander
Separation
Orbiter
EL2
Return
LL2 Stable Manifold Insertion
Lunar Orbit
AIAA/AAS Astrodynamics Specilaist Conference
8/6/2002
JPL Caltech

2. Agenda Lunar Sample Return Mission Overview Baseline Mission Scenario
Lunar L2 Case (LL2)
Mission Performance Comparison

3. Mission Overview Goal: Collect and Return Lunar Samples to Earth
Aitken Basin on Backside of Moon, (180°, -57°)
Launch Combo, the Combined Flight System
Communications Orbiter
Desire Continuous Communications Coverage Between Earth and Lander Module
Lander/Return Module
Sample Collection in Sun, ~2 Weeks Available
Return to Earth (non-specific target)

4. Key Results Metric: Total DV of Trade Time for Total DV
Combo
Lander/Return Module
Communications Orbiter
Trade Time for Total DV
Best Case 1446 m/s Less than Conic Case
Baseline 1020 m/s Less than Conic Case
Case
DT (days)
Total DV (m/s)
-Conic DV (m/s)
LL2
146
8586
1020
LL1
151
8663
943
EL1
553
8160
1446
Conic 23
9606

5. Interplanetary Superhighway in the Earth’s Neighborhood
Collection of Invariant Manifolds of Quasiperiodic Orbits in the Solar System
Coupled Three Body Systems
EARTH
EARTH L2 HALO ORBIT
MOON
LUNAR L1 HALO ORBIT
LUNAR L2 HALO ORBIT
LUNAR L1 GATEWAY

7. Key Concepts Used in the Paper
Lunar L2 Halo Link Earth to Lunar Backside
Colombo (L1)
Farquhar: Halo Orbits
Dynamical Systems Theory
Poincaré, Connelly, McGehee
Gomez, Jorba, Llibre, Martinez, Masdemont, Simó
Hiten-Like Transfers
Belbruno, Miller
Lo, Ross
Koon, Lo, Marsden, Ross
Heteroclinic Connection Theory
Barden, Howell
I will briefly summarize the development of the key ideas we used in this paper.
Colombo in 61 proposed putting a satellite at LL1.
Later, Farquhar proposed using a “halo orbit” around LL2 for communications to the backside of the Moon.
Around the same time, Charles Connely and Dick McGehee figured out the dynamics around L1 and L2 using invariant manifold theroy for the planar RTBP. Connelly even proposed a lunar mission with a trajectories designed with the invariant manifolds of the lunar lyapunov orbits.
In 1978, the first halo mission to Earth’s L1, ISEE3, was launched and successfully demonstrated that libration missions can be flown. Some of the mission design people who contributed to its success are: Dunham, Folta, Richard, Carey, and Byrnes (GMASS).
In the early 1980’s, Carles Simo’s group started working on this problem from a different point of view: using Dynamical Systems Theory, which Poincare developed in his celebrated study of the Three Body Problem.
In the late 1980’s Belbruno developed his “Weak Stability Boundary” theory for low-energy lunar capture orbits within the three body problem. When the Muses-B mission had a failure, Jim Miller and Belbruno worked out a trajectory which helped the salvage Muses-B to become the successful Hiten mission. But invariant manifolds of libration orbits were not used in their computation of this orbit.
I was convinced, like many others within the community, that the Weak Stability Boundary must be explanable using the invariant manifolds of libration orbits. Moreover, I wondered if these manifolds between planets intersected one another. After all, these two questions are addressing really the same problem: the intersection of the invariant manifolds of libration orbits within different three-body systems.
I worked with my student, Shane Ross, to answere these two questions by looking at the simplest manifolds: those of the L1 and L2 themselves. We quickly discovered that the manifolds of all of the planet’s L1 and L2 intersected one another in configuration space, except between Earth and Mars. This was true of the Galilean satellites and the Earth Moon system. Moreover, we discovered that some of the the quizotic motion of comets, asteroids, dust were goverened by these manifolds.
In the 1990’s, Howell and Barden started computing connecting orbits between halo and lissajous orbits at L1 and L2, which we call heteroclinic orbits. But, I think most of their solutions required some maneuvers. This is an insignificant point from the mission design point of view.
In order to understand the dynamics, I starting working with Marsden and Koon to explain mathematically if L1 and L2 are really heteroclinically connected? How to explain the capture phenomenon? How to explain the Hiten-transfer? Working together, we studied the work of the Barcelona School, the Connelly School which answered these two fundamental question.
In the Lunar Sample Return Mission, we have made use of almost all of these ideas to produce the trajectories in this paper.
[5] Colombo, G. “The Stabilization of an Aritificial Satellite at the Inferior Conjunction Point of the Earth-Moon System,” Smithsonian Astrophysical Observatory Special Report, No. 80, Nov

8. JPL LTool Team Martin Lo Section 312 Task Manager
Larry Romans Section 335
Cognizant S/W Engineer (Marthematica Developer)
George Hockney Section 367
S/W Architecture & Sys Engineer
Brian Barden Section 312
Trajectory Design & Algorithms
Min-Kun Chung Section 312
Astrodynamics Tools
James Evans Section 368
Infrastructure S/W, Visualization Tools

9. Case LL2 : 1020 m/s Cheaper Than Conic
BASELINE CASE
• LL1 •
LL2
Moon
Earth
EL2
EL1
Case
DT (day)
Total DV (m/s)
LL2
146
8586
LL1
151
8663
EL1
553
8160
Conic 23
9606

10. Case LL1 : 943 m/s Cheaper Than Conic•
LL2
Moon
Earth
EL2
EL1
Case
DT (day)
Total DV (m/s)
LL2
146
8586
LL1
151
8663
EL1
553
8160
Conic 23
9606

11. Case EL1 : 1446 m/s Cheaper Than Conic
DT (day)
Total DV (m/s)
LL2
146
8586
LL1
151
8663
EL1
553
8160
Conic 23
9606
• LL1 •
LL2
Moon
Earth
EL2
EL1

12. LL2 Case: Direct Transfer to LL2 Lissajous Orbit
EL1
Earth
Moon
EL2
Lander
Return
Lunar Transfer
LL2 Lissajous Orbit
Lunar Landing
Lander Return

13. LL2 Case: Trans-Lunar Phase
Trans-Lunar Injection
3122 m/s at 6/14/09
Earth
6/14/90
Lander
Return
LL1
LL2
Moon
LL2 Insertion
570 m/s at 6/18/09
Lander Return
11/7/90

14. LL2 Stable Manifold Insertion Lander LL2 Departure: 35 m/s at 7/7/09
LL2 Case: Lunar Phase
LL2 Stable Manifold Insertion
LL1
LL2
Moon
Trans-Lunar Orbit
Lander Return
Lander Orbit
Orbiter
Lander LL2 Departure: 35 m/s at 7/7/09
Lander Touchdown:
2335 m/s at 7/17/09
Lander Return:
2424 m/s
at 7/28/09

15. LL2 Case: Earth Moon Rotating Frame
EL1
Earth
Moon
EL2
Lander
Return

16. LL2 Case: EME2000 Inertial Frame
Lander
Return
Earth
Orbiter
LL2
LL1

17. LL2 Case: Sun-Earth Rotating Frame
Lander
Return
Earth
Orbiter
EL2
LL2
LL1

18. LL2 Case: Mission Sequence & DV’s
Date (2009)
DT (days)
Combo DV (m/s)
Lander DV (m/s)
Orbiter DV (m/s)
Translunar Injection
6/14
3122
Manifold Insertion
6/18 4
570
LL2 Halo Arrival
6/25 11
Lander LL2 Departure
7/7 23 35
Lander Landing
7/17 33
2335
Lander Liftoff
7/28 44
2424
Earth Return
11/7
146
Navigation 25 50
DV Total
3717
4844

19. Heteroclinic Connection
LL1 Case: LL2 via LL1
Insert into LL1 Stable Manifold
Heteroclinic Connection for Comm. Orbiter
Lunar Landing from LL1
Moon
LL1
LL2
Heteroclinic Connection
Moon
LL1
Lander Departs for Moon: 95 m/s
Landing: 2330 m/s
8.5 days later

20. LL1 Case: Mission Sequence & DV’s
Date (2009)
DT (days)
Combo DV (m/s)
Lander DV (m/s)
Orbiter DV (m/s)
Translunar Injection
6/9
3100
LL1 Halo Insertion
6/14 5
600
Orbiter LL1 Departure
6/19 10 14
Orbiter LL2 Arrival
7/7 28
Lander LL1 Departure
7/10 31 95
Lander Landing
7/16 37
2330
Lander Liftoff
7/28 49
2424
Earth Return
11/7
151
Navigation 25 50
DV Total
3725
4899 39
LL2 Case

21. FAIR/DART Trajctory EL1 Case: LL2 via Earth L1
Reduce LL2 LOI DV: Launch to EL1 Fall to LL2
Once There, Follows LL2 Case
EL1 LOI 60 m/s
LL1 LOI 13.2 m/s
FAIR/DART Trajctory
Earth Launch 3193 m/s
EL1
EL2

22. EL1 Case: Mission Sequence & DV’s
Date (2009)
DT (days)
Combo DV (m/s)
Lander DV (m/s)
Orbiter DV (m/s)
Earth Launch
5/30/08
3193
EL1 Insertion
8/29/08 91 60
LL2 Halo Arrival
6/25
391 13
Lander LL2 Departure
7/7
403 35
Lander Landing
7/17
413
2335
Lander Liftoff
7/28
424
2424
Earth Return
11/7
553
Navigation 25 50
DV Total
3291
4844
Reduction by Order of Magnitude
LL2 Case

23. Conic Case (S. Williams, JPL)
Conic Trans-Lunar Orbit
Lander in 100-km Lunar Parking Orbit
Orbiter in Highly Elliptical Orbit
100x8700 km, 12 hr Period

24. Conic Case (S. Williams, JPL)
Mission Sequence
Date (2009)
DT (days)
Combo DV (m/s)
Lander DV (m/s)
Orbiter DV (m/s)
Translunar Injection
7/16
3100
Separation
7/17 1
Lunar Orbit Insertion
7/20
4.5
979
481
Lander Apoapsis Burn
4.54 23
Lander Landing
4.58
1703
Lander Liftoff
8/3
18.5
3220
Earth Return
8/8
Navigation 25 50
DV Total
3125
5975
506

25. Libration Point Mission Lowers DV
Saves Up to 1446 m/s!
Provides Continuous Communication
Trade DV for Time
Case
DT (days)
ComboDV (m/s)
Lander DV (m/s)
Orbiter DV (m/s)
Total DV (m/s)
-Conic DV (m/s)
LL2
146
3717
4844 25
8586
1020
LL1
151
3725
4899 39
8663
943
EL1
553
3291
8160
1446
Conic 23
3125
5975
506
9606

26. References
Barden, Howell, Formation Flying in the Vicinity of Libration Point Orbits, AAS , Monterey, CA, 2/98
Barden, Howell, Dynamical Issues Associated with Relative Configurations of Multiple Spacecraft Near the Sun-Earth/Moon L1 Point, AAS , Girdwood, Alaska, 8/99
Gomez, Masdemon, Simo, Lissajous Orbits Around Halo Orbits, AAS , Huntsville, Alabama, 2/97
Howell, Barden, Lo, Applications of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission, JAS 45(2), April 1997,
Howell, Marchand, Lo, The Temporary Capture of Short-Period Jupiter Family Comets from the Perspective of Dynamical Systems, AAS , Clearwater, FL, 1/2000
Koon, Lo, Marsden, Ross, Heteroclinic Connections between Lyapunov Orbits and Resonance Transitions in Celestial Mechanics, to appear in Chaos

27. References
Koon, Lo, Marsden, Ross, The Genesis Trajectory and Heteroclinic Connections, AAS99-451, Girdwood, Alaska, August, 1999
Koon, Lo, Marsden, Ross, Shoot the Moon, AAS00-166, Clearwater, Florida, January, 2000
Lo, The InterPlanetary Superhighway and the Origins Program, IEEE Aerospace2002 Conference, Big Sky, MT, February, 2002
Lo et al., Genesis Mission Design, AIAA , Boston, MA, August, 1998
Serban, Koon, Lo, Marsden, Petzold, Ross, Wilson, Halo Orbit Correction Maneuvers Using Optimal Control, submitted to Automatica, April, 2000
Scheeres, Vinh, Dynamis and Control of Relative Motion in an Unstable Orbit, AIAA Paper , August, 2000