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 Martin.Lo@jpl.nasa.gov Min-Kun.Chung@jpl.nasa.gov 8/6/2002 JPL Caltech

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

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)

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

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

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. 1961.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

References Barden, Howell, Formation Flying in the Vicinity of Libration Point Orbits, AAS 98-169, Monterey, CA, 2/98 Barden, Howell, Dynamical Issues Associated with Relative Configurations of Multiple Spacecraft Near the Sun-Earth/Moon L1 Point, AAS 99-450, Girdwood, Alaska, 8/99 Gomez, Masdemon, Simo, Lissajous Orbits Around Halo Orbits, AAS 97-106, 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, 161-178 Howell, Marchand, Lo, The Temporary Capture of Short-Period Jupiter Family Comets from the Perspective of Dynamical Systems, AAS 00-155, Clearwater, FL, 1/2000 Koon, Lo, Marsden, Ross, Heteroclinic Connections between Lyapunov Orbits and Resonance Transitions in Celestial Mechanics, to appear in Chaos

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 98-4468, 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 2000-4135, August, 2000