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Low Energy Transfers in the Solar System: Applications I

Low Energy Transfers in the Solar System: Applications I Objectif Lune ( Tintin ). Martin.Lo @ jpl.nasa.gov. 7/5/2004. 2004 Summer Workshop on Advanced Topics in Astrodynamics. Interplanetary Superhighway. JPL Lagrange Group. 1/21/03. Outline.

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Low Energy Transfers in the Solar System: Applications I

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  1. Low Energy Transfers in the Solar System: Applications I Objectif Lune (Tintin) Martin.Lo@ jpl.nasa.gov 7/5/2004 2004 Summer Workshop on Advanced Topics in Astrodynamics

  2. Interplanetary Superhighway JPL Lagrange Group 1/21/03

  3. Outline • Restricted 3 Body Problem Review • Interactive Shooting Method • Weak Stability Boundary Method (Tuesday) • Dynamical System Methods • Goal and Philosophy • Low Energy Transfers in Earth-Moon Space • Shoot the Moon • Lunar L1 Gateway • Lunar Sample Return • New Mission Concepts & Orbits • Low Energy Transfers Between Galilean Moons • Petit Grand Tour • Jupiter Icy Moons Tour • Anatomy of a Flyby

  4. Outline I: Objectif Lune • Restricted 3 Body Problem Review • Low Energy Transfers in Earth-Moon Space • Shoot the Moon • Lunar L1 Gateway • Lunar Sample Return • Potential New Mission Orbits

  5. Some Historical Notes • Classical 3-Body Problem Newton, Euler, Lagrange, Jacobi , Moulton • Dynamical Systems Theory • Poincaré, Birkhoff, Moser, Conley, McGehee • Development of Libration Missions • Colombo, Farquhar, Dunham, Folta • Dynamical Systems Theory for Libration Missions (mid 1980’s) • Simó, Llibre, Goméz, Masdemont, Jorba, Martinez • Weak Stability Boundary • Miller & Belbruno (1990) • Resonant Transport via Invariant Manifolds • Bolt & Meiss (1995), Schroer & Ott (1996) • Mission Design Using Invariant Manifolds • Howell, Lo (1996)

  6. Goddard Space Flight Center First Halo Oribt Mission: ISEE3/ICE GSFC: Farquhar, Dunham, Folta, et al Courtesy of D. Folta, GSFC

  7. Goddard Space Flight Center Current Libration Missions • z WIND SOHO ACE MAP GENESIS JWST Courtesy of D. Folta, GSFC

  8. Genesis Mission Design, Comet Orbit • Martin Lo JPL • Genesis Mission Design Manager • Kathleen Howell Purdue University • Department of Aeronautics and Astronautics • Brian Barden JPL, Purdue University • Roby Wilson JPL, Purdue University • Belinda Marchand Purdue University

  9. UTTR84 x 30 km September 8th, 2004! Genesis Mission: Uses L1, L2 Heteroclinic Behavior to Collect & Return Solar Wind Samples to Earth

  10. 1. Transfer 2. Science 3. Return 4. Entry 5. Backup The Genesis Trajectory Begin Science End Science Lunar Orbit 2 3 1 L2 L1 Sun(size & position not to scale) 5 4

  11. Stable Manifold Transfer to Halo Orbit

  12. Stable Manifold for Genesis Transfer

  13. Genesis Unstable Manifold: Unifies Many Different Types of Orbital Motions Lunar Capture Lunar Orbit L2 Earth L1 Halo Orbit Portal Escape to Earth Trailer Lunar Flyby JPL Lagrange Group 10/17/2001 Earth Flyby & Capture Earth Return Via L2

  14. Restricted Three Body Problem (RTBP) • Newton, first studied the 3 Body Problem • Rotating Frame • Euler: L1, L2, L3 • Lagrange: L4, L5 • Restricted Problem • 3rd body infinitessimal • Two primaries move in circles • Sun-Earth-Spacecraft, Sun-Jupiter-Comet, … • Jacobi Integral

  15. Restricted Three Body Problem • Simplified model with energy integral • Useful for analytic studies • Symmetries avoid phasing and timing problems • Still non-integrable, i.e. no orbital elements • Solutions requires numerical integration • Key Problem: How to replace orbital elements? • Model sufficiently faithful for mission design • Can “move” solutions into full JPL ephemeris models • Key Problem: How to move solutions between models?

  16. Coupled Restricted Three Body Problem • Simplified Model of Solar System • More complex than Copernican coupled “two body problems” • Example: Sun-Earth-Moon-Spacecraft System • Earth-Moon-S/C: LL1, LL2, … LL5 • Sun-Earth-S/C: EL1, EL2, …

  17. x x x x Projection of Energy Surfaces at 4 Levels • (a) Planet, Sun, eXterior regions separated by grey • forbidden region • (b) L1 energy level opens regions between P and S • (c) L2 energy level opens regions between P, S, and X • (d) L4 and L5 regmain trapped in grey region

  18. Comet L1 , L2 Comet’s Potential Energy Surface From AU to au: Comets & Atomic Physics • Uncanny Similarity of Transport Theory in 3 Body Problem • Rydberg Atom In Cross Fields • Chemical Transition State Theory Atomic Halo Orbit • Nucleus Atomic L1 • Jupiter Atomic Potential Energy Surface • Jupiter

  19. Dynamical Systems Theory

  20. Orbital Zoology Near the Lagrange Points • Four Families of Orbits, Conley [1968], McGehee [1969], Ref. Paper • Periodic Orbit (Planar Lyapunov) • Spiral Asymptotic Orbit (Stable Manifold Pictured) • Transit Orbits • Non-Transit Orbits (May Transit After Several Revolutions)

  21. . . . . Poincare Map Orbits Poincare Sections • Invariant Manifold Structures in Higher Dimensions Too Complex • Poincare Sections Reduce the Dimensions by 1 • Turns Differential Equations into Maps in Phase Space • Periodic Orbits Become Finite Number of Points • Chaotic Orbits Cover Large Portions of Phase Space • Reveals Resonance Structure of Phase Space • Show the Existence of Chaos in the System

  22. . . . . Orbits Poincare Map . Mapping the Space Using Cross Sections

  23. Manifolds Connect Solar System Legend  Comets  Asteroids  Kuiper Belt Object L1 IPS Orbits  L2 IPS Orbits (Lo & Ross) Jupiter Saturn Uranus Neptune

  24. Invariant Manifolds & Jupiter Comets • Transport Between 3:2 and 2:3 resonances • Via heteroclinic orbits between orbits around JL1, JL2 • Temporary Capture (Ballistic Capture) Koon, Lo, Marsden, Ross, 2000 Howell, Marchand, Lo, 2000 Belbruno, B. Marsden, 1997: WSB Theory

  25. Shoot the Moon! RESCUE MISSION 911: Hiten, HAC, … Discover, June 1999

  26. Maneuver to Transfer to Stable Manifold of Earth-Moon L2 Lyapunov Orbit Lunar Orbit Shadowing Stable Manifold of Sun-Earth L2 Lyapunov Orbit to Leave Earth Earth Ballistic Lunar Capture Shadowing Unstable Manifold of Sun-Earth L2 Lyapunov Orbit Shoot the Moon: Low Energy Transfer & Ballistic Capture Shoot the Moon

  27. Lunar L2 Exit Portal LL2 Moon Lunar Orbit LL1 Lunar L1 Entry Portal Gateway Module Lunar L1 Gateway Station JPL Lagrange Group 7/5/04

  28. Problem: Human Service to Libration Missions • ISSUE: 3 Months Transfers to EL2 Too Long for Humans • Short Transfers Too Difficult • Infrastructure Too Expensive TPF @Earth L2 STA-103 astronauts replaced gyros needed for orientation of the Hubble Space Telescope. JSC

  29. . L1 . Lunar L2 . Earth L2 Lunar Lunar Rotating Frame Earth Rotating Frame Lunar L1 to Earth L2 Transfer • Build Instruments & S/C Lunar L1 Station • Transfer S/C from L1 to Earth-L2 LIO (Libration Oribit) • Service S/C at Earth L2 LIO from Lunar L1 Gateway Hub

  30. LUNAR L1 GATEWAY EARTH L2 HALO ORBIT MOON LUNAR L1 HALO ORBIT LUNAR L2 HALO ORBIT EARTH Solution: Human Servicing at Lunar L1 Gatewy • Build Instruments & S/C Lunar L1 Gateway for EL2 • Service S/C at Earth L2 from Lunar L1 Gateway Module ARTIST CONCEPTION

  31. LUNAR L1 GATEWAY EARTH L2 HALO ORBIT MOON LUNAR L1 HALO ORBIT LUNAR L2 HALO ORBIT EARTH IPS in Earth’s Neighborhood • Portals/Interchange = Halo Orbits, Unstable Orbits • Lanes = Invariant Manifold Tubes ARTIST CONCEPTION

  32. Gateway Architecture (JSC) “Earth’s Neighborhood” GPS Constellation Source: James Geffre, JSC Crew departs from and returns to ISS L1 Gateway Lunar Habitat Lunar Lander Crew Transfer Vehicle • L1 Gateway • “Gateway” to the Lunar surface • Outpost for staging missions to Moon, Mars and telescope construction • Crew safe haven • Lunar Lander • Transports crew between Gateway and Lunar Surface • 9 day mission (3 days on Lunar surface) • Lunar Habitat • 30-day surface habitat placed at Lunar South Pole • Enables extended-duration surface exploration and ops studies • Crew Transfer Vehicle • Transports crew between ISS and Gateway • Nominal aerocapture to ISS, or direct Earth return contingency capability

  33. Gateway Configurations (JSC) Source: James Geffre, JSC Launch Configuration LEO, Transit, L1 Stand-by Configuration Lunar Operations Configuration Telescope Operations Configuration

  34. Lunar Sample Return via the Interplanetary Supherhighway EL2 Lander Lander Return Moon Earth Moon LL2 Lander Return LL2 Stable Manifold Insertion Lander Separation Orbiter EL1 Lunar Orbit Goto LSR Vugraphs JPL Caltech 8/6/2002

  35. New Mission Concepts & Orbits

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