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

3. 1/21/03 JPL Lagrange Group Interplanetary Superhighway

4. Low Energy Transfer Applications MWL - 3 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics 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 L 1 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

5. Low Energy Transfer Applications MWL - 4 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Outline I: Objectif Lune Restricted 3 Body Problem Review Low Energy Transfers in Earth-Moon Space –Shoot the Moon –Lunar L 1 Gateway –Lunar Sample Return –Potential New Mission Orbits

6. Low Energy Transfer Applications MWL - 5 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics 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)

7. Low Energy Transfer Applications MWL - 6 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics First Halo Oribt Mission: ISEE3/ICE Goddard Space Flight Center GSFC: Farquhar, Dunham, Folta, et al Courtesy of D. Folta, GSFC

8. Low Energy Transfer Applications MWL - 7 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Current Libration Missions z WINDSOHOACE GENESISMAPJWST Goddard Space Flight Center Courtesy of D. Folta, GSFC

10. Low Energy Transfer Applications MWL - 9 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Genesis Mission Design, Comet Orbit  Martin LoJPL  Genesis Mission Design Manager  Kathleen Howell Purdue University  Department of Aeronautics and Astronautics  Brian BardenJPL, Purdue University  Roby WilsonJPL, Purdue University  Belinda MarchandPurdue University

11. Genesis Mission: Uses L 1, L 2 Heteroclinic Behavior to Collect & Return Solar Wind Samples to Earth UTTR 84 x 30 km September 8 th, 2004!

12. Low Energy Transfer Applications MWL - 11 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics The Genesis Trajectory L1L1 L2L2 Sun (size & position not to scale) 2 Lunar Orbit 1 3 4 5 Begin Science End Science 1. Transfer 2. Science 3. Return 4. Entry 5. Backup

13. Low Energy Transfer Applications MWL - 12 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Stable Manifold Transfer to Halo Orbit

14. Low Energy Transfer Applications MWL - 13 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Stable Manifold for Genesis Transfer

15. Low Energy Transfer Applications MWL - 14 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics More Background: Genesis Invariant Manifolds Provide Low Energy Transfers L 1 /L 2 Heteroclinic Connection Provide Day-Side Return Howell, Barden, Wilson, Lo L1 Lunar Orbit Halo Orbit

16. Lunar Orbit L1L1 L2L2 Halo Orbit Portal Earth 10/17/2001 Genesis Unstable Manifold: Unifies Many Different Types of Orbital Motions JPL Lagrange Group Earth Flyby & Capture Earth Return Via L 2 Lunar Capture Lunar Flyby Escape to Earth Trailer

17. Low Energy Transfer Applications MWL - 16 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Restricted Three Body Problem (RTBP) Newton, first studied the 3 Body Problem Rotating Frame Euler: L 1, L 2, L 3 Lagrange: L 4, L 5 Restricted Problem –3 rd body infinitessimal –Two primaries move in circles –Sun-Earth-Spacecraft, Sun-Jupiter-Comet, … Jacobi Integral

18. Low Energy Transfer Applications MWL - 17 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics 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?

19. Low Energy Transfer Applications MWL - 18 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics 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: LL 1, LL 2, … LL 5 –Sun-Earth-S/C: EL 1, EL 2, …

20. Low Energy Transfer Applications MWL - 19 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics (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 Projection of Energy Surfaces at 4 Levels xxxx

21. Low Energy Transfer Applications MWL - 20 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics From AU to au: Comets & Atomic Physics Atomic L 1 Comet’s Potential Energy Surface Comet L 1, L 2 Uncanny Similarity of Transport Theory in 3 Body Problem Rydberg Atom In Cross Fields Chemical Transition State Theory Jupiter Nucleus Jupiter Atomic Halo Orbit Atomic Potential Energy Surface

22. Low Energy Transfer Applications MWL - 21 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Dynamical Systems Theory

23. Low Energy Transfer Applications MWL - 22 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Pendulum Analogy for Conic Orbits The Sun-Earth-Spacecraft Three Body Problem Is Highly Nonlinear But Orbits Near Earth Are Stable Conics, Can Ignore Third Body Pendulum Is Also Nonlinear:  ’’ = - Sin  But for Small , Pendulum Motion is Stable and Acts Like Harmonic Oscillator:  ’’ = -  In Both Cases, Nonlinear Effects Are Not Noticeable, Linear Approximations Are Good

24. Low Energy Transfer Applications MWL - 23 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Pendulum’s Special “Return” Orbit Pendulum Manifolds Provide Special “Return” Orbit, Connects Inverted Pendulum Solution to Itself This Enables Travel Through Vast Regions of Space with Little or No Energy This Exploits Sensitivity of the Dynamics to Control the Orbit with Minimal Energy Similar to Genesis Earth Return Orbit Design

25. Low Energy Transfer Applications MWL - 24 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics 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 (MUST PASS THRU LYAPUNOV ORBIT) Non-Transit Orbits (May Transit After Several Revolutions) S: Sun Region J: Jupiter Region X: Exterior Region (Outside Jupiter’s Orbit) X S J

26. Low Energy Transfer Applications MWL - 25 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics 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)

27. Low Energy Transfer Applications MWL - 26 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Stable & Unstable Manifolds of Unstable Periodic Orbits MWL - 11 Unstable Periodic Orbits –Portals to the Network –Generate the Tubes Green Tube = Stable Manifold: Orbits Approach the L 1 Periodic Orbit, No  V Needed Red Tube = Unstable Manifold: Orbits Leave the L 1 Periodic Orbit Systematically Map Out Orbit Space Planet

28. Low Energy Transfer Applications MWL - 27 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Poincare Sections Orbits.... Poincare Map 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

29. Low Energy Transfer Applications MWL - 28 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Mapping the Space Using Cross Sections.. Orbits.. Poincare Map.

30. Low Energy Transfer Applications MWL - 29 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Manifolds Connect Solar System Legend  Comets Asteroids  Kuiper Belt Object L 1 IPS Orbits L 2 IPS Orbits Jupiter Saturn Uranus Neptune (Lo & Ross)

31. Low Energy Transfer Applications MWL - 30 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Map of the Orbital Families Near L 2 NORTHERN HALO ORBIT HORIZONTAL LYAPUNOV ORBIT LISSAJOUS ORBITS NORTHERN QUASIHALO ORBITS VERTICAL LYAPUNOV ORBIT SOUTHERN ORBITS Poincaré Section at L 2 JMS- 6 Orbits.. Poincare Map Simo, Gomez, Jorba, Llibre, Masdemont,

32. Courtesy of Josep Maria Mandella Tori of Lissajous Orbits Immersed in 3 Space

33. Low Energy Transfer Applications MWL - 32 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Manifolds Tunneling Through Phase Space Cross Section of Tube Intersection Partitions Global Behavior –Yellow Region Tunnels Through from X Through J to S Regions –Green Circle: J to S Region, Red Circle: X to J Region –Genesis-Type Trajectory Between L 2 and L 1 Halo Orbits (Heteroclinic)

34. Low Energy Transfer Applications MWL - 33 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics

35. Low Energy Transfer Applications MWL - 34 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics

36. Low Energy Transfer Applications MWL - 35 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Invariant Manifolds & Jupiter Comets Transport Between 3:2 and 2:3 resonances –Via heteroclinic orbits between orbits around JL 1, JL 2 –Temporary Capture (Ballistic Capture) Koon, Lo, Marsden, Ross, 2000 Howell, Marchand, Lo, 2000 Belbruno, B. Marsden, 1997: WSB Theory

37. Low Energy Transfer Applications MWL - 36 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Shoot the Moon! RESCUE MISSION 911: Hiten, HAC, … Discover, June 1999

38. Low Energy Transfer Applications MWL - 37 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Shoot the Moon Shadowing Unstable Manifold of Sun-Earth L2 Lyapunov Orbit Shadowing Stable Manifold of Sun- Earth L2 Lyapunov Orbit to Leave Earth Earth Lunar Orbit Maneuver to Transfer to Stable Manifold of Earth- Moon L2 Lyapunov Orbit Ballistic Lunar Capture Shoot the Moon: Low Energy Transfer & Ballistic Capture

39. 7/5/04 JPL Lagrange Group Gateway Module LL 1 Moon Lunar L 1 Entry Portal Lunar Orbit LL 2 Lunar L 2 Exit Portal Lunar L 1 Gateway Station

40. Low Energy Transfer Applications MWL - 39 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Problem: Human Service to Libration Missions ISSUE: 3 Months Transfers to EL 2 Too Long for Humans Short Transfers Too Difficult Infrastructure Too Expensive STA-103 astronauts replaced gyros needed for orientation of the Hubble Space Telescope. JSC TPF @Earth L 2

41. Low Energy Transfer Applications MWL - 40 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics

42. Low Energy Transfer Applications MWL - 41 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Lunar L 1 to Earth L 2 Transfer Build Instruments & S/C Lunar L 1 Station Transfer S/C from L 1 to Earth-L 2 LIO (Libration Oribit) Service S/C at Earth L 2 LIO from Lunar L 1 Gateway Hub L1L1  Lunar L 2  Earth L 2 Lunar Rotating FrameEarth Rotating Frame Lunar

43. Low Energy Transfer Applications MWL - 42 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Solution: Human Servicing at Lunar L 1 Gatewy Build Instruments & S/C Lunar L 1 Gateway for EL 2 Service S/C at Earth L 2 from Lunar L 1 Gateway Module EARTH EARTH L 2 HALO ORBIT MOON LUNAR L 1 HALO ORBIT LUNAR L 2 HALO ORBIT LUNAR L 1 GATEWAY ARTIST CONCEPTION

44. Low Energy Transfer Applications MWL - 43 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics IPS in Earth’s Neighborhood Portals/Interchange =Halo Orbits, Unstable Orbits Lanes =Invariant Manifold Tubes EARTH EARTH L 2 HALO ORBIT MOON LUNAR L 1 HALO ORBIT LUNAR L 2 HALO ORBIT LUNAR L 1 GATEWAY ARTIST CONCEPTION

45. Low Energy Transfer Applications MWL - 44 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Gateway Architecture (JSC) Crew departs from and returns to ISS L 1 Gateway GPS Constellation Lunar Lander Crew Transfer Vehicle Transports crew between ISS and Gateway Nominal aerocapture to ISS, or direct Earth return contingency capability “Earth’s Neighborhood” Lunar Habitat L 1 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 Source: James Geffre, JSC

46. Low Energy Transfer Applications MWL - 45 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics Gateway Configurations (JSC) LEO, Transit, L1 Stand-by Configuration Telescope Operations ConfigurationLunar Operations Configuration Launch Configuration Source: James Geffre, JSC

47. 8/6/2002 Goto LSR Vugraphs JPL Caltech Lunar Orbit Lunar Sample Return via the Interplanetary Supherhighway EL 1 Moon Earth Moon LL 2 Lander Separation Lander Orbiter EL 2 Lander Return LL 2 Stable Manifold Insertion Lander Return

48. Low Energy Transfer Applications MWL - 47 Martin.Lo@jpl.nasa.gov JPL 2004 Summer Workshop on Advanced Topics in Astrodynamics New Mission Concepts & Orbits