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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. - PowerPoint PPT Presentation
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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
1/21/03 JPL Lagrange Group
Interplanetary Superhighway
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 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
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 L1 Gateway
– Lunar Sample Return
– Potential New Mission Orbits
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)
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
LOGO.049
Goddard Space Flight Center
GSFC: Farquhar, Dunham, Folta, et al
Courtesy of D. Folta, GSFC
Low Energy Transfer Applications
MWL - 7
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
Current Libration Missions
• z
WIND SOHO ACE
GENESISMAP JWST
LOGO.049
Goddard Space Flight Center
Courtesy of D. Folta, GSFC
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 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
Genesis Mission: Uses LGenesis Mission: Uses L11, L, L22 Heteroclinic Heteroclinic Behavior to Collect & Return Solar Wind Behavior to Collect & Return Solar Wind
Samples to Earth Samples to Earth UTTR 84 x 30 km
September 8th, 2004!
Low Energy Transfer Applications
MWL - 11
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
The Genesis Trajectory
L1L2Sun (size &
position not to scale)
2Lunar Orbit
1 3
4 5
Begin Science
End Science
1. Transfer 2. Science3. Return4. Entry5. Backup
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
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
Lunar Orbit
L1
L2
Halo OrbitPortal
Earth
10/17/2001
Genesis Unstable Manifold: Unifies Many Different Types
of Orbital Motions
JPL Lagrange Group
Earth Flyby & Capture Earth Return
Via L2
Lunar Capture
Lunar Flyby Escape to Earth Trailer
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: L1, L2, L3
• Lagrange: L4, L5
• Restricted Problem– 3rd body infinitessimal– Two primaries move in
circles– Sun-Earth-Spacecraft,
Sun-Jupiter-Comet, …
• Jacobi Integral
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?
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: LL1, LL2, … LL5
– Sun-Earth-S/C: EL1, EL2, …
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
x x x x
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 L1
Comet’s Potential Energy Surface
Comet L1 , L2
• 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
Low Energy Transfer Applications
MWL - 21
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
Dynamical Systems Theory
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)
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
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
..
PoincareMap
.
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
L1 IPS Orbits
L2 IPS Orbits
Jupiter
Saturn
Uranus
Neptune
(Lo & Ross)
Low Energy Transfer Applications
MWL - 33
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
Low Energy Transfer Applications
MWL - 34
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
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 JL1, JL2
– Temporary Capture (Ballistic Capture)Koon, Lo, Marsden, Ross, 2000
Howell, Marchand, Lo, 2000Belbruno, B. Marsden, 1997: WSB Theory
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
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
7/5/04 JPL Lagrange Group
Gateway Module
LL1
Moon
Lunar L1 Entry Portal
Lunar Orbit
LL2Lunar L2 Exit Portal
Lunar L1 Gateway Station
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 EL2 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 L2
Low Energy Transfer Applications
MWL - 40
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
Low Energy Transfer Applications
MWL - 41
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
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
L1
Lunar L2
Earth
L2
Lunar Rotating Frame Earth Rotating Frame
Lunar
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 L1 Gatewy
• Build Instruments & S/C Lunar L1 Gateway for EL2
• Service S/C at Earth L2 from Lunar L1 Gateway Module
EARTH
EARTH L2 HALO ORBIT
MOON
LUNAR L1 HALO ORBIT
LUNAR L2 HALO ORBIT
LUNAR L1 GATEWAY
ARTIST CONCEPTION
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 L2 HALO ORBIT
MOON
LUNAR L1 HALO ORBIT
LUNAR L2 HALO ORBIT
LUNAR L1 GATEWAY
ARTIST CONCEPTION
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 ISSL1 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
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
Source: James Geffre, JSC
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
8/6/2002
Goto LSR Vugraphs
JPL Caltech
Lunar Orbit
Lunar Sample Return via the Interplanetary
Supherhighway
EL1
Moon
Earth
Moon
LL2
LanderSeparation
Lander
Orbiter
EL2
LanderReturn
LL2 Stable Manifold Insertion
LanderReturn
Low Energy Transfer Applications
MWL - 47
Martin.Lo@jpl.nasa.gov
JPL
2004 Summer Workshop on Advanced Topics in Astrodynamics
New Mission Concepts & Orbits
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