low energy transfers in the solar system: applications i

Low Energy Transfer Applications

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Martin.Lo@jpl.nasa.gov

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

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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

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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

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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)

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First Halo Oribt Mission: ISEE3/ICE

LOGO.049

Goddard Space Flight Center

GSFC: Farquhar, Dunham, Folta, et al

Courtesy of D. Folta, GSFC

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Current Libration Missions

WIND SOHO ACE

GENESISMAP JWST

LOGO.049

Goddard Space Flight Center

Courtesy of D. Folta, GSFC

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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!

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The Genesis Trajectory

L1L2Sun (size &

position not to scale)

2Lunar Orbit

Begin Science

End Science

1. Transfer 2. Science3. Return4. Entry5. Backup

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Stable Manifold Transfer to Halo Orbit

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Stable Manifold for Genesis Transfer

Lunar Orbit

Halo OrbitPortal

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

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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

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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?

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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, …

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• (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

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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

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Dynamical Systems Theory

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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)

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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

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Mapping the Space Using Cross Sections

.Orbits

PoincareMap

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Manifolds Connect Solar System

Legend

Comets

Asteroids

Kuiper Belt

Object

L1 IPS Orbits

L2 IPS Orbits

Jupiter

Saturn

Uranus

Neptune

(Lo & Ross)

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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

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Shoot the Moon!

RESCUE MISSION 911:

Hiten, HAC, …

Discover, June 1999

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Shoot the Moon

Shadowing Unstable Manifold of

Sun-Earth L2 Lyapunov Orbit

Shadowing Stable Manifold of Sun-

Earth L2 Lyapunov Orbit to Leave 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

Lunar L1 Entry Portal

Lunar Orbit

LL2Lunar L2 Exit Portal

Lunar L1 Gateway Station

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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.

TPF @Earth L2

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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

Lunar L2

Lunar Rotating Frame Earth Rotating Frame

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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 L2 HALO ORBIT

LUNAR L1 HALO ORBIT

LUNAR L2 HALO ORBIT

LUNAR L1 GATEWAY

ARTIST CONCEPTION

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IPS in Earth’s Neighborhood

• Portals/Interchange = Halo Orbits, Unstable Orbits

• Lanes = Invariant Manifold Tubes

EARTH L2 HALO ORBIT

LUNAR L1 HALO ORBIT

LUNAR L2 HALO ORBIT

LUNAR L1 GATEWAY

ARTIST CONCEPTION

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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

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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

LanderSeparation

Lander

Orbiter

LanderReturn

LL2 Stable Manifold Insertion

LanderReturn

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New Mission Concepts & Orbits

low energy transfers in the solar system: applications i

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