Genesis Orals template

1
Low Energy Transfers
in the Solar System Applications I Objectif
Lune (Tintin)
Martin.Lo_at_ 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 1980s)
• 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
First Halo Oribt Mission ISEE3/ICE
GSFC Farquhar, Dunham, Folta, et al
Courtesy of D. Folta, GSFC
7
Current Libration Missions

• z

WIND
SOHO
ACE
GENESIS
MAP
JWST
Courtesy of D. Folta, GSFC
8
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9
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

10

• Genesis Mission Uses L1, L2 Heteroclinic
  Behavior to Collect Return Solar Wind Samples
  to Earth

September 8th, 2004!
11
The Genesis Trajectory
1. Transfer 2. Science 3. Return 4. Entry 5.
Backup
Begin Science
End Science
Lunar Orbit
2
3
1
L2
L1
Sun (size position not to scale)
5
4
12
Stable Manifold Transfer to Halo Orbit
13
Stable Manifold for Genesis Transfer
14
More Background Genesis

• Invariant Manifolds Provide Low Energy Transfers
• L1/L2 Heteroclinic Connection Provide Day-Side
  Return
• Howell, Barden, Wilson, Lo

15
Earth Flyby Capture
Earth Return Via L2
16
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

17
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?

18
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,

19
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

20
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

21
Dynamical Systems Theory
22
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
• q - Sin( q )
• But for Small q, Pendulum Motion is Stable and
  Acts Like Harmonic Oscillator
• q - q
• In Both Cases, Nonlinear Effects Are Not
  Noticeable, Linear Approximations Are Good

23
Pendulums 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

24
Orbital Zoology Near the Lagrange Points

X
S Sun Region J Jupiter Region X Exterior
Region (Outside Jupiters Orbit)
S
J

• 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)

25
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)

26
Stable Unstable Manifolds of Unstable Periodic
Orbits

• Unstable Periodic Orbits
• Portals to the Network
• Generate the Tubes
• Green Tube Stable Manifold
  Orbits Approach the L1 Periodic Orbit, No
  DV Needed
• Red Tube Unstable Manifold
  Orbits Leave the L1 Periodic Orbit
• Systematically Map Out Orbit Space

Planet

MWL - 11
27
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

28
Mapping the Space Using Cross Sections
29
Manifolds Connect Solar System

(Lo Ross)
Jupiter

• Legend
• ? Comets
• ? Asteroids
• ? Kuiper Belt
• Object
• ? L1 IPS Orbits
• ? L2 IPS Orbits

Saturn
Uranus
Neptune
30
Map of the Orbital Families Near L2
Poincaré Section at L2
Simo, Gomez, Jorba, Llibre, Masdemont,
31
Tori of Lissajous Orbits Immersed in
3 Space
Courtesy of Josep Maria Mandella
32
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 L2 and L1 Halo
  Orbits (Heteroclinic)

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35
Invariant Manifolds Jupiter Comets

• Transport Between 32 and 23 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

36
Shoot the Moon! RESCUE MISSION 911 Hiten, HAC,
Discover, June 1999
37
Shoot the Moon

Shoot the Moon Low Energy Transfer Ballistic
Capture
38
Lunar L1 Gateway Station
JPL Lagrange Group
7/5/04
39
Problem Human Service to Libration Missions

• ISSUE 3 Months Transfers to EL2 Too Long for
  Humans
• Short Transfers Too Difficult
• Infrastructure Too Expensive

TPF _at_Earth L2
STA-103 astronauts replaced gyros needed for
orientation of the Hubble Space Telescope.
JSC
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41
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

42
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
43
IPS in Earths Neighborhood

• Portals/Interchange Halo Orbits, Unstable
  Orbits
• Lanes Invariant Manifold Tubes

ARTIST CONCEPTION
44
Gateway Architecture (JSC)
GPS Constellation
Earths Neighborhood
Source James Geffre, JSC
Crew departs from and returns to ISS
L1 Gateway
Lunar Habitat
Lunar Lander
Crew Transfer Vehicle

• Crew Transfer Vehicle
• Transports crew between ISS and Gateway
• Nominal aerocapture to ISS, or direct Earth
  return contingency capability

• 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

45
Gateway Configurations (JSC)
Source James Geffre, JSC
LEO, Transit, L1 Stand-by Configuration
Launch Configuration
Telescope Operations Configuration
Lunar Operations Configuration
46
Lunar Sample Return via the Interplanetary
Supherhighway
Lunar Orbit
Goto LSR Vugraphs
JPL Caltech
8/6/2002
47
New Mission Concepts Orbits