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Transcript of Jet Propulsion Laboratory, California Institue of Technology The InterPlanetary Superhighway and the...
Jet Propulsion Laboratory, California Institue of Technology
The InterPlanetary Superhighway
and the Development of Space
ASI Futuristic Space Technologies 5/2002
Martin.Lo @ jpl.nasa.gov
The InterPlanetary Superhighway
MWL - 2
Trajectory Is a Key Space Technology
• Golden Age of Trajectory Technology Just Around Corner
• Trajectory Is a Mission-Enabling, Intellectual Technology– Not All Technology Is Hardware!
• Space H/W Technology and Trajectory MUST Develop Side by Side– Like “Rail Road Tracks” for the Train– Example: Ion Engines Have Been Around a Long Time, Their Use
Have Been Limited by the Lack of ‘Low Thrust’ Trajectory Design Tools
The InterPlanetary Superhighway
MWL - 3
Outline
• The InterPlanetary Superhighway (IPS)
• A New Paradigm for the Solar System
• Low Energy Orbits for Space Missions
The InterPlanetary Superhighway
MWL - 4
How It All Began: ISEE3/ICE
LOGO.049
Goddard Space Flight Center
GSFC: FARQUHARFARQUHAR, Dunham, Folta, et al
Courtesy of D. Folta, GSFC
The InterPlanetary Superhighway
MWL - 5
Current Libration Missions
• z
WIND SOHO ACE
GENESISMAP NGST
LOGO.049
Goddard Space Flight Center
Courtesy of D. Folta, GSFC
The InterPlanetary Superhighway
MWL - 6
Lagrange Points in Earth’s Neighborhood
• Every 3 Body System Has 5 Fixed Points Called Lagrange Points
– Earth-Moon-S/C: LL1, LL2, … LL5
– Sun-Earth-S/C: EL1, EL2, …
• They Generate the InterPlanetary Superhighway
The InterPlanetary Superhighway
MWL - 7
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
The InterPlanetary Superhighway
MWL - 8
[email protected] by Stable & Unstable Manifolds of
Unstable Libration Orbits
MWL - 11
• Unstable Periodic Orbits– Generate the Tubes
– Portals to the Tubes
• The Tubes Govern Transport– Transport Must Occur Thru Tubes
– Systematically Map Out Orbit Space
• Green Tube = Stable Manifold: Orbits Approach the L1 Periodic Orbit, No V Needed
• Red Tube = Unstable Manifold: Orbits Leave the L1 Periodic Orbit
Planet
The InterPlanetary Superhighway
MWL - 9
[email protected] Halo Orbit Transfer and Insertion Via
The InterPlanetary Superhighway
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
The InterPlanetary Superhighway
MWL - 11
Nominal Trajectory NO Deterministic V!
13
8
1, 15, 16
23
46
7
9
11
14
-1
-0.5
0
0.5
1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
1 Launch 01/07/012 TCM-1 01/07/013 TCM-2 01/14/014 TCM-3 01/21/015 TCM-4 04/13/016 Halo Orbit Insertion (TCM-5) 04/23/017 Begin Science Phase 04/30/018 End Science Phase 03/22/039 Halo Orbit Departure (TCM-6) 04/01/0310 TCM-7 04/15/0311 TCM-8 06/10/0312 TCM-9 07/20/0313 TCM-10 08/09/0314 TCM-11 08/18/0315 Entry 08/19/0316 Backup Entry 09/07/03
ToSun
lunar orbit
haloorbit parking
orbit (option)
L+30d
Return
Transfer
Recovery
Science
14 11
976
43 2 1
8 13
-0.5
0.5
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
14 11
97 6
43 21
813
-0.5
0
0.5
-1 -0.5 0 0.5 1
5
10
12
5
10
125
10
12
Y
Axis, in millions of kilometers:X = Sun-Earth Line, positive anti-sunY = (Z) x (X)Z = Ecliptic Normal
X
View from N. Ecliptic (Z-axis)
ToSun
Z
X
View from Anti-Earth Velocity (-Y-axis) View from Anti-Sun (X-axis)
The InterPlanetary Superhighway
MWL - 12
Genesis Mission Design Collaboration
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
Pioneer Work:
Numerical Exploration by Hand
JPL Lagrange Group
JPL Lagrange Group
Lunar Orbit
L1
L2
Halo OrbitPortal
Earth
New Paradigm:
Dynamical Systems Automation
The InterPlanetary Superhighway
MWL - 15
Why Dynamical Systems Theory?• Traditional Approach
– Requires First Hand Numerical Knowledge of Phase Space
– Each Trajectory Must Be Computed Manually (VERY SLOW)
– Cannot Perform Extensive Parametric Study or Montecarlo Simulation
– Optimization Difficult, Nearly Impossible
• Dynamical Systems Theory Provides – S/W Automatic Generation of Trajectories
– S/W Automatically Maps Out Phase Space Structures
– Near Optimum Trajectory
– Automatable Parametric Studies & Montecarlo Simulations
L1 L2
Halo Orbit
Earth
GenesisReturn
ISEE3/ICE Orbit Genesis Unstable Manifold
The InterPlanetary Superhighway
MWL - 16
[email protected] Reduced Genesis End-to-End Orbit Design
from 8-12 Weeks to 1 Day
Trade Parameters LTool Funding Level OptionsTotal Cost (Millions of Dollars) 0 1.72 M 2.3 M
Genesis Critical3.4 M
Multi-MissionCritical
Tool Cost0 1 M 2.3 M 3.4 M
Increase Funding to Genesis MissionDesign Workforce 0 0.72 M (4 WY) 0 0Genesis Operational Tool at JPL(% at JPL) 50% 75% 100% 100%Genesis Mission Design UpdateTurnaround Time 8-12 Weeks 1-2 Week 1 Day 1 DayGenesis Nominal Mission Design Work(% Planned Work Accomplished) 25% 100% 100% 100%Genesis Contingency Analysis Work Current Genesis Mission Design Budget Plan Includes Only Contingency Analysis for
Launch Error (< 3 Genesis Contingency AnalysisCapability Some < 3 < 3 > 3 > 3 Genesis Mission Design Risk
High Risk Medium Risk Low Risk Low RiskMultimission Support
None Very Limited Limited GeneralAdvanced Mission SupportInfrastructure None None None Yes
High Complexity: Tool use requires extensive training, process is time-consuming and error-prone.Low Complexity: Tool enables users to work at higher level, reduces time, error, and complexity.Very Limited: Provides infrastructure and tools adaptable for future missions with additional funding
The InterPlanetary Superhighway
MWL - 17
LTool Supported Genesis Launch Delay
• Genesis Launch Delayed from 2/01 to 8/01
• LTool Enabled Designers to Replan Genesis Mission in 1 Week
• Without LTool, Genesis Would Require Costly Additional Delay
• LTool and Dynamical Systems Contributed Significantly to Genesis’ Successful Launch on 8/8/2001.
L1 L2
Halo Orbit
Earth
GenesisReturn
ISEE3/ICE Orbit Genesis Unstable Manifold
The InterPlanetary Superhighway
MWL - 18
JPL LTool Team
Martin Lo Section 312 Task Manager
Dr. Larry Romans Section 335 Cognizant S/W Engineer (Marthematica Developer)
Dr. George Hockney Section 367 S/W Architecture & Sys Engineer
Dr. Brian Barden Section 312 Trajectory Design & Algorithms
Min-Kun Chung Section 312 Astrodynamics Tools
James Evans Section 368 Infrastructure S/W, Visualization Tools
Lunar Orbit
L1
L2
Halo OrbitPortal
Earth
InterPlanetary Superhighway: Many Different Types of Orbital Motions
JPL Lagrange Group
Earth Flyby & Capture
Genesis Earth Return Via L2
Hiten Lunar Capture
Lunar Flyby Escape to SIRTF Earth Trailer Orbits
The InterPlanetary Superhighway
MWL - 20
Tunneling Through Phase Space Via IPS
• 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)
The InterPlanetary Superhighway
MWL - 21
Construction of Rapid Transition
• Manifold Intersections Computed Via Poincare Sections
• Reduce Dimension by 1, Tube Becomes Circle
• Intersections Provide Transit Orbits from L2 to L1
The InterPlanetary Superhighway
MWL - 22
Construction of Capture Orbits
• Manifold Intersections Computed Via Poincare Sections
• Reduce Dimension by 1, Tube Becomes Circle
The InterPlanetary Superhighway
MWL - 23
Construction of Heteroclinic Orbits
• Manifold Intersections Computed Via Poincare Sections
• Reduce Dimension by 1, Tube Becomes Circle
– Green Circle Leaves J to S Region
– Red Circle Enters J from X Region
• Intersections Provide Transit Orbits from L2 to L1
The InterPlanetary Superhighway
MWL - 24
[email protected] Chain
in Jupiter’s InterPlanetary Superhighway
• 2:3 to 3:2 Resonance Transport, No Energy Transfer Needed
• Source of Chaotic Motion in the Solar System
2:3 Resonance
Hilda 3:2 Resonance
The InterPlanetary Superhighway
MWL - 25
Genesis’ Homoclinic-Heteroclinic Chain
• Genesis Shadows Heteroclinic Cycle, Moon Plays Role (Bell et al.)
• SIRTF, SIM-Type Heliocentric Orbits Related to Homoclinic Orbits
The InterPlanetary Superhighway
MWL - 26
Theorem to Temporary Capture by Design
• The Existence of Homoclinic and Heteroclinic Cycles Implies We Can Choose An Infinite Sequence of Integers, Doubly Indexed,
N(i ,j) , i = Sun, L1, Jupiter, L2, Xsun; j = 1, 2, 3, …
N(i ,j) = Number of Revolutions Around Body(I), Called an ITINERARY
• THEOREM: There Exist an Orbit Which Realizes N(i ,j).
• Based on Conley-Moser’s Theorem on Symbolic Dynamics
• Voila! TEMPORARY CAPTURE BY DESIGN
Sun
N1
L1
N2
Jupiter
N3
L2
N4
XsunN5
The InterPlanetary Superhighway
MWL - 27
Orbit with Itinerary (X,J;S,J,X)
• Using Symbolic Dynamics Technique to Realize Complex Itinerary
• Capture Around Jupiter Multiple Revolutions (Specifiable)
• Note (2:3) to (3:2) Resonance Transition
The InterPlanetary Superhighway
MWL - 28
Foundation Dynamics Work
Wang Sang Koon Caltech
Martin Lo JPL, Principal Investigator
Jerrold Marsden Caltech Control and Dynamical Systems Department
Shane Ross Caltech
The InterPlanetary Superhighway
MWL - 29
[email protected] Paradigm of the Solar System
Copernican Model: Isolated Conic OrbitsNew Paradigm of the Solar System
InterPlanetary Superhighway Connects All
The InterPlanetary Superhighway
MWL - 30
IPS a New Pardigm of the Solar System
• InterPlanetary Superhighway Connects Entire Solar System
– Instead of Planets In Isolated Separate Conic Orbits
– Solar System Is An Organic and Integrated Whole Where Each Part Is Communicating with One Another
– Governs Transport and Morphology of Materials
• Shape Morphology of Rings and Belts
• Contributes to Theory of Motions of Comets, Asteroids, Dust
• Governs Planetary Impacts from Asteroids and Comets
– ShoemakerLevy9 Follwed Jupiter IPS to Final Impacts
– Genesis Trajectory Is an Impact Trajectory
– 1% of Near Earth Objects In Energy Regime of Genesis Trajectory, Considered Most Danerous
• This Theory Contributes to Understanding of our Origins
The InterPlanetary Superhighway
MWL - 31
Examples from Nature: Comet Oterma
• Theme: Use Natural Dynamics to Optimize V for Space Missions:
– Genesis 6 m/s Det. V
• Jupiter Family Comets
• (2:3) to (3:2) Free Resonance Transition
• Temporary Capture
• L1, L2 as Gate Keeper
• What Is Source of Chaotic Dynamics?
The InterPlanetary Superhighway
MWL - 32
L1, L2 Manifolds and Comet Orbits
• L1, L2 Manifolds Have (2:3) to (3:2) Resonance Transitions
• Manifolds Match Oterma’s Orbit Well
• Also Matches Gehrels3 Orbits
– Temporary Capture
– Near Halo Orbit
• L1, L2 Manifolds Are DNA of This Dynamics
• Need to Study Invariant Manifold Sturcture
The InterPlanetary Superhighway
MWL - 33
[email protected] Oterma Shadows
Jupiter’s Heteroclinic-Homoclinic Cycles
The InterPlanetary Superhighway
MWL - 34
[email protected] the Orbit Space
Using Poincare Sections
.
.Orbits
..Poincare Map
.
The InterPlanetary Superhighway
MWL - 35
Poincare Section of Jupiter’s IPS
3:2
Hilda Asteroid Group
4AU
2:1
Kirkwood Gap
2.1 AU
The InterPlanetary Superhighway
MWL - 36
Asteroid Belt Stucture Induced by IPS
• Poincare Section from Single Orbit Leaving Jupiter L1
– Each Dot Is a Rev Around the Sun
– Spirals Towards Inner Solar System
– Eccentricity Grows
• Indistiguishable from Ordinary Conic Orbits
• Controls Asteroid Belt Structures
• Controls Dust Transport and Morphology
• Intimate Connection with Low Thrust Trajectory Design
Semi-Major Axis
Ecc
entr
icit
yA
rg P
erih
elin
3:2 Stable
2:1 Mars Crosser
ECC = .5
ECC = .05
2.1 AU 4 AU
The InterPlanetary Superhighway
MWL - 37
IPS ExoZodi Dust Signatures for Planet Detection
• Earth’s Zodi Dust Ring Simulated WIth Lagrange Point Dynamics– Only Gravity, No PR Drag
• S: Sun Region, Earth: Planet Region, X: Exterior Region
• May Provide Planetary Signatures for Exo-Planet Detection
S
EARTH
X
The InterPlanetary Superhighway
MWL - 38
IPS and Transport in the Solar System
Legend
L1 IPS Orbits
L2 IPS Orbits
Comets
Asteroids
Kuiper Belt
Object
Poincare Section of the InterPlanetary Superhighway
The InterPlanetary Superhighway
MWL - 39
Discovery of InterPlanetary Superhighway
Martin Lo JPL Genesis Mission Design Manager
Shane Ross Caltech Control and Dynamical Systems
The InterPlanetary Superhighway
MWL - 40
Around the Solar System in 80K Days
• FREE Spiral Orbit Transfer of KBO to Asteroid Belt Produced by LTool Using IPS
– Origin of Jupiter Comets
– Replenish Asteroid Belt
– Escape from Solar System
• Less Than 1 Pluto Year
• Scales for Jupiter and Saturn Satellite Systems
• Suggests New Low Thrust Algorithm
Jupiter
Saturn
~Uranus (fictitious mass)
~Neptune (fictitious mass)
Kuiper Belt Object (KBO)
The InterPlanetary Superhighway
MWL - 41
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
The InterPlanetary Superhighway
MWL - 42
Mars Meteorite
• 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
The InterPlanetary Superhighway
MWL - 43
Asteroid Transport Rate Near Mars*
Charles Jaffe West Virgina University
Shane Ross Caltech
David Farelly Utah State University
Martin Lo JPL
Jerrold Marsden Caltech
Turgay Uzer Georgia Tech
* To appear in “Physical Review Letters” (7/1/02)
The InterPlanetary Superhighway
MWL - 46
1% Near Earth Objects Have IPS Energies
Armageddon Or Opportunity?
The InterPlanetary Superhighway
MWL - 47
IPS and Development of Life: Exobiology
• InterPlanetary Superhighway Brought Life Building Material from Comets and Asteroids to Earth
• InetrPlanetary Superhighway May Have Brought the Asteroid Killing the Dinosaurs Via a Genesis-Like Orbit
– Presence of Abundant Iridium Implies Slow Impact Velocity
– Conjectured by Mike Mueller et al (Nemesis Star)
• InterPlnaetary Superhighway Theory Can Provide Critical Transport Rates for Astrobiology
– How Rates Determine Formation of Life on a Planet
– Can Rates Be Obtained from ExoZodi Signatures to Find Potential Life Bearing ExoPlanets?
The InterPlanetary Superhighway
MWL - 48
RESCUE MISSION 911:
Hiten, HAC
Discover, June 1999
The InterPlanetary Superhighway
MWL - 50
Designing a Lunar Capture Orbit
TRAJECTORIES FROM SUN-EARTH EXTERIOR
REGION
TRAJECTORIES FROM SUN-EARTH
INTERIORREGION
TO EARTH-MOON INTERIOR REGION
CONTAINS ALL EARTH TO LUNAR CAPTURE ORBITS ON ENERGY SUFACE
A CROSS SECTION OF THE SUN-EARTH AND EARTH-MOON IPS PARTITIONS THE ORBITAL DESIGN SPACE INTO CLASSES
The InterPlanetary Superhighway
MWL - 51
Construction of Capture Orbits
• Manifold Intersections Computed Via Poincare Sections
• Reduce Dimension by 1, Tube Becomes Circle
Moon
The InterPlanetary Superhighway
MWL - 52
Shoot the Moon
Shadowing Unstable Manifold of Earth L2 Lyapunov Orbit
Shadowing Stable Manifold of Earth L2 Lyapunov Orbit to Leave Earth
Earth
Lunar Orbit
36 m/s Maneuver to Transfer to Stable Manifold of Moon L2 Lyapunov Orbit
Ballistic Lunar Capture
Hiten-Like Low Energy Transfer & Ballistic Lunar Capture
MWL - 14
Shoot the Moon
The InterPlanetary Superhighway
MWL - 53
Shoot the Moon: Lunar Capture
Wang Sang Koon Caltech
Martin Lo JPL, Principal Investigator
Jerrold Marsden Caltech Control and Dynamical Systems Department
Shane Ross Caltech
The InterPlanetary Superhighway
MWL - 54
TPF in Formation Flight Near L2
TPF Formation
L2To Sun & Earth
The InterPlanetary Superhighway
MWL - 55
TPF in SIRTF/SIM-Like Heliocentric Orbit
TPF Formation
The InterPlanetary Superhighway
MWL - 56
First Formation Flight Design Around L2
For the Terrestrial Planet Finder Mission (TPF)
Min Kun Chung JPL
Gerard Gomez Barcelona University
Martin Lo JPL, TPF Mission Design Lead
Josep Masdemont Polytechnic University of Catalunya
Ken Museth Caltech Computer Graphics Group
Larry Romans JPL
The InterPlanetary Superhighway
MWL - 57
[email protected]: 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
The InterPlanetary Superhighway
MWL - 58
[email protected]: 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
The InterPlanetary Superhighway
MWL - 59
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
The InterPlanetary Superhighway
MWL - 62
Lunar L1 Gateway Human Servicing
Mission Concept Development and Design
Martin Lo JPL, Principal Investigator
Initial Trajectory Design (2D, Coupled RTBP Model)
Shane Ross Caltech
Detailed Trajectory Design (3D, Full Ephemeris Model)
Min Kun Chung JPL
Animation
Cici Koenig Caltech Graphics Group
Alan Barr Caltech Graphics Group
The InterPlanetary Superhighway
MWL - 63
Transport Between the Jovian Moons
• Cross Section of Manifolds Plotted in {a, e} Elements
• L1 Manifold of Europa Intersects L2 Manifold of Ganymede, etc.
• Provide Transport Between Moons
• May Require V
– Much Lower than Hohmann
Transport Between Jovian Moons
The InterPlanetary Superhighway
MWL - 64
Petit Grand Tour of Jovian Moons
Mission Concept Flexible Itinerary, Visit Jovian Moons in Any Order
User Low Energy Transfer, Capture, Impact
Near Circular Orbits Reduce Jupiter Radiation
Proof of Concept Point Design Using the Interplanetary Superhighway 25 Day Transfer from Ganymede to Europa
Requires DV of 1452 m/s!
Compare to Hohmann Transfer of 2822 m/s!
Free Capture by Europa for 4 Orbits (More Possible) Tour Also Available for Saturn’s Moons
Applicable to Europa/Titan Orbiter, Lander, & Other Outer Planets Missions
The InterPlanetary Superhighway
MWL - 65
New Frontier: Petit Grand Tour?
• New Computation by Shane Ross
• Serial Visits to Galilean Moons, Final Europa Capture
• Total V ~ 20 m/s! 1500 Days Time of Flight
The InterPlanetary Superhighway
MWL - 66
Petit Grand Tour
Wang Sang Koon Caltech
Martin Lo JPL, Principal Investigator
Jerrold Marsden Caltech Control and Dynamical Systems Department
Shane Ross Caltech
The InterPlanetary Superhighway
MWL - 67
• To Design Low Thrust Orbits, You Must Understand IPS
• Computed from Single Orbit Leaving Europa L2
– Each Dot Is a Rev Around Jupiter
– Spirals Towards Europa
– Eccentricity Grows
• Full of Useful Unstable Orbits
– Similar to L1/L2 Halo’s
– More Tubes!
• Indistiguishable from Conic Orbits
• New Low Thrust Trajectory Design
– Use This Transition as First Guess
New Approach to Low Thrust Orbits
Europa’s IPS
The InterPlanetary Superhighway
MWL - 68
Low Thrust Orbit Naturally Uses IPS!
• Low Thrust Transfer to Mars Via Lunar L1 to L2 Transfer
• Courtesy of G. Whiffen Computed by MYSTIC
The InterPlanetary Superhighway
MWL - 69
Low Thrust to Lunar Gateway L1 Halo Orbit
• Low Thrust Trajectory Courtesy of G. Whiffen, Computed by MYSTIC
• Halo Orbit Computed by LTool
The InterPlanetary Superhighway
MWL - 70
IPS Technology Road Map
Three Steps: Discover, Understand, Apply
• Map the InterPlanetary Superhighway– First Step in Discovery and Exploration– Like “Human GENOME”, “Star Catalogs”, Rand McNally Maps
• Integrate Orbital Dynamics Theories– IPS Orbits– Continuous Thrust Orbits– Conics Orbits
• Develop New Mission Concepts
The InterPlanetary Superhighway
MWL - 71
References
• Barden, Howell, Formation Flying in the Vicinity of Libration Point Orbits, AAS 98-169, Monterey, CA, 2/98
• Barden, Howell, Dynamical Issues Associated with Relative Configurations of Multiple Spacecraft Near the Sun-Earth/Moon L1 Point, AAS 99-450, Girdwood, Alaska, 8/99
• Gomez, Masdemon, Simo, Lissajous Orbits Around Halo Orbits, AAS 97-106, Huntsville, Alabama, 2/97
• Howell, Barden, Lo, Applications of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission, JAS 45(2), April 1997, 161-178
• Howell, Marchand, Lo, The Temporary Capture of Short-Period Jupiter Family Comets from the Perspective of Dynamical Systems, AAS 00-155, Clearwater, FL, 1/2000
• Koon, Lo, Marsden, Ross, Heteroclinic Connections between Lyapunov Orbits and Resonance Transitions in Celestial Mechanics, to appear in Chaos
The InterPlanetary Superhighway
MWL - 72
References
• Koon, Lo, Marsden, Ross, The Genesis Trajectory and Heteroclinic Connections, AAS99-451, Girdwood, Alaska, August, 1999
• Koon, Lo, Marsden, Ross, Shoot the Moon, AAS00-166, Clearwater, Florida, January, 2000
• Lo, The InterPlanetary Superhighway and the Origins Program, IEEE Aerospace2002 Conference, Big Sky, MT, February, 2002
• Lo et al., Genesis Mission Design, AIAA 98-4468, Boston, MA, August, 1998
• Serban, Koon, Lo, Marsden, Petzold, Ross, Wilson, Halo Orbit Correction Maneuvers Using Optimal Control, submitted to Automatica, April, 2000
• Scheeres, Vinh, Dynamis and Control of Relative Motion in an Unstable Orbit, AIAA Paper 2000-4135, August, 2000