Libration Point Orbits and Applications: Proceedings of the Conference Aiguablava, Spain 10 - 14 June 2002

SECTION I: Mission Analysis and Operations......Page 14
Preface......Page 6
List of Participants......Page 8
1. INTRODUCTION......Page 18
2.1. International Sun-Earth Explorer-3 (ISEE-3)......Page 19
2.2. Solar Heliospheric Observatory (SOHO)......Page 21
2.3. Advanced Composition Ezplored (ACE)......Page 24
2.4. Microware Anisotropy Probe (MAP)......Page 26
3.1. Celestial Navigator (CelNav)......Page 27
3.2. Delta Diflerenced One-Way Range (DDOR)......Page 30
4. CONCLUSIONS......Page 33
References......Page 34
2. Performance Requirements and Kickstage Disposal Options for a Cislunar Gateway Station Transfer Vehicle G.L. Condon, S. Wilson and C.L. Ranieri......Page 36
2. Nominal Earth-to-Gateway Crew Transfer Sequence......Page 37
2.1. LPA Time Frame for Evaluation of Performance Requirements......Page 39
2.2. Nominal Earth-to-Gateway V Cost......Page 40
3. Kickstage Disposal Options......Page 43
3.2. Option 1 . Lunar Swing-by to Heliocentric Orbit (HO)......Page 44
3.3. Option 2. Lunar Vertical Impact (LVI)......Page 45
3.4. Option 3. Direct Return to Remote Ocean Area (DROA)......Page 47
3.5. Option 4. Lunar Swingby Return to Remote Ocean Area (SROA)......Page 49
3.6. Option 5. Transfer to a Long Lifetime Geocentric Orbit (GO)......Page 50
3.7. LT V Kickstage Disposal Options – Conclusion......Page 53
4. Earth Moon L1 Libration Point Lifetime Analysis......Page 54
4.2. Study One: Spacecraft left on a high eccentricity parking orbit......Page 55
4.3. Study Two: Spacecraft Left at EM L1 With No Station Keeping Capability......Page 56
4.4. Study Three: Spacecmft Left At EM L1 With No Station Keeping Capability And An Initial Impulsive V......Page 58
References......Page 59
1. Introduction......Page 62
2. History and Use......Page 63
3. ISEE-3......Page 65
4. Double Lunar Swingby Orbits......Page 70
5. The ISEE-3/ICE Extended Mission......Page 76
6. Relict-2, First Plans for an Lz Astronomical Satellite......Page 79
7. SOHO......Page 82
8. ACE......Page 83
9. WIND......Page 84
10. MAP......Page 85
11. Genesis......Page 86
12. Future Libration-Point Missions......Page 87
References......Page 88
1. Introduction......Page 92
2. List and nature of technical constraints......Page 93
4. Ascending node longitude influence on halo-orbit characteristics......Page 95
5. Parking orbits......Page 97
6. Feasibility of maneuvers with direction of thrust constraints......Page 99
References......Page 100
1. Introduction......Page 102
1.1. An Overview of NASA Themes Involving Libmtion Orbits......Page 103
1.2. Historical Missions......Page 104
1.3. Future Mission Challanges......Page 105
1.4. A Brief History of Trajectory Design and Capabilities......Page 106
2.1. Numerical Shooting Methods......Page 107
2.3. Invariant Manifolds......Page 111
2.4. Lissajous-Manifold-~nsfer Generation......Page 112
3.1. JWST Trajectory Design: Libration Orbit......Page 114
3.2. J WST Trajectory Design: Direct Transfer......Page 115
3.3. Continuous Low Thrust Options......Page 116
3.4. Earth Return / Servicing missions......Page 117
3.5. Constellation-X......Page 118
4. Libration Formation Flying......Page 120
4.2. SI Formation Flying Results......Page 123
4.3. Formation Maintenance Results......Page 125
5.1. Improved Tools......Page 127
References......Page 128
6. Herschel, Planck and GAIA Orbit Design M. Hechler and J. Cobos......Page 132
1. Introduction......Page 133
2.1. Escape Direction in the Linear Problem......Page 134
2.3. Numerical Construction of Transfer Orbit......Page 136
2.4. Transfer between Orbits of Different Size......Page 139
2.5. Eclipse Avoidance......Page 142
3.1. Launch Windows For Herschel/Planck......Page 145
3.2. Navigation and Orbit Maintenance......Page 147
3.3. Launch window for GAIA......Page 149
4. Conclusions......Page 150
References......Page 151
1. Introduction......Page 154
2. Baseline Trajectory & Orbit......Page 155
3. Triana as a Shuttle Payload......Page 156
4. Optional Shuttle Scenarios......Page 161
5. Looking for an ELV......Page 164
6. Triangular Transfer Trajectories......Page 165
7. Conclusion......Page 166
References......Page 168
1. Introduction......Page 170
2. Populating a Certain Distant Retrograde Orbit (DRO) with Small Satellites......Page 172
2.1. A Possible Deployment Stnztegy......Page 179
3. Deployment from an L1-halo Orbit onto Invariant Unstable Manifolds......Page 183
4. Conclusion......Page 186
References......Page 187
9. The SOHO Mission L1 Halo Orbit Recovery from the Attitude Control Anomalies of 1998 C.E. Roberts......Page 188
1. Introduction......Page 189
2.1. The Spacecraft......Page 191
2.2. The SOHO Mission Halo Orbit......Page 193
2.3. Overview of the SOHO Propulsion System......Page 195
3.1. Geneml Approach......Page 196
3.2. Use of the Swingby lhjectory Design Program for SOHO Stationkeeping......Page 198
3.3. Swingby Program Coordinate Frame Constructions......Page 199
3.5. SOHO SK Targeting Technique using the Swingby Progmm......Page 200
3.6. Brief History of SOHO SK Maneuvers prior to the 1998 Anomalies......Page 202
4.1. Emergency Sun Reacquisition (ESR) Events......Page 203
4.3. Early Post-anomaly Assessment......Page 204
4.4. Post-Anomaly Trajectory Prediction......Page 205
4.5. Decay Trajectory Sensitivities......Page 206
4.7. Detection of the Spacecraft......Page 209
4.8. The Recovery from the June 1998 Anomaly......Page 210
4.9. The Recovew Maneuvers......Page 211
4.10. Developments Complicating the Recovery......Page 212
4.11. Finally Out of the Woods ... or So W e Thought......Page 214
5. The Anomaly of December 21, 1998, and the “Great ESR”......Page 215
5.1. Modeling the ESR Using the Swingby Progmm......Page 216
5.2. Estimating the ESR-mode thruster duty cycles......Page 217
5.3. Early Assessment of the Problem......Page 219
5.4. The Struggle......Page 222
6. Epilogue to the 40-Day Mad Scramble......Page 225
7. Conclusion......Page 228
References......Page 229
1. Introduction......Page 236
2. Description of the orbits......Page 237
3. Summary of the transfer parameters......Page 239
SECTION II: Dynamics Around the Libration Points......Page 15
1. Introduction......Page 242
2. The Quasi-bicircular Problem......Page 244
3. The Halo family of the QBCP......Page 245
4. Translunar Halo orbits of the REMS......Page 246
References......Page 253
1. Introduction......Page 256
2. The planar circular restricted three-body problem......Page 257
3. Lemaitre regularization......Page 259
5. The Lambert’s three-body problem......Page 261
7. Numerical results......Page 262
7.2. Trajectories fmm L2......Page 263
7.3. Trajectories from L3......Page 264
7.4. Trajectories from L4......Page 265
7.5. Trajectories jhm L5......Page 267
7.6. Comparison between the trajectories......Page 268
References......Page 269
1. Introduction......Page 270
2. Linear Approach......Page 272
3. Changing in Plane and Out of Plane Amplitudes......Page 274
4. Changing Phases......Page 277
4.1. In Plane Phase Change Manoeuvres Maintaining Amplitudes......Page 278
4.2. Effective Phases......Page 279
4.3. Eclipse Avoidance Stmtegy. LOE W E problem......Page 280
Rough estimation of the cost of the manoeuvre......Page 282
References......Page 284
1. Introduction......Page 286
2. Equations of motion......Page 287
3. The family of halo orbits......Page 291
4. The stable halo orbits......Page 296
5. Conclusions......Page 302
References......Page 303
1. Introduction......Page 304
2.1. Description of the method......Page 308
Non-linear approximation of the stable manifold......Page 311
2.2. Fixing the arrival point and the time of flight......Page 314
2.3. Free time of flight......Page 319
3. Departing from the stable manifold......Page 321
Acknowledgements......Page 325
References......Page 326
1.1. The Restricted Three Body Problem and its perturbations......Page 328
1.2. Libration Points and dynamical substitutes......Page 331
2. The phase space about the Libration Points......Page 332
Reduction to the center manifold......Page 334
Lindstedt-Poincark procedures: halo, quasi-halo, and Lissajous orbits......Page 337
2.2. Numerical approach......Page 340
Normal behavior around a periodic orbit......Page 341
Invariant tori starting around vertical orbits......Page 343
A ((second view” of the center manifold......Page 346
3. Computations in very accurate models of motion......Page 347
3.1. Multiple shooting......Page 348
4.1. Transfer using invariant manifolds......Page 352
4.2. The TCM problem......Page 354
5. Transfers between libration point orbits......Page 357
5.1. Transfers between halo orbits......Page 358
5.2. Transfers between Lissajous orbits......Page 361
5.3. Homoclinic and heternclinic connections......Page 364
6. Low energy transfers......Page 366
6.1. Shoot the Moon......Page 367
6.3. Solar sytem low energy transfers and astronomical applications......Page 369
7.1. The Target mode approach and the Floquet mode approach......Page 370
Target Point Approach......Page 371
Floquet Mode Approach......Page 373
7.2. Numerical results......Page 378
8. Application of libration point orbits to formation flight......Page 380
8.1. The nominal orbit strategy......Page 381
8.2. Formation flight in the vicinity of a libration point. TPF case......Page 382
Deployment Phase......Page 383
Estimation of TPF budget for a ten year’s mission......Page 384
References......Page 385
1. Introduction......Page 390
2. General equations of motion......Page 392
3. Fourier analysis......Page 397
3.1. Fourier analysis of the bi functions......Page 398
3.2. Fourier analysis of the positions of the planets......Page 402
4.1. Adjustment using linear combinations of basic frequencies......Page 403
4.2. Simplified models for the Sun-(Earth+Moon) system......Page 404
4.3. Simplified models for the Sun-(Earth+Moon) system......Page 408
5. Dynamical substitutes of the collinear libration points......Page 410
References......Page 413
1. Introduction......Page 416
2.1. Dynamical System......Page 419
2.2. State Measurements and Orbit Determination......Page 420
2.3.1. Statistical Description of Orbits......Page 422
2.3.2. Probability measure as an integral invariant......Page 424
2.3.3. Probability Computation......Page 426
2.4. Statistical maneuver design......Page 429
3. Model Problems of Unstable Orbital Environments......Page 431
Restricted 3-body Problem......Page 432
Asteroid Orbiter Problem......Page 433
3.2. Simplified model for analytical study......Page 434
4.1.1. Distributions in Tame......Page 435
4.1.2. Application to the 1-DOF System......Page 438
4.2. Optimal Measurement Strategies......Page 442
4.2.1. Characterizing measurements in phase space......Page 443
4.3. Control of Unstable Trajectories......Page 446
4.3.1. Optimal Statastical Maneuver Placement......Page 447
4.3.2. Application to a 1-DOF system......Page 449
References......Page 453
1. Introduction......Page 456
2. The spacecraft concept......Page 457
3.1. Spiral ascent strategy......Page 459
3.2. Shadowing......Page 460
3.3. Pammeters of the spirall orbit......Page 461
4. Flight to L1 and insertion into halo orbit......Page 462
6.2. Models and methods used......Page 464
6.4. One complete orbit around the Earth......Page 467
6.5. Two complete orbits around the Earth......Page 468
7. Conclusion......Page 470
References......Page 471
SECTION IV: Solar System Dynamics and Applications......Page 16
1. Introduction......Page 472
2. Transfer to a libration point: Problem description......Page 474
3. Reference Absolute trajectory: Transfer to LZ orbit......Page 475
4. Dispersion analysis......Page 476
5. Relative motion in the RTBP (linear time-variant system)......Page 479
6. Controller design through analytical closed loop poles placement......Page 480
7. Closed loop performances and budgets......Page 484
8. Summary and conclusions......Page 485
References......Page 487
1. Introduction......Page 488
2. History and Use......Page 489
3. Design Methodology and Goals......Page 491
3.1. Process......Page 492
3.2. Requirements on Numerical Methods......Page 493
3.3. Analysis Through Operations Support......Page 494
3.4. Multiple Mission Support......Page 495
3.5. Seamless Operation with STK......Page 496
3.6. Automation support......Page 497
3.7. User Extensibility......Page 499
4. Visualization......Page 500
5. Summary......Page 501
References......Page 502
22. The Computation of Periodic Solutions of the 3-Body Problem Using the Numerical Continuation Software AUTO D. J. Dichmann, E. J. Doedel and R. C. Paffenroth......Page 506
1. Introduction......Page 507
2. Continuation of solutions......Page 509
3. Periodic Solutions of the Circular Restricted 3-Body Problem......Page 513
4. Physical Units......Page 515
5. Tour of the Bifurcation Diagram......Page 516
6. Rotating and Inertial Coordinates......Page 528
7.1. Lyapunov Orbits......Page 529
7.3. Axial Orbits......Page 532
7.4. Backflip Orbits......Page 534
8. Conclusion......Page 537
References......Page 542
1. Introduction......Page 546
2.1. Definition of the Basic Segment......Page 554
2.2. A Conceptual Modelling Example......Page 566
2.3. The Equations of Motion and the Propagation Reference Frame......Page 567
2.4. Multi-Body Reference Frames......Page 571
2.5. State Transformations......Page 575
2.6. Open Loop Solution of a Trajectory or a Mission......Page 577
3. Solution Methods......Page 579
4.1. Modular Architecture......Page 583
4.2. Algorithm and System Tuning......Page 584
4.3. Integmted Visualization......Page 586
5. Conclusions......Page 587
References......Page 588
1. Introduction......Page 590
2. The Bicircular Coherent Problem......Page 591
3.1. The reduced Hamiltonian of the Three Body Problem......Page 592
Numerical computation of invariant curves......Page 593
Discretization error......Page 594
3.3. Finding the desired torus......Page 595
4.1. The Hamiltonian of the SJSU problem......Page 598
4.2. Computation of a first torus......Page 599
4.3. The Tricircular solution of the SJSU problem......Page 601
5. Conclusions......Page 602
References......Page 603
25. Invariant Manifolds, the Spatial Three-Body Problem and Petit Grand Tour of Jovian Moons G. Gomez, W.S. Koon, M. W. Lo, J.E. Marsden, J. J. Masdemont and S.D. Ross......Page 604
1. Introduction......Page 605
2. Invariant Manifold as Separatrix......Page 608
3. Constructing Orbits with Desired Itinerary......Page 612
4. Spatial Petit Grand Tour of Jovian Moons......Page 614
References......Page 617
1. Introduction......Page 620
2. Method of calculation......Page 621
3. Results......Page 622
References......Page 627
1. Introduction......Page 630
2. Area of Motion......Page 631
3. Notes on Capture Possibility......Page 632
4. Numeric Research......Page 634
5. Geological Evidence......Page 636
6. Conclusions......Page 637
References......Page 638
Main Equations......Page 640
1. The Libration Point Coordinates......Page 647
2. Generalisation to the Case with 2N + 1 Particles......Page 649
3. Results and Conclusions......Page 652
References......Page 653
1. Introduction......Page 654
2. The Quasi-Hilda Group of Comets......Page 656
3. Transport in the Planar Circular Restricted Three-Body Problem......Page 658
References......Page 667
1. Introduction......Page 670
2. Definition of the smaller alignment index (SALI)......Page 672
3.1. Symplectic maps......Page 673
3.2. The He'non-Heiles Harniltonian system......Page 676
4. Conclusions......Page 680
References......Page 681
31. Locating Periodic Orbits by Topological Degree Theory C. Polymilis, G. Servizi, Ch. Skokos, G. Turchetti and M. N. Vrahatis......Page 682
1. The topological degree (TD) and its computation......Page 683
2. The characteristic bisection method......Page 685
3. Applications......Page 687
4. Synopsis......Page 692
References......Page 693