Perozzi / Ferraz-Mello Space Manifold Dynamics

Novel Spaceways for Science and Exploration
1. Auflage 2010
ISBN: 978-1-4419-0348-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 258 Seiten

The term "Space Manifold Dynamics" (SMD) was proposed during the workshop "Novel Spaceways for Scientific and Exploration Missions" for describing new types of spacecraft trajectories that could revolutionize how space missions are designed. Obtained by applying the dynamical system approach to mission design, these trajectories represent a fascinating alternative to elliptic motion and provide a deeper understanding of the classical three and N-body problems in celestial mechanics. This book gives a state-of-the-art overview of this new field of study together with applications of an interdisciplinary nature involving planetary science, astrophysics and the manned exploration of the solar system. TOC:Space Exploration Wide Vision.- Dynamical Systems Fundamental Topics for Spaceflight.- Invariant Manifolds, Lagrangian Trajectories and Space Mission Design (I).- Invariant Manifolds, Lagrangian Trajectories and Space Mission Design (II).- Weak Stability Boundary and Resonance Transitions.- Three-Body Invariant Manifold Transition with Electric Propulsion.- Optimization in Low-Thrust Transfer.- The Accessibility of the Moon.- Use of Lagrangian Points for Manned Missions.- Radiation Safety for Human Spaceflight.- Plans and Perspectives of Space Based Astronomy.- From Sputnik to Planck.- The Search for Habitable Planets and the Darwin Mission.- Sustainability and Affordability of Space Enterprises.- Space Manifolds for Interplanetary Missions and the Bepicolomobo Capture Orbit.- Open Architecture for Exploration.

Autoren/Hrsg.

Perozzi, Ettore

Ferraz-Mello, Sylvio

Inhaltsverzeichnis

1;Preface;5
2;Recommendations;8
3;Contents;10
4;Contributors;12
5;About the Editors;14
6;Invariant Manifolds, Lagrangian Trajectories and Space Mission Design;15
6.1;1 Introduction;15
6.1.1;1.1 The CRTBP and the Libration Points;16
6.1.2;1.2 Properties of the Libration Point Orbits;17
6.2;2 Libration Point Orbits and Their Synthetic Representation;19
6.2.1;2.1 Libration Point Orbits;19
6.2.2;2.2 Synthetic Representations;21
6.2.2.1;2.2.1 Poincaré Map Representation;21
6.2.2.2;2.2.2 Energy vs Rotation Number Representation;22
6.3;3 Computation of LPOs;25
6.3.1;3.1 LindstedtéPoincaré Computation of Tori and Their Stable and Unstable Manifolds;25
6.3.2;3.2 Numerical Computation of Tori and Their Stable and Unstable Manifolds;28
6.4;4 Homoclinic and Heteroclinic Orbits;29
6.5;5 Applications of Invariant Manifolds;31
6.5.1;5.1 Transfers from the Earth;31
6.5.2;5.2 Transfers using invariant manifolds;32
6.5.3;5.3 The TCM Problem;34
6.5.4;5.4 Transfers Between Halo Orbits;39
6.5.5;5.5 Transfers Between Lissajous Orbits;42
6.5.5.1;5.5.1 Effective Phases and Eclipse Avoidance;45
6.5.5.2;5.5.2 Rendez-vous in the Libration Zone;50
6.5.6;5.6 Transfers Between Earth-Moon and Sun-Earth Lissajous Orbits;54
6.6;6 Station Keeping;61
6.6.1;6.1 The Target Mode Approach and the Floquet Mode Approach;61
6.6.2;6.2 Numerical Results;67
6.7;7 Low Energy Transfers and the Weak Stability Boundary;69
6.7.1;7.1 The Weak Stability Boundary;70
6.7.2;7.2 Numerical Determination of WSB and Low Energy Transfers;73
6.7.3;7.3 Solar System Low Energy Transfers and Astronomical Applications;74
6.8;8 Rescue Trajectories from the Moons Surface;76
6.8.1;8.1 Stable Manifolds Associated with Halo Orbits;76
6.8.1.1;8.1.1 Numerical Results;79
6.8.2;8.2 Stable Manifolds Associated with Lissajous Orbits;85
6.8.2.1;8.2.1 Numerical Results;86
6.8.3;8.3 Summary of Results;88
6.9;9 Spacecraft Missions to LPOs;90
6.9.1;9.1 Introduction;90
6.9.2;9.2 Missions to LPO;90
6.9.3;9.3 Mission Design Problems;96
6.9.4;9.4 LPO in Lunar and Exploration Missions;97
6.9.5;9.5 LPO in Mission Recovery;99
6.9.6;9.6 Conclusions;102
6.10;10 Summary and Outlook;102
6.11;References;107
7;Chaos and Diffusion in Dynamical Systems Through Stable-Unstable Manifolds;111
7.1;1 Introduction;111
7.2;2 The Homoclinic Tangle of Hyperbolic Saddle Points;113
7.3;3 From Chaos to Diffusion in two Dimensional Symplectic Maps;116
7.4;4 Higher Dimensional Systems: from Arnolds Model to Four Dimensional Maps;119
7.5;References;125
8;Regular and Chaotic Dynamics of Periodic and Quasi-PeriodicMotions;127
8.1;1 Introduction;127
8.2;2 Around Equilibrium Points;128
8.3;3 From Floquet to Lyapunov;130
8.4;4 Integrable versus NonIntegrable;131
8.5;5 Getting Started with Perturbation Theory;133
8.6;6 Birth and Death of Invariant Tori;135
8.7;7 Diffusion and Exponential Stability;137
8.8;8 Hunting for Periodic Orbits;138
8.9;9 The Lagrangian Solutions;140
8.9.1;9.1 The Restricted, Planar, Circular Lagrangian Solutions;140
8.9.2;9.2 The Restricted, Planar, Elliptic Lagrangian Solutions;143
8.9.3;9.3 The Lagrangian Points in Flight Dynamics;143
8.10;Appendix A. Periodic and QuasiPeriodic Motions;144
8.11;References;145
9;Survey of Recent Results on Weak Stability Boundariesand Applications;147
9.1;1 Introduction;147
9.2;2 Restricted Three-Body Problem Model;149
9.3;3 Determination of the Weak Stability Boundary;151
9.4;4 Chaos Associated with the Weak Stability Boundary and Parabolic Motion;154
9.5;5 Applications to Astronomy;157
9.5.1;5.1 Formation of the Moon;157
9.5.2;5.2 Minimal Energy Transfer of Material Between Planetary Systems;159
9.6;References;160
10;On the Accessibility of the Moon;162
10.1;1 Introduction;162
10.2;2 H-plot;164
10.3;3 SMD Transfers;166
10.4;4 A Lunar Satellite Constellation;167
10.5;5 Mars and Geostationary Missions;169
10.6;6 Concluding Remarks;170
10.7;References;171
11;Optimal Low-Thrust Trajectories to the Interior Earth-Moon Lagrange Point;173
11.1;1 Introduction;173
11.2;2 Governing Equations;175
11.3;3 Numerical Optimization Method;177
11.4;4 Generation of Periodic Orbits;179
11.4.1;4.1 Results;181
11.4.2;4.2 Comparison with Shooting Method;184
11.5;5 Low Thrust Transfer to a Periodic Orbit;187
11.5.1;5.1 Results;192
11.6;6 Conclusions;195
11.7;References;195
12;On the Use of the Earth-Moon Lagrangian Point L1 for Supporting the Manned Lunar Exploration;197
12.1;1 Introduction;197
12.2;2 Transfers Between the Earth and EML1;198
12.2.1;2.1 From the Earth to EML1;198
12.2.2;2.2 From EML1 to the Earth;200
12.3;3 Analysis of Orbital Evolution of Orbits Around EML1;203
12.4;4 Transfers Between EML1 and the Moon;204
12.4.1;4.1 From EML1 to the Lunar Surface;204
12.4.2;4.2 From the Lunar Surface to EML1;207
12.5;5 Summary;210
12.6;References;212
13;Manifolds and Radiation Protection;214
13.1;1 Introduction;214
13.2;2 Classification of Radiation;215
13.2.1;2.1 Ionizing:;215
13.2.2;2.2 Non-Ionizing:;216
13.3;3 Radiation in Space Missions;216
13.4;4 Monitoring Systems on ISS;217
13.5;5 Protecting Space Crews;217
13.6;References;218
14;Three-Body Invariant Manifold Transition with ElectricPropulsion;219
14.1;1 Introduction;219
14.2;2 Mathematical Fundamentals;220
14.2.1;2.1 Circular Restricted Three-Body Model;220
14.2.2;2.2 Reference System Transformation;222
14.2.3;2.3 Thrust Acceleration;223
14.3;3 Interplanetary Phase;223
14.3.1;3.1 Trajectory Optimization;224
14.3.2;3.2 Trajectory Conjunction;224
14.4;4 Uranian Tour;225
14.4.1;4.1 Approach;225
14.4.2;4.2 Tour Optimization;227
14.5;5 Results;228
14.5.1;5.1 Interplanetary Trajectory;228
14.5.2;5.2 Uranian Tour;232
14.6;6 Conclusions;236
14.7;References;237
15;From Sputnik to the Moon: Astrophysics and Cosmologyfrom Space;238
15.1;1 The Birth of Space Astrophysics;238
15.2;2 From Planck to the Moon;240
15.3;3 Why from the Moon;240
15.4;4 CMB Anisotropies;241
15.5;5 CMB Polarization Anisotropy Beyond Planck;242
15.6;6 Small Scale Anisotropy Generated by Sunyaev-Zeldovich Effects;244
15.7;7 A Concept Proposal for a Moon-Based Project Dedicated to CMB Polarization Anisotropy;245
15.8;8 CMB Spectrum;246
15.9;9 CMB Spectrum Beyond COBE/FIRAS;247
15.10;10 A Concept Proposal for a Moon-Based Experiment Dedicated to CMB Spectrum;249
15.11;References;251
16;Space Exploration: How Science and Economy may WorkTogether;253
16.1;1 Why Space Exploration?;253
16.2;2 Space Exploration as a Challenge and an Opportunity for Europe;254
16.3;3 The Importance of Public Awareness;254
16.4;4 The Impact of Science;256
16.5;5 Manned Space Exploration Constraints;257
16.6;6 Economy and Science;257
16.7;7 Conclusions;260
16.8;References;261
17;Index;262