Theory and Design Methods of Special Space Orbits

248 Pages·2017·8.161 MB·English

by  Yasheng Zhang, Yanli Xu, Haijun Zhou (auth.)

Yasheng Zhang · Yanli Xu
Haijun Zhou
Theory and
Design Methods
of Special Space
Orbits
Theory and Design Methods of Special Space Orbits
Yasheng Zhang Yanli Xu
(cid:129)
Haijun Zhou
Theory and Design Methods
of Special Space Orbits
123
Yasheng Zhang HaijunZhou
Department ofSpace Equipment Department ofSpace Equipment
Academy of Equipment Academy of Equipment
Beijing Beijing
China China
YanliXu
Department ofSpace Equipment
Academy of Equipment
Beijing
China
Fundedbythe B&R Program.
ISBN978-981-10-2947-9 ISBN978-981-10-2948-6 (eBook)
DOI 10.1007/978-981-10-2948-6
JointlypublishedwithNationalDefenseIndustryPress,Beijing,China
LibraryofCongressControlNumber:2016954624
Translation from the Chinese language edition: 空间特殊轨道理论与设计方法 by Yasheng Zhang,
YanliXuandHaijunZhou,©NationalDefenseIndustryPress2015.AllRightsReserved.
©NationalDefenseIndustryPressandSpringerNatureSingaporePteLtd.2017
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Preface
Aspaceorbitreferstotheroutealongwhichacelestialbodytravelsinspace.Itcan
also be called a trajectory or an orbit for short. Generally, there are three types,
namely,launchorbit,operationalorbit,andre-entryorbit.Itfollowsthatspaceorbit
theory is about the principles and methods that the design of a space orbit should
complywith,whileorbitdesignisoneofthekeytechnologiesinspacecraftsystem
design.
Orbit design needs to take many factors into consideration, such as orbit
dynamics, space environment, mission requirement, and capability of effective
payload,amongothers.Theoriesregardingorbitdesignwereproposedlongbefore
the first man-made satellite was launched into space.
With the growing demands in space application and the advancements in space
technology, classical orbit theories and design methods can no longer meet the
requirements of new space missions. There is an urgent need for new space orbit
theories which can effectively bring advanced space technology into full play.
Onthebasisofdecade-longresearchfindings,thisbookaimstoanswerthecall
of these new developments. There are eight chapters in this book. The first part
consists of the first two chapters, which are a general review of recursive orbit,
synchronous orbit, frozen orbit, stay orbit, and other classical orbits, together with
their design methods. Based on this review, the focus of this book, i.e., concepts,
types, and applications of special space orbits are introduced. The second part is
from chapter three to chapter eight. Each chapter is about a specific orbit, together
with its concepts, characteristics, design methods, and applications. So altogether,
there are six special space orbits which are elaborated, namely, hovering orbit,
spiral cruising orbit, multi-target rendezvous orbit, initiative approaching orbit,
responsive orbit, and earth pole-sitter orbit.
Thisbookisbasedonthefindingsofourresearchteamovertheyears.Wewant
to thank Profs. Zhi Li and Lei Wang, postgraduate students Xiaojing Xu, Yuanfei
Li, and Haijun Zhou, for their contributions to this book.
Theoriesofspaceorbitdesignarecloselyrelatedtootherfast-changingareasof
study and develop along with new space applications. The authors are fully aware
v
vi Preface
ofthelimitationsofthisbookandwarmlywelcomecommentsinordertoimprove
their work.
This book can be used as a technical reference for people engaged in the
strategic studies of space development and engineering applications. It can also be
used as a textbook for students majoring in space sciences and technologies.
Beijing, China Yasheng Zhang
January 2014
Contents
1 Overview of Classical Orbits ... .... .... .... .... .... ..... .... 1
1.1 Recursive Orbit.. .... ..... .... .... .... .... .... ..... .... 1
1.1.1 Recursive Orbit: Definition.... .... .... .... ..... .... 2
1.1.2 Different Orbital Periods.. .... .... .... .... ..... .... 2
1.1.3 Geostationary Earth Orbit and Its Applications. ..... .... 4
1.2 Sun-Synchronous Orbit..... .... .... .... .... .... ..... .... 5
1.2.1 Sun-Synchronous Orbit: Definition.. .... .... ..... .... 6
1.2.2 Sun-Synchronous Orbit: Characteristics... .... ..... .... 7
1.2.3 Sun-Synchronous Regression Orbit
and Its Applications . .... .... .... .... .... ..... .... 9
1.3 Frozen Orbit.... .... ..... .... .... .... .... .... ..... .... 10
1.3.1 Frozen Orbit: Definition .. .... .... .... .... ..... .... 10
1.3.2 Molniya Orbit and Its Applications.. .... .... ..... .... 12
1.4 Stay Orbit.. .... .... ..... .... .... .... .... .... ..... .... 13
1.4.1 Stay Orbit: Definition .... .... .... .... .... ..... .... 13
1.4.2 Stay Orbit: Applications .. .... .... .... .... ..... .... 15
1.5 Summary .. .... .... ..... .... .... .... .... .... ..... .... 17
2 Special Space Orbit: Concept and Application. .... .... ..... .... 19
2.1 Special Space Orbit: Concept.... .... .... .... .... ..... .... 19
2.1.1 Differences in Orbit Design Concepts.... .... ..... .... 20
2.1.2 Coupling of Orbit Control and Orbit Design... ..... .... 21
2.1.3 Requirements for Special Space Application... ..... .... 23
2.2 Types of Special Orbit ..... .... .... .... .... .... ..... .... 25
2.2.1 Hovering Orbit ..... .... .... .... .... .... ..... .... 25
2.2.2 Cruising Orbit. ..... .... .... .... .... .... ..... .... 25
2.2.3 Multi-Target Rendezvous Orbit. .... .... .... ..... .... 28
2.2.4 Initiative Approaching Orbit... .... .... .... ..... .... 29
2.2.5 Fast Responsive Orbit.... .... .... .... .... ..... .... 31
2.2.6 Earth Pole-Sitter Orbit.... .... .... .... .... ..... .... 31
vii
viii Contents
2.3 Description of Special Space Orbit.... .... .... .... ..... .... 32
2.3.1 Orbit Element. ..... .... .... .... .... .... ..... .... 32
2.3.2 Non Singularity Orbit Elements .... .... .... ..... .... 33
2.3.3 Rectangular Coordinate Component . .... .... ..... .... 34
2.4 Summary .. .... .... ..... .... .... .... .... .... ..... .... 35
3 Theory and Design Method of Hovering Orbit. .... .... ..... .... 37
3.1 Hovering Orbit: Concept ... .... .... .... .... .... ..... .... 37
3.2 Design of Fixed-Point Hovering Orbit . .... .... .... ..... .... 38
3.2.1 Dynamic Model .... .... .... .... .... .... ..... .... 39
3.2.2 Open-Loop Control.. .... .... .... .... .... ..... .... 47
3.2.3 Closed Loop Control. .... .... .... .... .... ..... .... 52
3.3 Design of Regional Hovering Orbit ... .... .... .... ..... .... 56
3.3.1 Analysis of Confined Area Configuration. .... ..... .... 56
3.3.2 Control of Regional Hovering Orbit . .... .... ..... .... 63
3.3.3 Regional Hovering Orbit of Single-Pulse Trust. ..... .... 76
3.3.4 Regional Hovering Orbit of Multi-Pulse Trust . ..... .... 82
3.4 Design of Displaced Geostationary Orbit ... .... .... ..... .... 83
3.4.1 Displaced Orbit Deviating from Orbit Plane... ..... .... 86
3.4.2 Displaced Orbit in Orbit Plane . .... .... .... ..... .... 88
3.4.3 Energy Analysis of Orbit Displacement .. .... ..... .... 88
3.5 Summary .. .... .... ..... .... .... .... .... .... ..... .... 90
4 Theory and Design Method of Spiral Cruising Orbit.... ..... .... 91
4.1 Spiral Cruising Orbit: Concept... .... .... .... .... ..... .... 91
4.2 Precision Analysis of Relative Motion Model ... .... ..... .... 94
4.2.1 Accurate Relative Motion Dynamics Equation . ..... .... 94
4.2.2 Simplification of Relative Motion Dynamics Equation .... 96
4.2.3 Precision Analysis of Relative Motion Dynamics
Model... .... ..... .... .... .... .... .... ..... .... 98
4.2.4 Analysis of Relative Motion Dynamics Model
of Cruising Spacecraft.... .... .... .... .... ..... .... 99
4.3 Traversal Cruising Orbit: Design . .... .... .... .... ..... .... 103
4.3.1 Design Method Based on Hill Equation .. .... ..... .... 104
4.3.2 Design Method Based on E/I Vector Method.. ..... .... 106
4.3.3 Design Constraint ... .... .... .... .... .... ..... .... 107
4.3.4 Simulation Analysis . .... .... .... .... .... ..... .... 110
4.4 Design of the Round-Trip Itinerant Orbit... .... .... ..... .... 114
4.4.1 Design Method..... .... .... .... .... .... ..... .... 114
4.4.2 Design Constraints .. .... .... .... .... .... ..... .... 117
4.4.3 Simulation Analysis . .... .... .... .... .... ..... .... 118
4.5 Controllable Cruising Orbit: Design... .... .... .... ..... .... 121
4.5.1 Spiral Ring: Design.. .... .... .... .... .... ..... .... 122
4.5.2 Entry Corridor: Design ... .... .... .... .... ..... .... 124
4.5.3 Single-Pulse Control Strategy.. .... .... .... ..... .... 127
Contents ix
4.5.4 Fast Cruising Control Strategy . .... .... .... ..... .... 133
4.6 Summary .. .... .... ..... .... .... .... .... .... ..... .... 137
5 Theory and Design Method of Multi-Target Rendezvous
Orbit Based on Traversing Points ... .... .... .... .... ..... .... 139
5.1 Multi-Target Orbital Rendezvous: Problem Description ..... .... 139
5.2 Traversing Point: Concept and Determination Method. ..... .... 142
5.2.1 Traversing Point: Concept. .... .... .... .... ..... .... 142
5.2.2 Traversing Point: Determination Method.. .... ..... .... 144
5.3 Orbital Rendezvous: Strategies Based on Traversing Point... .... 147
5.3.1 Design Principles Based on Traversing Point .. ..... .... 147
5.3.2 Rendezvous Orbit: Design Method.. .... .... ..... .... 148
5.3.3 Orbital Rendezvous: Control Method .... .... ..... .... 150
5.4 Non-Coplanar Homogeneous Multi-Target Rendezvous
Orbit: Design Method. ..... .... .... .... .... .... ..... .... 153
5.5 Non-Coplanar Heterogeneous Multi-Target Rendezvous
Orbit: Design Method. ..... .... .... .... .... .... ..... .... 157
5.5.1 Design Procedures... .... .... .... .... .... ..... .... 158
5.5.2 Rendezvous Orbit: Design Method.. .... .... ..... .... 158
5.5.3 Traversing Point Set: Determination Method... ..... .... 161
5.5.4 Rendezvous Trajectory: Design Method .. .... ..... .... 162
5.6 Simulation Analysis and Method Correction. .... .... ..... .... 166
5.6.1 Simulation of Orbital Rendezvous Based
on Traversing Point.. .... .... .... .... .... ..... .... 166
5.6.2 Method Correction of Orbital Rendezvous Based
on Traversing Point.. .... .... .... .... .... ..... .... 169
5.7 Summary .. .... .... ..... .... .... .... .... .... ..... .... 173
6 Theory and Design Method of Initiative Approaching Orbit... .... 175
6.1 Initiative Approaching Orbit: Concept . .... .... .... ..... .... 175
6.2 Approaching Orbit: Design.. .... .... .... .... .... ..... .... 176
6.2.1 Phasing Orbit . ..... .... .... .... .... .... ..... .... 176
6.2.2 Short-Range Approaching Orbit .... .... .... ..... .... 180
6.3 Dynamics Model of Relative Position and Attitude ... ..... .... 181
6.3.1 Dynamics Model of Relative Attitude.... .... ..... .... 182
6.3.2 Dynamics Model of Relative Position.... .... ..... .... 184
6.4 Ultimate Approaching Orbit: Design .. .... .... .... ..... .... 187
6.4.1 The Final Approach for Three-Axis-Stabilized
Target Spacecraft ... .... .... .... .... .... ..... .... 187
6.4.2 Final Approach to the Target Without Attitude
Control .. .... ..... .... .... .... .... .... ..... .... 191
6.4.3 Simulation and Realization.... .... .... .... ..... .... 194
6.5 Summary .. .... .... ..... .... .... .... .... .... ..... .... 196
x Contents
7 Theory and Design Method of Responsive Orbit ... .... ..... .... 199
7.1 Fast Responsive Orbit: Concept .. .... .... .... .... ..... .... 199
7.2 Circular Fast Flying-Around Orbit .... .... .... .... ..... .... 203
7.2.1 Circular Fast Flying-Around Orbit: Design.... ..... .... 203
7.2.2 Target Forbidden Zone: Definition .. .... .... ..... .... 208
7.2.3 Safety Analysis..... .... .... .... .... .... ..... .... 209
7.3 Fast Access Orbit.... ..... .... .... .... .... .... ..... .... 218
7.3.1 Low-Earth-Orbit Fast Access Orbit: Design ... ..... .... 219
7.3.2 Cobra Orbit: Design . .... .... .... .... .... ..... .... 221
7.4 Summary .. .... .... ..... .... .... .... .... .... ..... .... 223
8 Theory and Design Method of Earth Pole-Sitter Orbit .. ..... .... 225
8.1 Earth Pole-Sitter Orbit: Concept.. .... .... .... .... ..... .... 225
8.2 Earth Pole-Sitter Orbit: Design Method .... .... .... ..... .... 226
8.2.1 Dynamic Model in Circular Restricted Three-Body
Problem.. .... ..... .... .... .... .... .... ..... .... 226
8.2.2 Design of Earth Pole-Sitter Orbit with Fixed
Residence Distance.. .... .... .... .... .... ..... .... 228
8.2.3 Design of Earth Pole-Sitter Orbit with Unfixed
Residence Distance.. .... .... .... .... .... ..... .... 230
8.3 Optimization Design of Earth Pole-Sitter Orbit... .... ..... .... 233
8.4 Summary .. .... .... ..... .... .... .... .... .... ..... .... 235
Appendix A: Optimization Design of Rendezvous Orbit
with MATLAB . ..... .... .... .... .... .... ..... .... 237
References.... .... .... .... ..... .... .... .... .... .... ..... .... 243