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E-raamat: Low-Energy Lunar Trajectory Design

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Based on years of research conducted at the NASA Jet Propulsion Laboratory, Low-Energy Lunar Trajectory Design provides high-level information to mission managers and detailed information to mission designers about low-energy transfers between Earth and the moon. The book answers high-level questions about the availability and performance of such transfers in any given month and year. Low-energy lunar transfers are compared with various other types of transfers, and placed within the context of historical missions.

Using this book, designers may reconstruct any transfer described therein, as well as design similar transfers with particular design parameters.

An Appendix, Locating the Lagrange Points, and a useful list of terms and constants completes this technical reference.





Surveys thousands of possible trajectories that may be used to transfer spacecraft between Earth and the moon, including transfers to lunar libration orbits, low lunar orbits, and the lunar surface Provides information about the methods, models, and tools used to design low-energy lunar transfers Includes discussion about the variations of these transfers from one month to the next, and the important operational aspects of implementing a low-energy lunar transfer Additional discussions address navigation, station-keeping, and spacecraft systems issues
Foreword xi
Preface xiii
Acknowledgments xv
Authors xxi
1 Introduction and Executive Summary
1(26)
1.1 Purpose
1(1)
1.2 Organization
1(1)
1.3 Executive Summary
2(9)
1.3.1 Direct, Conventional Transfers
5(1)
1.3.2 Low-Energy Transfers
6(1)
1.3.3 Summary: Low-Energy Transfers to Lunar Libration Orbits
7(1)
1.3.4 Summary: Low-Energy Transfers to Low Lunar Orbits
8(2)
1.3.5 Summary: Low-Energy Transfers to the Lunar Surface
10(1)
1.4 Background
11(1)
1.5 The Lunar Transfer Problem
12(2)
1.6 Historical Missions
14(9)
1.6.1 Missions Implementing Direct Lunar Transfers
15(1)
1.6.2 Low-Energy Missions to the Sun-Earth Lagrange Points
15(5)
1.6.3 Missions Implementing Low-Energy Lunar Transfers
20(3)
1.7 Low-Energy Lunar Transfers
23(4)
2 Methodology
27(90)
2.1 Methodology Introduction
27(1)
2.2 Physical Data
28(1)
2.3 Time Systems
29(3)
2.3.1 Dynamical Time, ET
29(1)
2.3.2 International Atomic Time, TAI
29(1)
2.3.3 Universal Time, UT
30(1)
2.3.4 Coordinated Universal Time, UTC
30(1)
2.3.5 Lunar Time
30(1)
2.3.6 Local True Solar Time, LTST
31(1)
2.3.7 Orbit Local Solar Time, OLST
31(1)
2.4 Coordinate Frames
32(3)
2.4.1 EME2000
32(1)
2.4.2 EMO2000
33(1)
2.4.3 Principal Axis Frame
33(1)
2.4.4 IAU Frames
33(1)
2.4.5 Synodic Frames
34(1)
2.5 Models
35(6)
2.5.1 CRTBP
36(3)
2.5.2 Patched Three-Body Model
39(1)
2.5.3 JPL Ephemeris
40(1)
2.6 Low-Energy Mission Design
41(73)
2.6.1 Dynamical Systems Theory
42(1)
2.6.2 Solutions to the CRTBP
43(6)
2.6.3 Poincare Maps
49(1)
2.6.4 The State Transition and Monodromy Matrices
50(2)
2.6.5 Differential Correction
52(15)
2.6.6 Constructing Periodic Orbits
67(7)
2.6.7 The Continuation Method
74(3)
2.6.8 Orbit Stability
77(4)
2.6.9 Examples of Practical Three-Body Orbits
81(5)
2.6.10 Invariant Manifolds
86(9)
2.6.11 Orbit Transfers
95(11)
2.6.12 Building Complex Orbit Chains
106(7)
2.6.13 Discussion
113(1)
2.7 Tools
114(3)
2.7.1 Numerical Integrators
114(1)
2.7.2 Optimizers
114(1)
2.7.3 Software
115(2)
3 Transfers to Lunar Libration Orbits
117(110)
3.1 Executive Summary
117(3)
3.2 Introduction
120(2)
3.3 Direct Transfers Between Earth and Lunar Libration Orbits
122(39)
3.3.1 Methodology
122(3)
3.3.2 The Perigee-Point Scenario
125(2)
3.3.3 The Open-Point Scenario
127(3)
3.3.4 Surveying Direct Lunar Halo Orbit Transfers
130(22)
3.3.5 Discussion of Results
152(5)
3.3.6 Reducing the AV Cost
157(1)
3.3.7 Conclusions
158(3)
3.4 Low-Energy Transfers Between Earth and Lunar Libration Orbits
161(60)
3.4.1 Modeling a Low-Energy Transfer using Dynamical Systems Theory
163(6)
3.4.2 Energy Analysis of a Low-Energy Transfer
169(8)
3.4.3 Constructing a Low-Energy Transfer in the Patched Three-Body Model
177(6)
3.4.4 Constructing a Low-Energy Transfer in the Ephemeris Model of the Solar System
183(4)
3.4.5 Families of Low-Energy Transfers
187(3)
3.4.6 Monthly Variations in Low-Energy Transfers
190(18)
3.4.7 Transfers to Other Three-Body Orbits
208(13)
3.5 Three-Body Orbit Transfers
221(6)
3.5.1 Transfers from an LL2 Halo Orbit to a Low Lunar Orbit
224(3)
4 Transfers to Low Lunar Orbits
227(36)
4.1 Executive Summary
227(2)
4.2 Introduction
229(2)
4.3 Direct Transfers Between Earth and Low Lunar Orbit
231(2)
4.4 Low-Energy Transfers Between Earth and Low Lunar Orbit
233(25)
4.4.1 Methodology
233(2)
4.4.2 Example Survey
235(4)
4.4.3 Arriving at a First-Quarter Moon
239(7)
4.4.4 Arriving at a Third-Quarter Moon
246(4)
4.4.5 Arriving at a Full Moon
250(3)
4.4.6 Monthly Trends
253(4)
4.4.7 Practical Considerations
257(1)
4.4.8 Conclusions for Low-Energy Transfers Between Earth and Low Lunar Orbit
258(1)
4.5 Transfers Between Lunar Libration Orbits and Low Lunar Orbits
258(1)
4.6 Transfers Between Low Lunar Orbits and the Lunar Surface
258(5)
5 Transfers to the Lunar Surface
263(36)
5.1 Executive Summary
263(2)
5.2 Introduction for Transfers to the Lunar Surface
265(2)
5.3 Methodology
267(1)
5.4 Analysis of Planar Transfers between the Earth and the Lunar Surface
268(9)
5.5 Low-Energy Spatial Transfers Between the Earth and the Lunar Surface
277(17)
5.5.1 Trajectories Normal to the Surface
277(10)
5.5.2 Trajectories Arriving at Various Angles to the Lunar Surface
287(7)
5.6 Transfers Between Lunar Libration Orbits and the Lunar Surface
294(4)
5.7 Transfers Between Low Lunar Orbits and the Lunar Surface
298(1)
5.8 Conclusions Regarding Transfers to the Lunar Surface
298(1)
6 Operations
299(52)
6.1 Operations Executive Summary
299(1)
6.2 Operations Introduction
300(1)
6.3 Launch Sites
301(1)
6.4 Launch Vehicles
301(3)
6.5 Designing a Launch Period
304(28)
6.5.1 Low-Energy Launch Periods
305(2)
6.5.2 An Example Mission Scenario
307(4)
6.5.3 Targeting Algorithm
311(5)
6.5.4 Building a Launch Period
316(1)
6.5.5 Reference Transfers
317(1)
6.5.6 Statistical Costs of Desirable Missions to Low Lunar Orbit
317(8)
6.5.7 Varying the LEO Inclination
325(3)
6.5.8 Targeting a Realistic Mission to Other Destinations
328(3)
6.5.9 Launch Period Design Summary
331(1)
6.6 Navigation
332(17)
6.6.1 Launch Targets
333(1)
6.6.2 Station-Keeping
333(16)
6.7 Spacecraft Systems Design
349(2)
Appendix A Locating the Lagrange Points
351(8)
A.1 Introduction
351(1)
A.2 Setting Up the System
351(2)
A.3 Triangular Points
353(1)
A.4 Collinear Points
354(3)
A.4.1 Case 132: Identifying the Li point
355(1)
A.4.2 Case 123: Identifying the L2 point
355(1)
A.4.3 Case 312: Identifying the L3 point
356(1)
A.5 Algorithms
357(2)
A.5.1 Numerical Determination of L1
357(1)
A.5.2 Numerical Determination of L2
358(1)
A.5.3 Numerical Determination of L3
358(1)
References 359(18)
Terms 377(5)
Constants 382
Jeffrey S. Parker, Ph.D., was a member of the technical staff at the Jet Propulsion Laboratory (JPL) from 2008 to 2012. Currently Dr. Parker is an Assistant Professor of Astrodynamics at CU-Boulder. His research interests are focused on astrodynamics, space exploration, and autonomous spacecraft operations.

Rodney L. Anderson, Ph.D., is a member of the JPL technical staff, where he is involved in mission design and navigation and develops new methods for trajectory design. His research interests are focused on the application of dynamical systems theory to astrodynamics and mission design.
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