Low-Energy Lunar Trajectory Design E-Book

Jeffrey S. Parker

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: JPL Deep-Space Communications and Navigation Series
• Sprache: Englisch

Seitenzahl: 573

Veröffentlichungsjahr: 2014

Beschreibung

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

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Foreword

Preface

Acknowledgments

Authors

Chapter 1: Introduction And Executive Summary

1.1 Purpose

1.2 Organization

1.3 Executive Summary

1.4 Background

1.5 The Lunar Transfer Problem

1.6 Historical Missions

1.7 Low-Energy Lunar Transfers

Chapter 2: Methodology

2.1 Methodology Introduction

2.2 Physical Data

2.3 Time Systems

2.4 Coordinate Frames

2.5 Models

2.6 Low-Energy Mission Design

2.7 Tools

Chapter 3: Transfers To Lunar Libration Orbits

3.1 Executive Summary

3.2 Introduction

3.3 Direct Transfers Between Earth And Lunar Libration Orbits

3.4 Low-Energy Transfers Between Earth And Lunar Libration Orbits

3.5 Three-Body Orbit Transfers

Chapter 4: Transfers To Low Lunar Orbits

4.1 Executive Summary

4.2 Introduction

4.3 Direct Transfers Between Earth And Low Lunar Orbit

4.4 Low-Energy Transfers Between Earth And Low Lunar Orbit

4.5 Transfers Between Lunar Libration Orbits And Low Lunar Orbits

4.6 Transfers Between Low Lunar Orbits And The Lunar Surface

Chapter 5: Transfers To The Lunar Surface

5.1 Executive Summary

5.2 Introduction For Transfers To The Lunar Surface

5.3 Methodology

5.4 Analysis Of Planar Transfers Between The Earth And The Lunar Surface

5.5 Low-Energy Spatial Transfers Between The Earth And The Lunar Surface

5.6 Transfers Between Lunar Libration Orbits And The Lunar Surface

5.7 Transfers Between Low Lunar Orbits And The Lunar Surface

5.8 Conclusions Regarding Transfers To The Lunar Surface

Chapter 6: Operations

6.1 Operations Executive Summary

6.2 Operations Introduction

6.3 Launch Sites

6.4 Launch Vehicles

6.5 Designing A Launch Period

6.6 Navigation

6.7 Spacecraft Systems Design

Appendix A: Locating the Lagrange Points

A.1 Introduction

A.2 Setting Up The System

A.3 Triangular Points

A.4 Collinear Points

A.5 Algorithms

References

Terms

Constants

Index

Low-Energy Lunar Trajectory Design

DEEP-SPACE COMMUNICATIONS AND NAVIGATION SERIES

The Deep-Space Communications and Navigation Systems Center of Excellence Jet Propulsion Laboratory California Institute of Technology

Joseph H. Yuen, Editor-in-Chief

Published Titles in this Series

Radiometric Tracking Techniques for Deep-Space Navigation C. L. Thornton and J. S. Border

Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation Theodore D. Moyer

Bandwidth-Efficient Digital Modulation with Application to Deep-Space Communications Marvin K. Simon

Large Antennas of the Deep Space Network William A. Imbriale

Antenna Arraying Techniques in the Deep Space Network David H. Rogstad, Alexander Mileant, and Timothy T. Pham

Radio Occultations Using Earth Satellites: A Wave Theory Treatment William G. Melbourne

Deep Space Optical Communications Hamid Hemmati

Spaceborne Antennas for Planetary Exploration William A. Imbriale, Editor

Autonomous Software-Defined Radio Receivers for Deep Space Applications Jon Hamkins and Marvin K. Simon, Editors

Low-Noise Systems in the Deep Space Network Macgregor S. Reid, Editor

Coupled-Oscillator Based Active-Array Antennas Ronald J. Pogorzelski and Apostolos Georgiadis

Low-Energy Lunar Trajectory Design Jeffrey S. Parker and Rodney L. Anderson

Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Parker, Jeffrey S.   Low-energy lunar trajectory design / Jeffrey S. Parker and Rodney L. Anderson.       pages cm   Includes index.   ISBN 978-1-118-85387-0 (cloth) 1. Lunar probes—Trajectories. 2. Space flight to the moon—Cost control. I. Anderson, Rodney L. II. Title.   TL1075.P37 2014   629.4’11—dc23

2014001158

Jeffrey Parker:

I dedicate the majority of this book to my wife Jen, my best friend and greatest support throughout the development of this book and always. I dedicate the appendix to my son Cameron, who showed up right at the end.

Rodney Anderson:

I dedicate this book to my wife Brooke for her endless support and encouragement.

We both thank our families and friends for their support throughout the process.

FOREWORD

The Deep Space Communications and Navigation Systems Center of Excellence (DESCANSO) was established in 1998 by the National Aeronautics and Space Administration (NASA) at the California Institute of Technology’s Jet Propulsion Laboratory (JPL). DESCANSO is chartered to harness and promote excellence and innovation to meet the communications and navigation needs of future deep-space exploration.

DESCANSO’s vision is to achieve continuous communications and precise navigation—any time, anywhere. In support of that vision, DESCANSO aims to seek out and advocate new concepts, systems, and technologies; foster key technical talents; and sponsor seminars, workshops, and symposia to facilitate interaction and idea exchange.

The Deep Space Communications and Navigation Series, authored by scientists and engineers with many years of experience in their respective fields, lays a foundation for innovation by communicating state-of-the-art knowledge in key technologies. The series also captures fundamental principles and practices developed during decades of deep-space exploration at JPL. In addition, it celebrates successes and imparts lessons learned. Finally, the series will serve to guide a new generation of scientists and engineers.

Joseph H. Yuen, DESCANSO Leader

PREFACE

The purpose of this book is to provide high-level information to mission managers and detailed information to mission designers about low-energy transfers between the Earth and the Moon. This book surveys thousands of trajectories that one can use to transfer spacecraft between the Earth and various locations near the Moon, including lunar libration orbits, low lunar orbits, and the lunar surface. These surveys include conventional, direct transfers that require 3–6 days as well as more efficient, low-energy transfers that require more transfer time but which require less fuel. Low-energy transfers have been shown to be very useful in many circumstances and have recently been used to send satellites to the Moon, including the two ARTEMIS spacecraft and the two GRAIL spacecraft. This book illuminates the trade space of low-energy transfers and illustrates the techniques that may be used to build them.

ACKNOWLEDGMENTS

We would like to thank many people for their support writing this book, including people who have written or reviewed portions of the text, as well as people who have provided insight from years of experience flying spacecraft missions to the Moon and elsewhere. It is with sincere gratitude that we thank Ted Sweetser for his selfless efforts throughout this process, providing the opportunity for us to perform this work, and reviewing each section of this manuscript as it has come together. We would like to thank A1 Cangahuala, Joe Guinn, Roby Wilson, and Amy Attiyah for their valuable feedback and thorough review of this work in each of its stages. We would also like to thank Tim McElrath for his feedback, insight, and excitement as we considered different aspects of this research.

We would like to give special thanks to several people who provided particular contributions to sections of the book. We thank Ralph Roncoli for his assistance with Sections 2.3 and 2.4, as well as his feedback throughout the book. Kate Davis assisted with Sections 2.6.3 and 2.6.11.3, most notably with the discussions of Poincaré sections. Roby Wilson provided particular assistance with Section 2.6.5 on the subject of the multiple shooting differential corrector. We would like to sincerely thank Andrew Peterson for his contribution to the development of Chapter 4. Finally, George Born and Martin Lo provided guidance for this research as it developed in its early stages, leading to the authors’ dissertations at the University of Colorado at Boulder.

Jeffrey Parker’s Ph.D. dissertation (J. S. Parker, Low-Energy Ballistic Lunar Transfers, Ph.D. Thesis, University of Colorado, Boulder, 2007) provides the backbone to this manuscript and much of the dissertation has been repeated and amplified in this book. Much of the additional material that appears in this manuscript has been presented by the authors at conferences and published in journals. Such material has been reprinted here, with some significant alterations and additions. Finally, a number of additional journal articles and conference proceedings directly contributed to each chapter in the following list. In addition to the listing below, they are cited in the text where the related material appears.

Chapter 2:

J. S. Parker, K. E. Davis, and G. H. Born, “Chaining Periodic Three-Body Orbits in the Earth–Moon System,” ACTA Astronautica, vol. 67, pp. 623–638, 2010.M. W. Lo, and J. S. Parker, “Chaining Simple Periodic Three-Body Orbits,” AAS/AIAA Astrodynamics Specialist Conference (Lake Tahoe, California), Paper No. AAS 2005-380, August 7–11, 2005, vol. 123, Advances in Astronautical Sciences (B. G. Williams, L. A. D’Amario, K. C. Howell, and F. R. Hoots, editors), AAS/AIAA, Univelt Inc., San Diego, CA, 2006.R. B. Roncoli, Lunar Constants and Models Document, JPL D-32296 (internal document), Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, September 23, 2005.R. L. Anderson and J. S. Parker, “Survey of Ballistic Transfers to the Lunar Surface,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 4, pp. 1256–1267, July–August 2012.

Chapter 3:

J. S. Parker, “Monthly Variations of Low-Energy Ballistic Transfers to Lunar Halo Orbits,” AIAA/AAS Astrodynamics Specialist Conference, (Toronto, Ontario, Canada), Paper No. AIAA 2010-7963, August 2–5, 2010.J. S. Parker, “Targeting Low-Energy Ballistic Lunar Transfers,” AAS George H. Born Special Symposium, (Boulder, Colorado), May 13–14, 2010, American Astronautical Society, 2010.J. S. Parker, “Targeting Low-Energy Ballistic Lunar Transfers,” Journal of Astronautical Sciences, vol. 58, no. 3, pp. 311–334, July–September, 2011.J. S. Parker, “Low-Energy Ballistic Transfers to Lunar Halo Orbits,” AAS/AIAA Astrodynamics Specialist Conference, (Pittsburgh, Pennsylvania, Paper No. AAS 09-443, August 9–13, 2009, Advances in Astronautical Sciences, Astrodynamics 2009 (A. V. Rao, A. Lovell, F. K. Chan, and L. A. Cangahuala, editors), vol. 135, pp. 2339–2358, 2010.J. S. Parker, and G. H. Born, “Modeling a Low-Energy Ballistic Lunar Transfer Using Dynamical Systems Theory,” AIAA Journal of Spacecraft and Rockets, vol. 45, no. 6, pp. 1269–1281, November–December 2008.J. S. Parker and G. H. Born, “Direct Lunar Halo Orbit Transfers,” Journal of the Astronautical Sciences, vol. 56, issue 4, pp. 441–476, October–December 2008.J. S. Parker and G. H. Born, “Direct Lunar Halo Orbit Transfers,” AAS/AIAA Spaceflight Mechanics Conference (Sedona, Arizona, January 28–February 1, 2007), Paper No. AAS 07-229, Advances in Astronautical Science, vol. 127, pp. 1923–1945, 2007.J. S. Parker, “Families of Low-Energy Lunar Halo Transfers,” AAS/AIAA Spaceflight Dynamics Conference, (Tampa, Florida, January 22–26, 2006) Paper No. AAS 06-132, (S. R. Vadali, L. A. Cangahuala, J. P. W. Schumacher, and J. J. Guzman, editors), vol. 124 of Advances in Astronautical Sciences, San Diego, CA, AAS/AIAA, Univelt Inc., 2006.J. S. Parker and M. W. Lo, “Shoot the Moon 3D,” Paper AAS 05-383, AAS/AIAA Astrodynamics Conference held August 7–10, 2005, South Lake Tahoe, California, (originally published in) AAS publication, Astrodynamics 2005 (edited by B. G. Williams, L. A. D’Amario, K. C. Howell, and F. R. Hoots) American Astronautical Society (AAS) Advances in the Astronautical Sciences, vol. 123, pp. 2067–2086, 2006, American Astronautical Society Publications Office, San Diego, California (Web Site: http://www.univelt.com), pp. 2067–2086.

Chapter 4:

J. S. Parker and R. L. Anderson, “Targeting Low-Energy Transfers to Low Lunar Orbit,” Astrodynamics: Proceedings of the 2011 AAS/AIAA Astrodynamics Specialist Conference, (Girdwood, Alaska, July 31–August 4), Paper AAS 11-459, edited by H. Schaub, B. C. Gunter, R. P. Russell, and W. T. Cerven, Vol. 142, Advances in the Astronautical Sciences, American Astronautical Society, Univelt Inc., San Diego, California, pp. 847–866, 2012.J. S. Parker, R. L. Anderson, and A. Peterson, “A Survey of Ballistic Transfers to Low Lunar Orbit,” 21st AAS/AIAA Space Flight Mechanics Meeting, (February 13–17, 2011, New Orleans, Louisiana), Paper AAS 11-277, Vol. 140, Advances in the Astronautical Sciences (edited by M. K. Jah, Y. Guo, A. L. Bowes, and P. C. Lai), American Astronautical Society, Univelt Inc., San Diego, California, pp. 2461–2480, 2011.

Chapter 5:

R. L. Anderson, and J. S. Parker, “Survey of Ballistic Transfers to the Lunar Surface,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 4, pp. 1256–1267, July–August 2012.R. L. Anderson and J. S. Parker, “Comparison of Low-Energy Lunar Transfer Trajectories to Invariant Manifolds,” Celestial Mechanics and Dynamical Astronomy, vol. 115, DOI 10.10075 10569-012-9466-3, pp. 311–331, published online February 16, 2013.R. L. Anderson, and J. S. Parker, “Comparison of Low-Energy Lunar Transfer Trajectories to Invariant Manifolds,” AAS/AIAA Astrodynamics Specialist Conference (Girdwood, Alaska, July 31–August 4, 2011), Paper AAS 11-423, edited by H. Schaub, B. C. Gunter, R. P. Russell, and W. T. Cerven, Vol. 142, Advances in the Astronautical Sciences, American Astronautical Society, Univelt Inc., San Diego, California, pp. 333–352, 2012.R. L. Anderson, and J. S. Parker, “A Survey of Ballistic Transfers to the Lunar Surface,” Proceedings of the 21st AAS/AIAA Space Flight Mechanics Meeting (New Orleans, Louisiana, February 13–17, 2011), Paper AAS 11-278, edited by M. K. Jah, Y. Guo, A. L. Bowes, and P. C. Lai, Vol. 140, Advances in the Astronautical Sciences, vol. 140, American Astronautical Society, Univelt Inc., San Diego, California, pp. 2481–2500, 2011.

Chapter 6:

J. S. Parker, “Targeting Low-Energy Ballistic Lunar Transfers,” Journal of Astronautical Sciences, vol. 58, no. 3, pp. 311–334, July–September, 2011.J. S. Parker and R. L. Anderson, “Targeting Low-Energy Transfers to Low Lunar Orbit,” Astrodynamics 2011: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference (Girdwood, Alaska, July 31–August 4, 2011), Paper AAS 11-459, edited by H. Schaub, B. C. Gunter, R. P. Russell, and W. T. Cerven, Vol. 142, Advances in the Astronautical Sciences, American Astronautical Society, Univelt Inc., San Diego, California, pp. 847–866, 2012.J. S. Parker, “Targeting Low-Energy Ballistic Lunar Transfers,” AAS 09-443, AAS George H. Born Special Symposium (Boulder, Colorado, May 13–14), American Astronautical Society, 2010.

A large portion of the research in this book, and the compilation of related research documentation from other sources, were carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This work has been supported through funding by the Multi-mission Ground System and Services Office (MGSS) in support of the development of the Advanced Multi-Mission Operations System (AMMOS).

Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not constitute or imply its endorsement by the United States Government or the Jet Propulsion Laboratory, California Institute of Technology.

Jeffrey S. Parker & Rodney L. Anderson

AUTHORS

Jeffrey S. Parker received his B.A. in 2001 in physics and astronomy from Whitman College (Walla Walla, Washington) and his M.S. and Ph.D. in aerospace engineering sciences from the University of Colorado at Boulder in 2003 and 2007, respectively. Dr. Parker was a member of the technical staff at the Jet Propulsion Laboratory (JPL) from January 2008 to June 2012. While at JPL he supported spacecraft exploration as a mission design and navigation specialist. He worked both as a spacecraft mission designer and as a navigator on the GRAIL mission, which sent two spacecraft to the Moon via low-energy ballistic lunar transfers. He supported India’s Chandrayaan-1 mission to the Moon, also as a mission designer and spacecraft navigator. Dr. Parker led the mission design development for numerous design studies and mission proposals, including missions to the Moon, near-Earth objects, the nearby Lagrange points, and most of the planets in the Solar System. At present, Dr. Parker is an assistant professor of astrodynamics at the University of Colorado at Boulder, teaching graduate and undergraduate courses in many subjects related to space exploration. His research interests are focused on astrodynamics and the exploration of space, including the design of low-energy trajectories in the Solar System, the optimization of low-thrust trajectories in the Solar System, autonomous spacecraft operations, and use of these engineering tools to provide new ways to achieve scientific objectives.

Rodney L. Anderson received his B.S. in 1997 in aerospace engineering from North Carolina State University at Raleigh and his M.S. and Ph.D. in aerospace engineering sciences from the University of Colorado at Boulder in 2001 and 2005, respectively. Upon the completion of his Ph.D., he worked as a research associate at the University of Colorado at Boulder, conducting a study for the U.S. Air Force that focused on understanding the effects of atmospheric density variations on orbit predictions. Dr. Anderson has been a member of the JPL technical staff since 2010, where he has participated in mission design and navigation for multiple missions, and continues to work on the development of new methods for trajectory design. His research interests are concentrated on the application of dynamical systems theory to astrodynamics and mission design. Some specific applications that he has focused on are the design of lunar trajectories, tour and endgame design in the Jovian system using heteroclinic connections, missions to near-Earth asteroids, and low-energy trajectories in multi-body systems. He has worked closely with multiple universities and has taught at both the University of Colorado at Boulder and the University of Southern California, with an emphasis on the intersection of dynamical systems theory with astrodynamics.

CHAPTER 1

INTRODUCTION AND EXECUTIVE SUMMARY

1.1 PURPOSE

This book provides sufficient information to answer high-level questions about the availability and performance of low-energy transfers between the Earth and Moon in any given month and year. Details are provided to assist in the construction of desirable low-energy transfers to various destinations on the Moon, including low lunar orbits, halo and other three-body orbits, and the lunar surface. Much of the book is devoted to surveys that characterize many examples of transfers to each of these destinations.

1.2 ORGANIZATION

This document is organized in the following manner. The remainder of this chapter first provides an executive summary of this book, presenting an overview of low-energy lunar transfers and comparing them with various other modes of transportation from near the Earth to lunar orbit or the lunar surface. It then provides background information, placing low-energy lunar transfers within the context of historical lunar missions. The chapter describes very high-level costs and benefits of low-energy transfers compared with conventional transfers.

Chapter 2 provides information about the methods, coordinate frames, models, and tools used to design low-energy lunar transfers. This information should be sufficient for designers to reconstruct any transfer presented in this book, as well as similar transfers with particular design parameters.

Chapter 3 presents information about transfers from the Earth to high-altitude three-body orbits, focusing on halo orbits about the first and second Earth–Moon Lagrange points. The chapter includes surveys of the transfer types that exist and discussions about how to construct a particular, desirable transfer.

Chapter 4 presents information about transfers from the Earth to low-altitude lunar orbits, focusing on polar mapping orbits. The techniques presented may be used to survey and construct conventional direct lunar transfers as well as low-energy transfers.

Chapter 5 presents information about transfers from the Earth to the lunar surface, including discussions and surveys of transfers that intersect the lunar surface at a steep 90 degree (deg) angle, as well as transfers that target a shallow flight path angle. The techniques illustrated in Chapter 5 may be used to generate conventional direct transfers as well as low-energy transfers.

Chapters 3–5 also include discussions about the variations of these transfers from one month to the next. The discussions are useful for mission designers and managers to predict what sorts of transfers exist in nearly any month and what sorts of transfers are particular to specific months.

Chapter 6 discusses several important operational aspects of implementing a low-energy lunar transfer. The section begins with a discussion of the capabilities of current launch vehicles to inject spacecraft onto low-energy trajectories. The section then describes how to design a robust launch period for a low-energy lunar transfer. Additional discussions are provided to address navigation, station-keeping, and spacecraft systems issues.

1.3 EXECUTIVE SUMMARY

This book characterizes low-energy transfers between the Earth and the Moon as a resource to mission managers and trajectory designers. This book surveys and illustrates transfers between the Earth and lunar libration orbits, low lunar mapping orbits, and the lunar surface, including transfers to the Moon and from the Moon to the Earth.

There are many ways of transporting a spacecraft between the Earth and the Moon, including fast conventional transfers, spiraling low-thrust transfers, and low-energy transfers. Table 1-1 summarizes several of these methods and a sample of the missions that have flown these transfers.

Table 1-1 A summary of several different methods used to transfer between the Earth and the Moon.

The vast majority of lunar missions to date have taken quick, 3–6 day direct transfers from the Earth to the Moon. The Apollo missions took advantage of 3–3.5 day transfers: transfers that were as quick as possible without dramatically increasing the transfers’ fuel requirements. The Lunar Reconnaissance Orbiter (LRO) followed a slightly more efficient 4.5-day transfer. The additional transfer duration saved fuel and relaxed the operational timeline of the mission. The Apollo missions and LRO had very limited launch opportunities: they had to launch within a short window each month. Clementine and Chandrayaan-1 implemented phasing orbits about the Earth to alleviate this design constraint and expand their launch periods. SMART-1 was also able to establish a wider launch period using low-thrust propulsion. The low-thrust system requires less fuel mass than conventional propulsion systems, but the transfer required significantly more transfer time than any typical ballistic transfer.

The Gravity Recovery and Interior Laboratory (GRAIL) mission was the first mission launched to the Moon directly on a low-energy transfer. GRAIL’s low-energy transfer required much less fuel than a conventional transfer, though it required a longer cruise that traveled farther from the Earth. The longer cruise (~90–114 days) made it possible to establish a wide, 3-plus week long launch period and significantly relaxed the operational timeline. Furthermore, GRAIL launched two satellites on board a single launch vehicle and leveraged the longer cruise to separate their orbit insertion dates by more than a day. Finally, GRAIL’s low-energy transfer reduced the orbit insertion change in velocity (ΔV) for each vehicle, permitting each spacecraft to perform its lunar orbit insertion with a smaller engine and less fuel.

In general, a low-energy transfer is a nearly ballistic transfer between the Earth and the Moon that takes advantage of the Sun’s gravity to reduce the spacecraft’s fuel requirements. The only maneuvers required are typical statistical maneuvers needed to clean up launch vehicle injection errors and small deterministic maneuvers to target specific mission features. A spacecraft launched on a low-energy lunar transfer travels beyond the orbit of the Moon, far enough from the Earth and Moon to permit the gravity of the Sun to significantly raise the spacecraft’s energy. The spacecraft remains beyond the Moon’s orbit for 2–4 months while its perigee radius rises. The spacecraft’s perigee radius typically rises as high as the Moon’s orbit, permitting the spacecraft to encounter the Moon on a nearly tangential trajectory. This trajectory has a very low velocity relative to the Moon: in some cases the spacecraft’s two-body energy will even be negative as it approaches the Moon, without having performed any maneuver whatsoever. As the spacecraft approaches the Moon, it may target a trajectory to land on the Moon, to enter a low lunar orbit, or to enter any number of three-body orbit types, such as halo or Lissajous orbits. No matter what its destination, the spacecraft requires less fuel to reach it than it would following a conventional transfer.

Low-energy transfers provide many benefits to missions when compared with conventional transfers. Six example benefits include the following:

1. They require less fuel. A low-energy transfer to a lunar-libration orbit saves 400 meters per second (m/s) of ΔV and often more. This is a significant savings, which is fully demonstrated in Chapter 3. A low-energy transfer to a 100-kilometer (km) lunar orbit saves more than 120 m/s of ΔV for cases when a mission can use an optimized conventional transfer. The savings are far more dramatic for missions that cannot use an optimized conventional transfer.

2. Low-energy transfers are more flexible than conventional transfers and may be used to transfer spacecraft to many more orbits on a given date. It is shown in Chapter 4 that low-energy transfers may be used to reach polar orbits with any node at any arrival date—conventional transfers may only target specific nodes at any given date.

3. Low-energy transfers have extended launch periods. It requires very little fuel to establish a launch period of 21 days or more for a mission to the Moon that implements a low-energy transfer. Conventional transfers may be able to accomplish similar launch periods, but they require multiple passes through the Van Allen Belts, necessitating improved radiation protection. The low-ΔV costs of establishing a launch period for a low-energy transfer are discussed in Chapter 6.

4. Low-energy transfers have a relaxed operational timeline. Modern launch vehicles, such as the Atlas V family with their Centaur upper stages, place spacecraft on their trajectories with small errors. Missions such as GRAIL, which launched aboard a Delta II launch vehicle, may be able to wait 6 days or more before performing a maneuver. In fact, GRAIL was able to cancel the first trajectory correction maneuver (TCM) for both spacecraft; the first TCM performed was executed 20 days after launch. In this way, a spacecraft operations team has a great deal more time to prepare the spacecraft before requiring a maneuver, when compared to conventional transfers that typically require a maneuver within a day or less.

5. Low-energy transfers may place several vehicles into very different orbits at the Moon using a single launch vehicle. The GRAIL mission separated two lunar-orbit insertions by over a day using very little fuel. Chapter 3 illustrates how to place multiple spacecraft in many different orbit types using a single launch vehicle. This typically requires a large amount of fuel when using conventional transfers.

6. Low-energy transfers may be used to transfer a spacecraft from the Moon directly to any location on the surface of the Earth. Typical conventional transfers, for example, those used by the Apollo missions, return spacecraft to a near-equatorial landing site. Low-energy transfers may be used to target any location (such as the different hemispheres of the Utah Test and Training Range in North America and the Woomera Weapons Testing Range in South Australia) using relatively small quantities of fuel.

The typical drawbacks of low-energy transfers between the Earth and the Moon are the longer transfer durations for missions that are very time-critical and the longer link-distances, as the spacecraft travels as far as 1.5–2 million kilometers away from the Earth.

The next sections define direct and low-energy transfers to provide a clear understanding of what trajectories are presented in this book.

1.3.1 Direct, Conventional Transfers

A direct lunar transfer is a trajectory between the Earth and the Moon that requires only the gravitational attraction of the Earth and Moon. A spacecraft typically begins from a low altitude above the surface of the Earth as a result of an injection by a launch vehicle, as a result of a maneuver performed by the spacecraft, or as a result of some intermediate orbit. The spacecraft then cruises to the Moon on a trajectory that typically remains within the orbit of the Moon about the Earth. It is a trajectory whose dynamics are dominated by the gravitational attraction of the Earth and Moon, and all other forces (such as the Sun or any spacecraft events) may be considered to be perturbations. The spacecraft then enters some orbit about the Moon via a maneuver. Direct transfers may be constructed from the Moon to the Earth in much the same way as they are constructed to the Moon.

Figure 1-1 illustrates a 3-day transfer nearly identical to the one the Apollo 11 astronauts used to go from the Earth to the Moon in 1969 [1]. The mission implemented a low-Earth parking orbit with an inclination of approximately 31.38 deg. From there, the launch vehicle was required to attain a trans-lunar injection energy (C3) of approximately −1.38 km2/s2 to reach the Moon in approximately 3.05 days. Upon arrival at the Moon, the vehicle injected into an elliptical orbit with a periapse altitude of approximately 110 km and an apoapse altitude of approximately 310 km, followed soon after by a circularization maneuver [1]. In order to compare the Apollo 11 transfer with the transfers in the surveys presented here, the Apollo 11 transfer would have a velocity of approximately 2.57 kilometers per second (km/s) at an altitude of 100 km above the mean lunar surface, requiring a hypothetical, impulsive ΔV of approximately 0.94 km/s to insert into a circular 100-km orbit.

Figure 1-1 A modified version of the Apollo 11 Earth–Moon transfer, as if it had performed an impulsive lunar-orbit insertion (LOI) maneuver directly into a circular 100-km lunar orbit [2].

(Copyright © 2011 by American Astronautical Society Publications Office, all rights reserved, reprinted with permission of the AAS.)

Direct transfers may be constructed between the Earth and the Moon with durations as short as hours or as long as a few weeks. In general, the most fuel-efficient direct transfers require about 4.5 days of transfer duration. Any longer duration typically sends the spacecraft beyond the orbit of the Moon before it falls back and encounters the Moon.

Direct transfers may also be constructed between the Earth and lunar libration orbits for similar amounts of fuel as required to transfer directly to low lunar orbits. The launch energy requirement is very similar for missions to the Moon, to Lagrange 1 (L1), and to Lagrange 2 (L2), and to a first order may be treated as equal. A direct transfer requires 400–600 m/s of ΔV to insert into a lunar libration orbit about either L1 or L2, though a powered lunar flyby en route to a libration orbit about L2 may be used to reduce the total transfer cost by 100–200 m/s. These transfers are examined in Chapter 3.

Several missions have added Earth phasing orbits to their mission itineraries, such that they launch into a high-altitude, temporary Earth orbit and remain in that orbit for several orbits before arriving at the Moon. A mission designer may add these orbits to a flight plan for several reasons. First, they may be used to establish an extended launch period, since the mission planners can adjust the size of the phasing orbits to compensate for varying launch dates. Second, they may be used to reduce the operational risk of the mission by increasing the amount of time between each maneuver en route to the Moon. They may also be used if the launch vehicle is not powerful enough or accurate enough to send the spacecraft directly to the Moon, such as Chandrayaan-1 [3]. Drawbacks of Earth phasing orbits include additional passes through the Van Allen Belts and an extended transfer duration.

1.3.2 Low-Energy Transfers

Low-energy transfers take advantage of the Sun’s gravity to reduce the transfer fuel costs. They involve trajectories that take the spacecraft beyond the orbit of the Moon, where the Sun’s gravity becomes more influential. The Sun’s gravity works slowly and steadily, gradually raising the spacecraft’s periapse altitude until it has risen to the altitude of the Moon’s orbit about the Earth. When the spacecraft falls back toward the Earth, it arrives at the Moon with a velocity that closely matches the Moon’s orbital velocity. The result is that the spacecraft’s lunar orbit insertion requires much less fuel than required by a conventional, direct lunar transfer. Figure 1-2 illustrates an example 84-day low-energy transfer that arrives at the Moon when the Moon is at its first quarter. More explanation of these transfers is provided in Section 1.7 and in later chapters.

Figure 1-2 An example 84-day low-energy lunar transfer to a low, polar lunar orbit [2].

(Copyright © 2011 by American Astronautical Society Publications Office, all rights reserved, reprinted with permission of the AAS.)

Low-energy transfers typically travel far beyond the orbit of the Moon; hence, they may be designed to take advantage of one or more lunar flybys on their outbound segment. The lunar flybys may be used to reduce the injection energy requirements, or to change the spacecraft’s orbital plane, similar to the flight of each of the two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) spacecraft [4]. If a mission takes advantage of a lunar flyby immediately after launch, it may be useful to add one or more Earth phasing orbits into the design, as described above.

1.3.3 Summary: Low-Energy Transfers to Lunar Libration Orbits

Low-energy transfers may be used to save a great deal of fuel when a mission’s destination is a lunar libration orbit, such as a halo orbit, a Lissajous orbit, or some other three-body orbit. Many studies have demonstrated practical applications of lunar libration orbits, including locations for communication satellites [5–7], navigation satellites [8–13], staging orbits [14–18], and science orbits [4, 19]. The ARTEMIS mission took advantage of the geometries of several orbits about both the lunar L1 and L2 points, and it used two different low-energy transfers to arrive at those orbits.

Chapter 3 presents a full study of the characteristics and performance of low-energy transfers to lunar libration orbits. The results demonstrate that a typical transfer requires 70–120 days to travel from Earth departure to an arrival state that is within 100 km of the target libration orbit. The transfers arrive asymptotically, such that they do not require any insertion maneuver. This is an extraordinary benefit: it saves a mission upwards of 500 m/s of ΔV when compared to conventional, direct transfers to lunar libration orbits. The typical transfers studied in Chapter 3 depart the Earth with a C3 of −0.7 to −0.3 km2/s2, which is higher than the conventional transfer that has a C3 of approximately −2.0 km2/s2, but the low-energy transfer requires only small TCMs after the Earth-departure maneuver. Studies show (Section 6.5) that two or three deterministic maneuvers with a total of only ~70 m/s of ΔV may be used to depart the Earth from a specific inclination (such as 28.5 deg), and from any day within a 21-day launch period, and arrive at a particular location in a specified libration orbit.

Figures 1-3 and 1-4 illustrate two example direct transfers and two example low-energy transfers to lunar libration orbits, respectively. One can see that these transfers are ballistic in nature: they require a standard trans-lunar injection maneuver, a few TCMs, and an orbit insertion maneuver (which is essentially zero for the low-energy transfers). One may also add Earth phasing orbits and/or lunar flybys to the trajectories, which change their performance characteristics. Figure 1-5 illustrates two transfers that a spacecraft may take to depart the libration orbit using minimal fuel and transfer to a low lunar orbit or to the lunar surface.

Figure 1-3 The profile for a simple, direct transfer from the Earth to a lunar libration orbit about either the Earth–Moon L1 or L2 point, viewed from above in the Earth–Moon rotating coordinate frame.

Figure 1-4 The profile for a simple, low-energy transfer from the Earth to a lunar libration orbit about either the Earth–Moon L1 or L2 point, viewed from above in the Earth–Moon rotating coordinate frame.

Figure 1-5 The profile for a simple, low-energy transfer from a libration orbit to either a low lunar orbit or the surface of the Moon, viewed from above in the Earth–Moon rotating coordinate frame.

1.3.4 Summary: Low-Energy Transfers to Low Lunar Orbits

Robotic spacecraft may take advantage of the benefits of a low-energy transfer when transferring to a low lunar orbit, such as GRAIL’s target lunar orbit. The transfer duration is about the same as a low-energy transfer to a lunar libration orbit, namely, 70–120 days. This duration is typically far too long for human occupants, unless the purpose of the mission is to demonstrate a long deep-space transfer. There are many benefits for robotic missions, including smaller orbit insertion maneuver requirements, the capability to establish an extended launch period, and a relaxed operational schedule. The GRAIL mission took advantage of these benefits, as well as the characteristic that it requires very little ΔV to separate the two spacecraft from their joint launch. GRAIL’s two spacecraft flew independently to the Moon and arrived 25 hours apart: a feat that requires a great deal more ΔV and/or operational complexity when implementing direct lunar transfers. Low-energy transfers may also access a much broader range of lunar orbits for a particular arrival date than direct transfers.

Chapter 4 presents a full study on the characteristics and performance of low-energy transfers to low lunar, polar orbits. The examination uses 100-km circular, polar orbits as the target orbits to simplify the trade space. It remains relevant to practical mission design since many spacecraft missions have inserted into very similar orbits, including Lunar Prospector, Kaguya/Selenological and Engineering Explorer (SELENE), Chang’e 1, LRO, and GRAIL, among others. The results of the study indicate that low-energy transfers typically depart the Earth with an injection C3 of −0.7 to −0.3 km2/s2, much like low-energy transfers to lunar libration orbits, and require 70–120 days to reach the Moon. A spacecraft may implement a lunar flyby on the outbound segment to reduce the launch energy requirement, but such an event would increase the complexity and operational risk of the mission. When the spacecraft arrives at the Moon, it arrives traveling at a slower relative speed than if it had used a direct lunar transfer. The examination shows that the lunar-orbit insertion maneuver is at least 120 m/s smaller for any low-energy mission; the ΔV savings are often much greater.

Low-energy transfers may also be used in such a way that a spacecraft transfers to a lunar libration orbit, or some other three-body orbit, before transferring to the target orbit. This strategy was used in the ARTEMIS mission and has been used in a number of spacecraft proposals.

Figure 1-6 illustrates an example direct transfer and an example low-energy transfer to two low lunar orbits. The transfers are very similar to those presented in the previous section, except of course that these target low lunar orbits instead of lunar libration orbits.

Figure 1-6 The profiles for both a direct and a low-energy transfer from the Earth to a low lunar orbit.

1.3.5 Summary: Low-Energy Transfers to the Lunar Surface

Low-energy transfers from the Earth to the lunar surface may be constructed in much the same way as transfers to low lunar orbit. They have the same sorts of benefits and drawbacks as other low-energy transfers.

Chapter 5 presents a full study on the characteristics and performance of low-energy transfers to the lunar surface. There are two main classes of missions studied: those that arrive at the surface with a high impact angle and those that arrive at the surface with a shallow flight path angle. The shallow angles are useful for missions that aim to land on the surface, and then it is useful that the low-energy transfers yield trajectories that arrive at the surface with lower velocities. The steeper arrival conditions are useful for lunar impactors, such as the Lunar Crater Observatory and Sensing Satellite (LCROSS). In this case, higher velocities are typically preferred. Low-energy transfers may not result in the highest impact velocities achievable, but they do offer the capability of targeting any location on the surface of the Moon with ease.

As with the low-energy transfers studied in Chapters 3 and 4, the typical transfers to the lunar surface require 70–120 days. They typically depart the Earth with C3 values between −0.7 and −0.3 kilometers squared per square second (km2/s2) and only require small trajectory correction maneuvers after launch. The same sort of two- or three-burn strategies may be used to target a particular low-energy transfer from a specified low Earth parking orbit, and from any day within a 21-day launch period.

The lunar surface may also be accessed from a lunar libration orbit or from a low lunar orbit. Hence, a mission may implement a low-energy transfer to either type of orbit studied in Chapters 3 or 4 and then follow a transfer to the lunar surface. This sort of trajectory design is also studied in Chapter 5.

Figure 1-7 illustrates an example direct transfer and an example low-energy transfer to the lunar surface. Again, the transfers are very similar to those presented in the previous two sections, except (of course) that these target the lunar surface.

Figure 1-7 The profiles for both a direct and a low-energy transfer from the Earth to the lunar surface. Transfers may be constructed to arrive with a shallow or steep flight path angle.

1.4 BACKGROUND

This section reviews historical lunar missions as a reference for the discussions about designing future lunar missions, including future missions that use direct transfers as well as low-energy transfers. Nearly one hundred spacecraft have flown conventional, direct transfers between the Earth and the Moon, including the Union of Soviet Socialist Republics’ (USSR’s) Luna spacecraft, the USA’s Apollo spacecraft, and the most recent international missions. Only five spacecraft have flown low-energy lunar transfers, though several others have followed low-energy transfers to other destinations near the Earth. The complexity of lunar missions has gradually grown, as has the need to save money and collect a greater scientific return using less fuel. Modern flight operations, spacecraft hardware, and infrastructure have opened the door to low-energy techniques as a method to reduce costs.

The first two missions to implement low-energy transfers—Hiten and ARTEMIS—demonstrated the technique as a method to extend their missions to the Moon, despite not having the fuel to reach lunar orbit using conventional techniques. The GRAIL mission, launched on September 10, 2011, was the first mission to implement a low-energy lunar transfer as part of its primary mission. The GRAIL mission benefited from its low-energy route to the Moon in more ways than just saving fuel. It is fully expected that more missions will follow this lead, and low-energy transfers will become common among lunar missions.

1.5 THE LUNAR TRANSFER PROBLEM

Soon after the dawn of the Space Age, people were designing trajectories for spacecraft to travel to the Moon [20, 21]. In fact, not even a full year had elapsed since the launch of Sputnik (October 4, 1957) before the United States attempted to launch the Pioneer 0 probe to the Moon (August 17, 1958). The first probes designed to explore the Moon were plagued with launch vehicle failures, including four Pioneer failures by the United States and three Luna failures by the Soviet Union. It was not until 1959 that Luna 1 finally flew by the Moon. Later in 1959, Luna 2 became the first probe to impact the Moon.

As technology improved, spacecraft were able to fly to the Moon using less fuel. Several general bounds exist that limit the movement of a spacecraft in the Earth–Moon system when other perturbations, such as the Sun’s gravity, are ignored. Research in the circular restricted three-body problem (examined in Section 2.6.2) reveal that a spacecraft with enough energy to reach the Earth–Moon L1 point has the minimum energy required to transfer to the Moon, without considering other perturbations. Sweetser computed that the theoretical minimum ΔV that a spacecraft would require to travel from a 167-km altitude circular orbit at the Earth to a 100-km altitude circular orbit at the Moon, just passing through L1, is approximately 3.721 km/s [22]. Actual trajectories have since been computed that approach this theoretical minimum [23].

Early investigations concluded that it is impossible to launch from the Earth and arrive at the Moon such that the spacecraft becomes captured without performing a maneuver [21]; however, these analyses did not include the effects of the Sun’s gravity. As early as 1968, Charles Conley began using dynamical systems methods to explore the construction of a theoretical trajectory that could become temporarily captured by the Moon without performing a capture maneuver [24]. A spacecraft with the proper energy could target the neck region near one of the collinear libration points in the Earth–Moon system (see Section 2.6.2). A planar periodic orbit exists in each of those regions that acts as a separatrix, separating the interior of the Moon’s region from the rest of the Earth–Moon region. Conley’s method implemented dynamical systems techniques to construct the transfer by targeting the gateway periodic orbit. His transfers were restricted to the Moon’s orbital plane.

In the late 1980s and early 1990s, Belbruno and Miller began developing a method to construct lunar transfers using a new technique, which they have referred to as the weak stability boundary (WSB) theory [25–27]. The method involves targeting the region of space that is in gravitational balance between the Sun, Earth, and Moon, without involving any three-body periodic orbits or other dynamical structures. Ballistic capture occurs when the spacecraft’s two-body energy becomes negative, as described by Yamakawa [28, 29]. In 1991, the Japanese mission Hiten/MUSES-A used the effects of the Earth, Moon, and Sun for its transfer to the Moon [30].

In the early 2000s, Ivashkin also developed a method to construct transfers between the Earth and Moon using the Sun’s gravitational influence [31–34]. His methods involve beginning from a low lunar orbit, or from the surface of the Moon, and numerically targeting trajectories that depart from the Moon in the direction of the Earth’s L1 or L2 points. A spacecraft on such a trajectory departs from the Moon with a negative two-body energy with respect to the Moon, but as it climbs away from the Moon, it gains energy from the effect of the Earth’s and Sun’s gravity. Eventually, it gains enough energy to escape the Moon’s vicinity. The trajectory is then targeted such that it lingers near the chosen Lagrange point long enough to allow the Sun to lower the perigee radius of the next perigee passage down to an altitude of approximately 50 km.

In the mid 1990s, other methods were developed to construct a lunar transfer that takes advantage of the chaos in the Earth–Moon three-body system. Bollt and Meiss constructed a trajectory that sent a spacecraft into an orbit without sufficient energy to immediately reach the Moon, but with enough to get close enough to become substantially perturbed by the Moon [35]. Using a series of four very small maneuvers, the spacecraft could then hop between nearby trajectories in the chaotic sea of possible trajectories to become captured by the Moon using far less energy than standard direct transfers. In 1997, Schroer and Ott reduced the time of transfer for the chaotic lunar transfer by targeting specific three-body orbits near the Earth [36]. The total cost remained approximately the same as the transfer constructed by Bollt and Meiss, but the transfer duration was reduced from approximately 2.05 years to 0.8 years.

In 2000, Koon et al. [37, 38] constructed a planar lunar transfer that was almost entirely ballistic using the techniques involved in Conley’s method [38]. Following Conley, Koon et al. [37] observed that the planar libration orbits act as a gateway between the interior and exterior regions of space about the Moon. Koon et al. [37, 38] constructed a trajectory that targets the interior of the stable invariant manifold of a planar libration orbit about the Earth–Moon L2 point. Once inside the interior of the stable manifold, the spacecraft ballistically arrives at a temporarily captured orbit about the Moon. Many authors have debated what it means to be temporarily captured at the Moon; Koon et al., define a similar term, “ballistically captured” to be a trajectory that comes within the sphere of influence of the Moon and revolves about the Moon at least once [38].

Further advances have been made since 2004 to apply dynamical systems theory to the generation of three-dimensional low-energy lunar transfers [39–44]. Parker mapped out numerous families of low-energy transfers, illuminating different geometries that are available for spacecraft to travel to the Moon and arrive in lunar libration orbits without requiring any capture maneuver [2, 45–47]. Several authors have begun applying low-thrust techniques to further improve low-energy transfers, including transfers from the Earth to the Moon and transfers from one libration orbit to another [48–55]. In 60 years, research has advanced the knowledge of lunar transfers from the early spacecraft missions that implemented direct lunar transfers to modern analyses that reveal maps of entire families of low-energy transfers to the Moon.

1.6 HISTORICAL MISSIONS

Many historical missions have taken direct transfers from the Earth to the Moon, including a large number of spacecraft in the Luna, Zond, Ranger, Surveyor, Lunar Orbiter, and Apollo programs. A few of these missions implemented direct transfers back to the Earth again: most notably Luna-16 and the nine Apollo missions that ventured to the Moon and returned. Several other missions have also flown direct transfers since the 1960s, and they are summarized below.

Low-energy lunar transfers are closely related to low-energy transfers in the Sun–Earth system, as is described later in this book. Since the 1970s, several spacecraft have been placed on three-body trajectories in the Sun–Earth system to conduct their scientific and technological missions, including International Sun–Earth Explorer-3 (ISEE-3), Solar and Heliospheric Observatory (SOHO), Advanced Composition Explorer (ACE), Wind, Wilkinson Microwave Anisotropy Probe (WMAP), and Genesis, among others. Three spacecraft are known to have followed three-body trajectories in the Earth–Moon system, including SMART-1 and the two ARTEMIS spacecraft. Between 1991 and 2011, five spacecraft have traversed low-energy transfers from the Earth to the Moon, including Hiten/MUSES-A in 1991, the two ARTEMIS spacecraft in 2010 and the two GRAIL spacecraft in 2011. A brief summary of each of these missions will be presented here.

1.6.1 Missions Implementing Direct Lunar Transfers

Table 1-2 summarizes many historical missions that have taken direct lunar transfers, noting their launch date and transfer duration, among other things. One notices that early missions implemented very quick transfers that required fewer than 1.5 days to reach the Moon. These involved lunar flybys or impacts, with no intention of inserting into orbit or landing softly. Indeed, their velocities at the Moon would be quite high. The first soft landing was performed by the Soviet Union’s Luna 9, which took a 79-hour transfer to the Moon. The first robotic sample return attempt was performed by the Soviet Union’s Luna 15, which took a 101.6-hour transfer to the Moon: longer to save fuel mass so that it would be capable of returning to the Earth. Luna 16 was the first successful robotic sample return, taking a 105.1-hour lunar transfer. The first human landing, and first successful sample return was performed earlier, by Apollo 11. The direct transfer that Apollo 11 took required about 73 hours, which was shorter in time and required more fuel, but required less total consumable mass than a longer transfer since the mission involved human occupants.

Table 1-2 The transfer durations, among other information, of several historical missions that have implemented direct lunar transfers [56–59].

1.6.2 Low-Energy Missions to the Sun–Earth Lagrange Points

ISEE-3. On August 12, 1978, the International Sun–Earth Explorer 3 (ISEE-3) spacecraft was launched and placed in a halo orbit about the Sun–Earth L1 point. It was the first spacecraft to be inserted into an orbit about a Lagrange point. On June 10, 1982, the spacecraft began performing 15 very small maneuvers to guide it on a series of lunar flybys. Its fifth and final lunar flyby was performed on December 22, 1983, coming within 120 km of the lunar surface. The lunar flyby ejected the spacecraft from the Earth–Moon system and it entered a heliocentric orbit. The spacecraft was renamed the International Cometary Explorer (ICE) as it readied for its encounter with the comet Giacobini-Zinner. On June 5, 1985, ICE entered the comet’s tail and collected scientific information about the tail. ICE is expected to return to the vicinity of the Earth in 2014, when it may be captured and brought back to Earth, or repurposed for another comet observation mission. Figure 1-8 shows a plot of the trajectory of ISEE-3/ICE [60, 61].

Figure 1-8 The trajectory of ISEE-3 / ICE [62].

Wind. The Wind mission was launched on November 1, 1994, and placed in a halo orbit about the Sun–Earth L1 point. Its scientific objectives were to characterize the solar wind using a variety of particle and field measurements, all of which complemented several other spacecraft in a variety of other orbits, including the Polar and Geotail satellites, as part of the International Solar-Terrestrial Physics (ISTP) Science Initiative. After several years of measurements from the Sun–Earth L1 environment, Wind’s orbit was altered to give it access to new areas in the near-Earth environment, including a campaign of “petal orbits” to send it out of the ecliptic plane (1998–1999), a lunar backflip (April, 1999), several revolutions about a distant prograde orbit (2001–2003), and a complex orbit that involved repeated lunar flybys and excursions out beyond the Sun–Earth L1 and L2 points (2003–2006). The first part of Wind’s trajectory resembles the first part of ISEE-3’s trajectory shown in Fig. 1-8. Figure 1-9 illustrates Wind’s orbits in the Sun–Earth system from 2003 through 2006 [63], illustrating a unique aspect of its low-energy mission design.

Figure 1-9 The trajectory of Wind from 2003 through 2006, viewed from above in the Sun–Earth rotating frame [63].

SOHO. The Solar and Heliospheric Observatory (SOHO) was launched on December 2, 1995, on a path taking it directly toward a libration orbit about the Sun–Earth L1 point. On March 17, 1996, SOHO performed a small orbit insertion maneuver to formally enter the quasi-halo L1 orbit 1.5 million kilometers away from the Earth. The L1 halo orbit is ideal for the observatory because it provides an unobstructed view of the Sun on one side and a near-constant view of the Earth on the other side. Hence, it can collect scientific data about the Sun continuously, while being able to communicate with the Earth at any time. Figure 1-10 shows a plot of the trajectory that SOHO used to transfer to its halo orbit [64–67].

Figure 1-10 The transfer trajectories and mission phases of SOHO [68], used with permission of ESA.

ACE. In 1997, the Advanced Composition Explorer (ACE) was launched and placed in a Lissajous orbit about the Sun–Earth L1 point. Its mission, much like SOHO’s, is dedicated to collecting energetic particles to study the solar corona, interplanetary medium, solar wind, and cosmic rays. Its transfer appears very similar to SOHO’s transfer, shown in Fig. 1-10 [68, 69].

WMAP. Launched on June 30, 2001, the Wilkinson Microwave Anisotropy Probe (WMAP) is currently residing in a small-amplitude Lissajous orbit about the Sun–Earth L2 point. From this orbit, WMAP continues to measure cosmic background radiation, unobstructed by the radiation originating from the Sun, Earth, or Moon. Figure 1-11 shows a plot of the trajectory that WMAP used to reach its libration orbit about L2 [70].

Figure 1-11 The transfer trajectory of WMAP [76].

Genesis. On August 8, 2001, Genesis launched and was quickly injected into a halo orbit about the Sun–Earth L1 point. It traversed the halo orbit approximately five times, spending more than 2 years in the libration orbit collecting solar wind samples before turning back toward the Earth. Before returning to the Earth, however, it made a 3-million-mile (4.8 × 106 km) detour to visit the Sun–Earth L2 point. The detour allowed it to deposit its science payload on the sunlit-side of the Earth. Figure 1-12 shows a plot of the trajectory that Genesis followed during its primary mission [71, 72].

Figure 1-12 The low-energy trajectory that the Genesis spacecraft followed [77], viewed from above in the Sun–Earth rotating frame.

Herschel and Planck. The Herschel and Planck space observatories were launched together on May 14, 2009 [73–75]. The two spacecraft separated soon after launch and traveled separately to Lissajous orbits about the Sun–Earth L2 point. Their orbit transfers were heuristically similar to WMAP’s transfer to L2, illustrated in Fig. 1-11.

Future Missions. There are plans to place the proposed James Webb Space Telescope [78] and the proposed Terrestrial Planet Finder [79] missions, among others, at the Sun–Earth L2 point. Low-energy trajectories to the Sun–Earth Lagrange points have been shown to be very useful for solar observatories (L1) and astrophysics observatories (L2), and they frequently appear in spacecraft proposals.

1.6.3 Missions Implementing Low-Energy Lunar Transfers

Hiten/MUSES-A. In 1991, the Japanese spacecraft Hiten was the first spacecraft to transfer to the Moon using a low-energy lunar transfer. The spacecraft was not designed to go to the Moon, but rather to send a probe to the Moon. After the probe’s communication system failed, mission designers scrambled to find a new mission for Hiten. Edward Belbruno and James Miller constructed a new trajectory—a “WSB transfer”—that required less fuel than traditional lunar transfers [80, 81]. The spacecraft Hiten did not have the fuel required for a conventional lunar transfer, but had the fuel to use this new lunar transfer to reach the Moon. Hiten became Japan’s first lunar mission.

SMART-1. On September 27, 2003, the European Space Agency’s SMART-1 spacecraft followed a low-thrust 2-year trajectory to reach the Moon, becoming the first low-thrust spacecraft to transfer to the Moon [82].

ARTEMIS. The Time History of Events and Macroscale Interactions during Substorms (THEMIS) constellation was launched on February 17, 2007, to monitor the Earth’s magnetic field from five different vantage points in high-altitude orbits, tracking the large-scale evolution of substorms. In 2009, two of those spacecraft were maneuvered to begin an extended mission called ARTEMIS [4]. The two spacecraft performed numerous maneuvers near their orbital perigees to gradually raise their orbits until they could take advantage of several lunar flybys to propel them onto two low-energy transfers. Both ARTEMIS spacecraft arrived at the Moon near the Earth–Moon L2 point; one of them remained there and one immediately transferred to a libration orbit about the Earth–Moon L1 point. After several months, the second spacecraft made the transfer and both orbited the L1 point. After several more months, the two spacecraft departed their respective L1 orbits, descended to the Moon, and entered smaller Keplerian orbits about the Moon. The two ARTEMIS spacecraft are the first two spacecraft to orbit either LL1 or LL2, and they each orbited both points.

GRAIL. The GRAIL mission (Fig. 1-13) [83–85] was launched on September 10, 2011, aboard a Delta II Heavy launch vehicle. Two vehicles, GRAIL-A (Ebb) and GRAIL-B (Flow), were separated soon after launch and flew independently to the Moon via two similar low-energy transfers. The two spacecraft arrived at the Moon approximately 25 hours apart, on December 31, 2011 and January 1, 2012. After a few months of orbit reductions and adjustments, the two spacecraft inserted into a formation, such that one spacecraft trailed the other in almost identical orbits about the Moon. By tracking each other, the two spacecraft were able to recover the Moon’s gravity field to unprecedented precision and map the interior structure of the Moon. The two GRAIL spacecraft were the first ever to fly low-energy lunar transfers as part of their primary mission, and they were the first ever to arrive at the Moon and perform lunar orbit insertions directly from low-energy transfers.

Figure 1-13GRAIL’s mission design, including a 26-day launch period and two deterministic maneuvers for both GRAIL-A and GRAIL-B, designed to separate their lunar orbit insertion times by 25 hours (Ref. [83], originally published by AAS).

GRAIL’s trajectory design is illustrated in Fig. 1-13, including the first and last launch opportunity in a 26-day launch period. This is the launch period published in Ref. [83], however, it was actually extended by many days as the mission developed. As one can see in Fig. 1-13, GRAIL’s mission design includes two significant deterministic maneuvers executed per spacecraft during the cruise, performed primarily to separate their lunar orbit insertion dates.

1.7 LOW-ENERGY LUNAR TRANSFERS

Low-energy transfers between the Earth and the Moon are the focus of this book; this section heuristically describes these transfers and how they are used.