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"Almost fifty years after the beginning of space flight, Belbruno's work offers a realistic beginning for minimum—fuel and maximum—payload trajectories for interplanetary operations. It is a mark of sophistication in the evolution of space travel that simplified solutions to the vexing many-body problem are found to have practical applications. Belbruno's three-body solution for low-thrust minimum-fuel trajectories serves well not only the future of space flight but helps astronomy in understanding the sometimes erratic motions of celestial
"Almost fifty years after the beginning of space flight, Belbruno's work offers a realistic beginning for minimum—fuel and maximum—payload trajectories for interplanetary operations. It is a mark of sophistication in the evolution of space travel that simplified solutions to the vexing many-body problem are found to have practical applications. Belbruno's three-body solution for low-thrust minimum-fuel trajectories serves well not only the future of space flight but helps astronomy in understanding the sometimes erratic motions of celestial bodies."—Edgar D. Mitchell, Apollo 14 astronaut
"Fly Me to the Moon is a fast, easy read that explains in simple nonscientific terms very complex matters of celestial mechanics, and it is delightful reading for students and professionals to update or learn very important new background materials. It is also a must-read for the lawyer-scientist."—Ambassador Edward R. Finch, Jr.
"This is an excellent book. The author succeeds in writing an exciting story about his research on low-fuel space travel, a subject that is not widely known but that will interest many readers. Moreover, the mathematical aspects of chaos in the context of space missions is well treated at the level of the nonexpert."—Florin Diacu, University of Victoria
"This is a good story. It is rare to see a nonpedantic book on celestial mechanics that gives some backroom stories about trajectory geeks. Belbruno ties very abstract concepts to real problems and situations."—Wendell W. Mendell, NASA Johnson Space Center, Astromaterials Research & Exploration Science Directorate
"This is an excellent book. It is an inside look at the important new field of chaotic trajectories by one of the masters and originators of the field. As we continue into space, I think we will be hearing more and more about these clever trajectories. Ed Belbruno has covered in a beautiful and interesting way the important applications of chaos to astrophysics and spacecraft trajectories. He also tells a very interesting personal story of his battles to get these trajectories used, and how he was able to save the Hiten spacecraft and get it to the moon. This is a great story, and he tells it very well."—Richard Gott, Princeton University
"The author's newly discovered interplanetary highways offer a romantic reflection of the pre-rocket, pre-airplane era, where balloons would transport us, with hardly any energy of our own, from one unexplored vista to another."—From the foreword by Neil deGrasse Tyson, astrophysicist and Director of the Hayden Planetarium, American Museum of Natural History, author of Death by Black Hole: And Other Cosmic Quandaries
"A small group of scientists has worked on new orbits that take into account the inherently chaotic motion of object in a multibody system. . . . One of the innovators in what is known as 'capture dynamics', Ed Belbruno, provides a basic and eminently readable introduction to the topic in Fly Me to the Moon."—Jeff Foust, The Space Review
"This book does for mathematics what The Double Helix did for biochemistry, without the gossip and diatribe that made The Double Helix so controversial...Overall, this book is a superb introduction to the life of a real mathematician, and a gentle introduction to some very complex mathematics."—Jeff Suzuki, MAA Review
"Fly Me to the Moon provides a fast, very readable account of new developments in chaotic celestial mechanics, especially low-fuel space travel, at a level appropriate for a general audience. By the end, nonmathematicians will have gained some intuition about one of the hallmarks of chaos, sensitive dependence on initial conditions, and how chaos can be harnessed to good purpose. All readers will walk away thinking differently about the cosmos. Far from being a clockwork, it will seem more dynamic, more turbulent, and full of diverse possibilities."—Shane Ross, Notices of the American Mathematical Society
"Belbruno beautifully describes his novel low-fuel concept in Fly Me to the Moon, using copious sketches to explain his theory without resorting to a single equation. . . . The author has laid out the book very well—a teaser of an introduction with just enough details of the Hiten rescue to whet the appetite, but leaving you hungry for more. The language is friendly yet enticing, with nice snappy chapter lengths and informative illustrations in just the right places. There is a good story line running through the book with little surprises like the author being granted a patent for his special route to the Moon in 2003, with many more patents to follow for routes to other destinations."—Gerard McMahon, Astronomy and Space
"[A] wonderfully informative book. . . . For anyone with an interest in this remarkable development in spaceflight the book is a must."—Colin Keay, Australian Physics
As astrophysicist and NASA consultant Belbruno explains in this short book, one of the reasons for the exorbitant cost of space flight is the need for huge amounts of fuel. In addition to the cost of the fuel itself, is its weight: "it is very expensive to bring one pound of anything to the Moon—about a quarter million dollars." By solving what are known as three-body equations (the three bodies, for example, being Earth, the Moon and a spacecraft), Belbruno has discovered trajectories between celestial bodies that make use of both chaos theory and gravitational forces, and enable space travel with a fraction of the fuel normally used. The downside is the greater time needed for travel. A trip to the Moon using Belbruno's method, might take three months rather than three days. But this difference poses no trouble for sending supplies and could dramatically lower the cost of building a permanent base on the Moon. Although Belbruno's main ideas are expressed simply enough for the average reader to appreciate, his account of his efforts is disjointed and not as rewarding as the underlying science. Illus. (Mar.)Copyright 2006 Reed Business Information.
"Houston, we have a problem." That plea for help got Tom Hanks and his crew out of a jam on Apollo 13. But, who do you call when you don't work for NASA? ... NASA!
At my door was a person I had never seen before. He introduced himself as James Miller. He had a problem.
The Japanese had launched a space probe to the Moon about three months earlier, in late January 1990. The main purpose of the mission was to demonstrate Japan's technical prowess in spaceflight. They had been gradually developing their technical abilities in space travel since the 1970s with less ambitious Earth orbiting missions. By 1990 they had built a considerable infrastructure to handle missions beyond Earth orbit including the Kagoshima Space Center. Now they wanted to become the first country to reach our neighbor after the Americans and Soviets. For Japan, this was an important mission, supported with national pride and a great deal of publicity.
But the mission had failed. Miller wanted to know: Could I save it? He had tried all the other obvious solutions and I was the last resort.
The Japanese had launched two robotic spacecraft MUSES-A & B into Earth orbit. These two spacecraft were attached to each other as they orbited the Earth. The smaller one, MUSES-B (renamed Hagoromo), the size ofa grapefruit, detached on March 19 and went off to the Moon on a standard route, called a Hohmann transfer. But the Japanese lost contact with it, and it wasn't known if it ever made it to lunar orbit. It was last observed approaching the Moon, and preparing to go into orbit by firing its rocket engines, when communication was lost.
I was familiar with the mission, since it was widely broadcast in the press. One headline read, "Japan's Lunar Probe Lost." I didn't know much beyond what I heard through informal gossip from engineers in the hallways-that Japan was desperate to somehow get things back on track. The other spacecraft, MUSES-A, was renamed Hiten, meaning "A Buddhist angel that dances in heaven." Hoping to salvage the mission, Japan wanted to get Hiten to the Moon since Hagoromo appeared to be lost.
The Buddhist angel was the size of a desk, and was never designed to go to the Moon, but rather to remain in Earth orbit and be a communications relay for the now lost Hagoromo.
Miller was an aerospace engineer at NASA's Jet Propulsion Laboratory (JPL). He explained that he was trying to find ways for Japan to get Hiten to the Moon and into lunar orbit. But there were major problems-Hiten had very little fuel; it was not built to go to the Moon; and it would be impossible for it to reach the Moon by normal methods.
He asked if my theory of low fuel routes to the Moon could do it. He had heard that I had figured out a way to go to the Moon with much less fuel than conventional methods. He knew it was controversial, but was "willing to try anything."
I hadn't quite figured it out, but as soon as he asked me this question, it was like a light was turned on. As if the answer just jumped into my mind! I suggested that he do a computer simulation, and assume that Hiten was already at the Moon at the desired distance from it, and traveling with the right speed as specified from my theory. This was the first time I had ever applied my work to a real spacecraft, and there was no way to know if my suggested approach would be successful. The problem presented to me by Miller triggered the missing piece in my research that was needed to make my method work. It was one of those rare moments of scientific discovery that happen in the blink of an eye.
Miller was a bit skeptical that it would work. I gave him some initial critical parameters he would need to use in the computer simulation, and he left to try it out. I knew it was going to work.
He came by my office the next day, looking both excited and stunned-with computer output in hand, saying, "It worked!" I was excited as well. Our results looked promising, but it would take some work to come up with a fully completed solution. So we started to determine a polished usable path to the Moon within the required margins. Not only would this path salvage the Japanese lunar mission, it would represent a new and revolutionary route to the Moon.
Excerpted from Fly Me to the Moon by Edward Belbruno Copyright © 2006 by Princeton University Press. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Foreword by Neil deGrasse Tyson ix
Chapter 1 A Moment of Discovery 1
Chapter 2 An Uncertain Start 5
Chapter 3 Conventional Way to the Moon 9
A Fuel Hog 14
Chapter 4 A Question 17
Chapter 5 Chaos and Surfing the Gravitational Field 29
What Is Chaos? 31
Chapter 6 Using Art to Find Chaotic Regions 37
An Oil Painting Unveiling Dynamical
Chapter 7 WSB—A Chaotic No-Man's-Land 41
Chapter 8 Getting to the WSB—Low Energy Transfers 49
Chapter 9 Rescue of a Lunar Mission 55
Skepticism, Politics, and a Bittersweet Success 63
Chapter 10 Significance of Hiten 69
Chapter 11 Salvage of HGS-1, and a Christmas Present 77
Chapter 12 Other Space Missions and Low Energy Transfers 83
LGAS Reincarnated: SMART 1 83
Europa Orbiter and Prometheus 85
A Lunar Transportation System 91
Chapter 13 Hopping Comets and Earth Collision 95
Potential Earth Collision 108
Jupiter-Hopping Earth-Crossing Comets Present a Danger 111
Kuiper Belt Objects and Neptune Hopping 113
Ballistic Escape from the Earth-Moon System, and Asteroid Capture 115
Chapter 14 The Creation of the Moon by Another World 119
Chapter 15 Beyond the Moon and to the Stars 129
Pluto to Alpha Centauri 129
Comets Moving between the Sun and Alpha Centauri 133
Chapter 16 A Paradigm Shift and the Future 137