Fly Me to the Moon: A Conversation
with Mathematician and Artist,
Ed Belbruno doesn’t sit still easily. On a sunny, winter afternoon, he perches at the edge of his sofa talking about his latest book, Fly Me to the Moon (Princeton University Press), and about chaos. Specifically chaos theory. In his book, Belbruno tells the story of how he used chaos theory to get the world’s first spaceship (a Japanese spaceship named Hiten, which means “A Buddhist Angel that Dances in Heaven”) to the moon without using fuel. To illustrate a point, his hands move through the air, creating a sunlit swirl of fine dust particles.
Belbruno’s own paintings adorn the walls of his living room, one of which gave him the solution for Hiten. In the corner, tubes of oil paint lie on a drafting table next to an easel exhibiting his latest work, gorgeous splashes of color representing microwaves.
“Chaos is a way to describe the motion of an object where the motion appears to be very unpredictable,” he says. “Some things are not chaotic and some things are.”
“For example,” he continues. “If you look at a leaf falling to the ground on a windy day, it doesn’t fall like a piece of lead rocketing to the ground. It floats. And if the wind catches that leaf, it will dart around from place to place, and the resulting path is not something you know ahead of time. So from moment to moment, you cannot say where the leaf will go. Therefore, chaos has a sense of unpredictability to it. You could say, ’Well does it mean that I can’t really know where something is going?’ In a sense you can’t, because you have to know every little detail of the atmosphere of the earth, about how the wind varies from point to point, and we don’t. The same holds true for space and the orbit of the planets.”
Belbruno knows that out of seeming chaos, a path can be found between two points. He was born in Heidelberg, Germany on a military base to a mother of German heritage, and a father of Sicilian heritage. After his father’s tour of duty, the family came back to the states when Belbruno was nearly two.
“On the ship, my mother was pregnant with my sister when my father told her she was cramping his style and that he wanted a new life,” says Belbruno. “So he took off. Mom showed up at her mother’s doorstep in New London, Connecticut. And although my father visited regularly, they were not a match made in heaven. He had a Sicilian background and she had a German background, and her parents hated Italians.”
So how did Belbruno, currently a Visiting Research Collaborator in the Department of Astrophysical Sciences at Princeton University, get from an army base in Heidelberg to solving a problem that has bedeviled scientists for generations, flying a spaceship to the moon using no fuel? His answer has everything to do with chaos theory and his own sense of destiny.
WRR: When did you first become interested in science?
Science has always been in my blood. I was thinking about planets at four or five years old. I remember asking my mother, “What is an astronaut?”
Likewise, art was always in my blood. When I was seven, my mother took me to an art shop in downtown New London, and bought me some oil paints. I started painting at eight.
Because I lived near the ocean, I was also interested in oceanography and that’s where I conducted my first experiment. I saw an article in Life magazine about how the navy was keeping mice alive in aquariums in fresh water blocked off from any kind of air. The application was ultimately meant to be used by scuba divers. Scientists put silicon membranes on the aquarium and submerged it in water. The membranes let oxygen pass through the water into the aquarium and the mice breathed this oxygen, expelling carbon dioxide through the membrane. They were able keep the mice alive with no external apparatus.
So, my friends and I said, “Hey let’s do the same thing. We’ll buy this material, build an aquarium, put silicone all over it, put a mouse in the aquarium, and take it to the beach.” Which is what we did.
We stayed up all night for two or three days, diving to check on the mouse, making sure it was alive. Which it was. The Hartford Current found out about this and put us on the front page. At fifteen years old, I ended up getting a National Science Foundation Grant, which I couldn’t use because I was too young.
WRR: You knew what you wanted to do at such a young age. So it would seem that science has always been a calling.
I have always had a very deep sense that science was much more than a calling. I knew that in pursuing this path, I would somehow be taken care of and nothing was going to get in the way of that. When I applied to Mitchell College where my mother worked, they said I wasn’t college material, but I knew I was. The first semester there I took remedial classes in math and English, and got in. But I ultimately took on too much and failed miserably. The next semester I had a teacher who was miraculous at teaching math and I clicked with this guy. I went from being a mediocre student to the best math student they’d had. I was doing two-hour math exams in 15 minutes and getting perfect scores. That’s when I knew I had a calling to do it. And likewise I had a calling for art. It was such a strong feeling in the core of my being that I knew if I didn’t follow this path, something bad might happen to me.
I remember when I got my Associate Degree from Mitchell College, I decided to attend New York University, and was accepted. My mom told me, “You’re not going to college. You’re going to stay here and get a job as a bank teller and bring home money for the family.”
But again I want to emphasize that I had this deep sense that everything was taken care of. Out of nowhere I got a phone call from a philanthropist in New London. And she said, “I was talking to the President of Mitchell College. I’ve heard about you and I would like to fund your education. You’re taken care of from Bachelors through your Masters to PhD.”
When that happened, although I was stunned, another part of me said, “Oh, this is how it’s going to happen.”
WRR: What did you study?
My goal was always to go into the space field. I initially majored in chemistry because I wanted to study astrochemistry. Carl Sagan was just beginning to get noticed and I realized that a lot of possibilities were open to me. So I took a course in physical chemistry.
I was just as curious about the process of discovery as I was about how one arrived at an answer so I asked the professor to show me how the answer was discovered.
He said, “In chemistry, we don’t care how you arrive at the answer; we just want to use it.”
When he said that to me, I dropped the class.
Because I was very much interested in space, I asked myself, how do I deal with space if I’m a mathematician? And I thought, aha! There’s a field called Celestial Mechanics, which describes the way things, move in space. They had the best guy in the world teaching the course, Juergen Moser. And he became my mentor.
WRR: What did you learn from Moser?
Moser wasn’t interested in hardcore issues of sending a spaceship anywhere or how the planets moved. He was a theoretician and a mathematician, really. And he taught me the theoretical underpinnings of celestial mechanics.
For example, celestial mechanics is a subfield of math. We look to French mathematician Henri Poincaré who wrote down these very simple-looking equations. But they gave rise to very deep things in mathematics, particularly chaos theory. In the 1960s, Moser rigorously proved that chaos existed in the field of celestial mechanics. His theory is called the Kolmogorov-Arnold-Moser Theorem (KAM). And it’s one if THE major theorems in the field of mathematics called dynamical systems.
Moser was interested in what is called a Three Body Problem. You start with a point. For this purpose, imagine it being the earth. Then you have a little thing going around the earth called the moon. Since you know the motions of these two planets, you can write down the equations for their motion and solve it. When you add a spaceship, which has zero mass, things get complicated.
Without the moon, you can solve the equations of motion for the spaceship. You have a spaceship and the earth, and from the work of Johannes Keppler, father of Celestial Mechanics, you know that the spaceship’s either going around by an ellipse or a parabola or a hyperbola. When you add the moon into the picture, all those parabolas change, and the problem becomes completely unsolvable. Three particles, and two of them you know, and we still don’t know how to solve the problem for the motion of the spaceship to this day.
The kind of work that Moser got me into was the mathematical beauty of the Two Body Problem, and all the complications that arise when you add a third body.
WRR: But you’ve also used your art to solve very difficult mathematical problems.
I do these two things but they’re completely different, almost as if I have two personalities. For years I struggled with these two parts of my personality. When I was in graduate school working with math, I turned the art off for a while. They really are separate, but the way art interfaces with math and science ultimately gave me the solution to getting the Japanese spaceship Hiten to the moon.
After I made the decision to leave academia, out of the blue, I got a call from the Jet Propulsion Laboratory (JPL) offering me a job to work in Pasadena for the Outer Planet Division. Something drove me to go there so I gave it all up including my fiancée and went.
Right before I left, I thought again about the philanthropist who gave me my education and I thought there’s really some kind of trend going on here. I was listening to Beethoven’s ninth symphony with a friend. The lights were out and candles were lit. We got to the end of the ninth symphony, the gorgeous crescendo and suddenly all the lights in the apartment went on and we both heard a booming voice say, “Universal simplicity.” From that moment on my life changed.
WRR: How did your life change?
When the JPL opportunity came up, I decided that from then on out I would trust the voice. However, when I got to JPL I thought, what a mistake.
I arrived as an academic mathematician trained in theory. With theory, you don’t care if you apply it in the real world. The question a mathematician would ask is, “How can the object move? What are the possibilities for movement if chaos is involved? They’re excellent questions and you need to ask them in order to solve equations. But they might not translate into physical applications until years later.”
At that time, JPL hired sixty PhDs including me in the orbit section just to design trajectories for spaceships. My job, while romantic on paper, turned out to be boring. I sat there all day making columns of numbers: Trajectory A goes to Jupiter. Trajectory B goes to Jupiter, varying the times by seconds.
I knew right away that this was not my cup of tea. So I got to thinking about the Three Body Problem. If the moon orbits around the earth, I wondered how you could get something to move around the moon in a stable orbit. That’s a hard problem. If you’re a spaceship and you’re moving around the earth in an ellipse, the moon doesn’t have a strong enough gravitational force to change your orbit. So it’s easy to go around the earth.
If you want something to go around the moon, the problem becomes more difficult because the moon is little and the earth has quite a gravitational force and can easily alter the orbit of the spaceship about the moon. So that’s the problem we don’t know how to solve.
All of my work had been to try and understand this problem. At JPL I saw that the problem had an important application. If spaceships go the standard direct route to the Moon, like the Apollo did, then when they arrive near to the Moon they are going too fast and must use their rocket engines and a lot of fuel to slow down enough to go into lunar orbit.
Let’s suppose you arrive at the moon much more slowly. Then you might be able to get the spacecraft captured without using its rocket engines to slow down. It would be captured into lunar orbit automatically. This would save a lot of fuel. But the path to the moon could be very complicated and the spacecraft would just meander along and not go directly like the standard route. This is the problem I looked at - finding a way to get a spacecraft automatically captured at the moon.
WRR: And you kept working on it.
I ended up talking to a professor at Cal Tech. He, too, saw that it was an interesting problem and encouraged me to stick with it. It was already a longstanding proposition called the Capture Problem where an object can get captured by a small body orbiting a big one. The Russians started to look at this in the sixties and no one could solve the problem. But everyone knew that chaos was involved and because of that they also knew it would be a very complicated problem. So I tried to understand it with no idea of how to apply it. In the back of my mind I knew that if we could understand it, there would be applications for capturing spaceships using very little fuel.
Then the Challenger blew up in 1986, and JPL began looking for an excuse to get rid of me. One guy said, “You’re one of those thinking types, aren’t you?”
“Don’t you think here?” I replied.
But they didn’t want people to think, they just wanted people to get spaceships to planets, period.
In other words, they already had it figured out. The federal government gave the Galileo Mission four billion dollars, and another four billion for the Cassini Mission. This is big business. They know how to get spacecraft there by using the standard techniques of high fuel. Why fiddle with it if it works?
To have someone at the lab like me making inroads into other ways of doing ‘orbit design’ where chaos was involved, they didn’t want to hear it, because chaos looks risky.
WRR: How did you save your job?
But I had another one of my knowing/trusting experiences. Something told me not to worry about it. A few weeks later my boss came in and said, “I can’t believe it. We got a grant. The director wants you to work with a group of scientists to get a little spaceship to the moon using no fuel. It was a paper study only (called LGAS for Lunar Get Away Special) but a very visible one at the lab.
They didn’t expect me to solve the problem. Which would have given the reason to send me to the door. So I freaked out and said, ”I’m going to solve it.“
And that’s when I made the painting that solved the problem. For me, Vincent Van Gogh’s art holds a key to the meaning of life. He obviously trusted forces we don’t understand yet. And I thought, maybe if I do a painting of the moon system in the way Van Gogh painted, it might show me a way to capture the route for nothing.
I painted, and suddenly I could see the route to the moon, how a spaceship could go right in. Then, I went to the computer and mimicked that. And it worked!
WRR: What kind of process kicked in?
When I got to the point that I wanted to use the art, I told myself to work so fast that I couldn’t think. I let the unconscious forces take over because I realized at that point that the art was a completely different way of thinking than the science.
The brush strokes showed me how to capture the moon’s gravity. And that led to designing a computer program that allowed me to map out this region of the moon where you could get captured for free.
We tried it out and it worked on the computer, although the route took two years. Everyone was very happy and the story made the front page of the LA Times. I thought JPL would love me because I had worked on the project and found a solution. I thought they would throw flower petals at my feet. Instead everyone was upset because the article talked about chaos.
Bob Mitchell, who is now the manager of the Cassini Mission, got some funding for me to see if I could now get a spaceship to Jupiter using my ideas for automatic capture. He was throwing me a bone, but I don’t think he expected me to solve it. And I didn’t.
He and his colleagues likely anticipated my ideas would fail in the Jupiter problem, and that would justify the suspicion that my work was weird and not useful. In fact, my theory at the time was called Fuzzy Boundary Theory, because the chaos regions about the moon were not well defined. This name together with the term chaos was not the kind of terminology that they wanted associated with multi-billion dollar missions they were working on. They thought my work was a bit crazy.
And they said to me, ”Two years to get to the moon! I don’t care how much fuel we’re saving, who would want to take that long?“
I think they felt that two years to the moon was just a waste. It was a fluky thing I did. Basically they said, ”It’s a cool technique, but it doesn’t have any application.“
WRR: But then you figured out a way to get Hiten to the moon in much shorter time.
I think the universe set me up to solve the problem of useful automatic capture four years later for a real mission. Three months after I was fired in January 1990 due to my ideas, I had finally let go of all the anxiety I had accumulated with JPL over both being fired and trying to convince them of the usefulness of my work. And in a flash, I suddenly saw how to solve it. The irony of it all is that it wasn’t a Three Body problem; it was a Four Body problem using earth, moon, and sun, which gave rise to a route that takes only three months. I needed a break from the pressure in order to solve it.
WRR: Which brings us to Hiten.
Yes. I was told that the Japanese had a failed mission where the mother craft was locked in orbit around the moon in early 1990 soon after I was fired from my job.
Japan had already lost a spacecraft designed to go into orbit about the moon. It was lost just around the time I was fired. The mother craft, Hiten, was going around the earth with no fuel in it. Hiten was never designed to go to the moon and was to be only a communications relay for the spacecraft that was lost. They asked around quietly if there was a way to rescue the mission by getting the mother craft to the moon even though it had no fuel.
Jim Miller, an engineer at JPL was assigned to try and find a way to get Hiten to the moon in order the salvage the Japanese lunar mission. He soon found that Hiten had basically no fuel to get to the Moon and into orbit. He had exhausted all standard ways to try and get Hiten there and automatically captured. One day in April 1990, I heard a knock at my door and Miller was standing there. He said, ”I heard about your work. I heard it was bullshit. But, I’ll try anything at this point.“
Then a flash of light went on in my head. I suggested they use my theory, but that they should model it by adding the sun, and they would probably find the route they wanted. He came back the next day, and said, ”My god this works.“
And this is the route we used for Hiten. Instead of two years, it took three months to get to the Moon.
WRR: It’s interesting that Hiten means ”Buddhist Angel that Dances in Heaven.“ You practice hard science, yet in your book, Fly Me to the Moon, you mention that Hiten’s name was no accident. Where does divinity fit into science?
To me, divinity rests in the fact that there was a clear sequence of events. The moment I arrived at JPL, I was already set up to fail. There was no way I would have come up with the route Hiten used even if they had thrown money at me. It really took a dramatic situation for my brain to put the puzzle pieces together. And the route I discovered not only saved Hiten, it became a new way to think about space travel.
The universe clearly set things up so that I had to let go of everything in order to see the answer. Because frankly I was in the way of myself.
WRR: Even after you made this major discovery people still weren’t happy.
Well, the discovery happened because it was intended to happen. Yet, it wasn’t enough to vindicate me. Even though I did this with Jim Miller, the Japanese didn’t like it because they didn’t want it to look like an American was saving their mission. So they wanted me to sign a paper saying I wasn’t going to talk about it. But I refused to sign.
There were call-ins at WABC because the LA Times had published an article about Hiten. People were angry with JPL, Miller, and me because they said we were giving away secrets to Japan. We gave away the car industry, they said. And now we’re giving away the space industry. JPL did not say to me, ”Here’s your job back“ because that would be admitting the error that was made in judging my work.
Finally, I left and drove to Minnesota where I stayed for five years to chill out and I lived in an art studio. I painted and was affiliated with the University of Minnesota. Then, a friend asked if I could patent this work. So we filed for a patent and made a little company. Shortly after that, Princeton asked me to join the math group.
Now, I’m pursuing research problems in this field, writing books, and building my art career.
WRR: What is your opinion about the current space program?
That’s a tough question. But like anything else, they operate under the model that if you can make it cheap, it is successful. I think the big hope everyone has always had is how to solve the danger of rocket ships blasting off from earth. Plus the space program is extremely expensive even when they try to make things on the cheap.
To me, the only time space travel will really take off is if we can find an easy way to get into space. We don’t have that. Getting into space is still very expensive and risky.
WRR: Now that you’ve finished Fly Me to the Moon, what are you working on?
I’m painting microwaves, which are relatively short currents of energy that burst forth in wonderful patterns. I don’t know what it is about those paintings, except whatever they are, they’re me.
They represent my letting go. I call it a core letting go. If we can let go of major obstacles holding us back in our lives, if we can let go of them in an instant, we’re going to find that things will happen for us that we can’t imagine in our wildest dreams.
To learn more about Ed Belbruno, his science, his books and his art, go to www.EdBelbruno.com.