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Low energy interplanetary travel.

 by harnessing the gravitational fields created between  multiple bodies within our universe,

References: Edward  Belbruno Princeton University

1991 Low Energy Pathways.


2004 Capture Dynamics and Chaotic Motions in Celestial Mechanicsby Edward  Belbruno (Princeton)

ISBN13: 978-0-691-09480-9

2007 Fly me to the moon by Edward  Belbruno ( Princeton) ISBN13: 978-0-691-12822-1

1990 Japanese Moon mission recovery.


1997 Resonance hopping in comets. 

European Space Agency SMART1 Lunar probe used a similar low energy strategy for its mission.


After travelling  a certain distance away from Earth SMART 1 passes through the Lagrange gravitational equilibrium point between Earth >Moon and becomes captured by the gravitational pull of the Moon progressively spiralling towards the Moon's center.

This effect can be used to reduce the energy needed to send a satellite to the moon.

Example to travel the 348.103 Kms from the Earth to the moon.

SMART 1 took a 100.106 Km spiralling route that  only consumed 60Litres of Xenon fuel and the solar energy collected by its solar panels to create the ion stream.

At worst this indicates an effective consumption of 5.8.103 Km/L.

Or 1.67.106Km/L distance travelled.

DV = 3.5Km/s



Lagrange was a true European. Born in Turin in 1736  he later worked both in Germany and Paris, France where he died in 1813. Lagrange used mthematics to identify the existance of points of gravitational equilibrium.



An interesting property about points of  gravitational equilibrium is that they can be used to reduce the energy required by space craft to tour the universe. Put the space craft in orbit around a Legrange point and wait for it (the Legrange point) to revolve around the  solar system. Would take less energy than flying directly to a destination A>B.

Alternatively you can imagine the possibility of using a system of space corridors that link these Legrange points together forming a low energy space  link. It might take a lot longer than travelling direct to the intended destination but you could travel further and longer with the same amount of propellant. Increased flight time with unmanned space probes this isn't a problem.


nasa link of Lagrange pointshttp://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html



But you still need to be able to launch the space craft into an escape orbit. So the initial Dv  required  to escape the originating planet is still the same. But the Dv  for the interplanetary voyage will be reduced.


Article in American Scientist May June 2007



Fly Me to the Moon:
An Insider's Guide to the New Science of Space Travel

Edward Belbruno

A Moment of Discovery

“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 of a 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.


Relativity Gravity wells

Figure 4. Marbles circling...
Figure 4. Marbles circling in a gravity well—or planets circling the Sun—do so at a rate that depends on the size of their orbits: The smaller the orbit, the larger the angular frequency required to achieve balance (left). A demonstration device engineered to mimic the gravitational field that arises from a pair of massive objects, say the Sun and Earth, would be shaped like a large funnel with a small funnel embedded in it (lower right). Here the small funnel would have to orbit the large one, just as Earth orbits the Sun. A marble traveling around the large funnel at the same angular frequency could balance at two spots that straddle the small funnel (white crosses beneath marbles)—corresponding to Earth's L1 and L2 Lagrange points. With care, a marble could be positioned and given an initial velocity such that it would then "orbit" such special locations (at least for a limited time), just as Genesis was made to orbit Earth's L1 Lagrange point (upper right).
Jen Christiansen


Genesis Probe nasa



Here the LeGrange points L1 and L2 mark the Earth > Sun gravitational equilibrium points.

 LOOP-DE-LOOP. The Genesis spacecraft's superhighway path took it to the Earth-sun gravitational-equilibrium point L1, where it made five "halo" orbits before swinging around L2 and heading home.


- J. E. Marsden et S. D. Ross, New method in celestial mechanics and mission design, in Bulletin of the American Mathematical Society, vol. 43, pp. 43-73, 2006.
- C. Jaffé et al., Statistical theory of asteroids escape rates, in Physical Review Letters, vol. 89, article 011101, 2002.
- D.L. Smith, Next exit 0,5 million kilometers, in Enginnering & Science, vol. lxv(4), pp. 6-15, 2002.
- Animations et schémas sur le site de Shane Ross :  


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