Systems Engineering Seminar

Low Energy Transfers to the Moon and Beyond,
Exploiting Resonance Transitions

Presented by: Edward Belbruno,
Princeton University and Innovative Orbital Design (IOD), Inc.

October 2, 2007, 1:00 p.m.
GSFC Building 3 Auditorium


In the late 1980s, new routes to the Moon were found that demonstrated for the first time that a spacecraft could travel from the Earth to the Moon, and be captured into lunar orbit automatically – that is, with no rocket engines required. This approach uses the concept of weak capture, where a spacecraft will be tenuously connected gravitationally to the Moon, moving chaotically. In 1991 a Japanese spacecraft was rescued and brought to the Moon using this methodology. Another such route was used in 2004 for an ESA lunar mission (SMART-1). However, an understanding of the weak capture process remained elusive. Recently, the nature of weak capture and a region supporting it about the Moon has been obtained. It is associated to a very interesting form of motion called a resonance transition, where an object jumps rapidly between different resonance motions- these are motions about the Earth, in resonance with respect to the Moon. (This process is analogous to an electron jumping between resonance states). We’ll show how to visualize the resonance structure associated to weak capture.. This shows that when an object is weakly captured by the Moon, it is actually in a resonance transition with respect to the Earth. This is a surprising result. It is uncovered through the use of special visualizations on so called surfaces of section, which have an exquisite geometric appearance. These results have already led to a new understanding of ballistic capture transfers from the Earth to the Moon, as trajectories undergoing resonance transitions. This understanding has led to the discovery of an interesting type of low fuel transfer that may be used for Mars missions and beyond. New types of low energy orbits are also described about the Moon which allow inclination changes by a factor of 12 less Delta-V than traditional orbits, enabling new lunar architectures in support of a lunar base.



Dr. Edward Belbruno received his PhD from NYU”s Courant Institute (1981) in mathematics, as a student of Juergen Moser. From there he was an assistant professor at Boston University, then he went to NASA’s JPL in 1986 as a trajectory designer for: Galileo, Cassini, Magellan, Ulysses, Mars Observer.

His work led to the first application of dynamical systems to space travel, finding low energy routes to the Moon and other places. The first was used in 1991 to rescue a Japanese lunar mission with a new type of route and transport its spacecraft, Hiten, to the Moon. Another such route was used by ESA’s SMART 1 lunar spacecraft in 2004. He recently published a technical textbook in 2004 on this subject, Capture Dynamics and Chaotic Motions in Celestial Mechanics and a popular version of this just came out this year entitled Fly Me to the Moon: An Insiders Guide to the New Science of Space Travel (Princeton University Press).

He has published many papers in the fields of mathematics, aerospace engineering and astronomy, and is editor of five proceedings volumes. He’s president of the company, Innovative Orbital Design, Inc. based in Princeton and holds a number of patents on routes in space.

He is also an artist (oil painter) and has had international exhibitions, including Paris, Rome, Los Angeles, Washington DC, New York, Minneapolis, and a painting of his is in NASA’s executive collection.


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