Interplanetary Transport Network

The Interplanetary Transport Network (ITN) [Ross, S. D. 2006 [http://dx.doi.org/10.1511/2006.59.994 The Interplanetary Transport Network] . American Scientist 94:230-237.] is a collection of gravitationally determined pathways through the solar system that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space can be redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them, despite the absence of any material object therein.

History

The key to the Interplanetary Transport Network was investigating the exact nature of these winding paths near the points. They were first investigated by Jules-Henri Poincaré in the 1890s, and he noticed that the paths leading to and from any of these points would almost always settle, for a time, on the orbit around it [Marsden, J.E. and S.D. Ross. 2006. [http://www.ams.org/bull/2006-43-01/S0273-0979-05-01085-2/home.html New methods in celestial mechanics and mission design] . Bull. Amer. Math. Soc. 43:43-73] . There are in fact an infinite number of paths taking you to the point and back away from it, and all of them require no energy to reach. When plotted, they form a tube with the orbit around the point at one end, a view which traces back to mathematicians [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=8576&fChrono=1 Charles C. Conley] and [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=5602&fChrono=1 Richard P. McGehee] in the 1960s [Conley, C. C. 1968. Low energy transit orbits in the restricted three-body problem, SIAM Journal on Applied Mathematics 16:732-746.] . Theoretical work by Edward Belbruno in 1994 [Belbruno, E. 1994. [http://www.spaceroutes.com/papers/FTM1008.pdf The Dynamical Mechanism of Ballistic Lunar Capture Transfers in the Four-Body Problem from the Perspective of Invariant Manifolds and Hill's Regions] ] provided the first insight into the nature of the ITN between the Earth and the Moon that was used by "Hiten".

As it turns out, it is very easy to transit from a path leading to the point to one leading back out. This makes sense, since the orbit is unstable which implies you'll eventually end up on one of the outbound paths after spending no energy at all. However, with careful calculation you can pick "which" outbound path you want. This turned out to be quite exciting, because many of these paths lead right by some interesting points in space, like the Earth's Moon or the Galilean moons of Jupiter [Ross, S.D., W.S. Koon, M.W. Lo and J.E. Marsden. 2003. [http://www.esm.vt.edu/~sdross/papers/AAS-03-143.pdf Design of a Multi-Moon Orbiter] . 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico. Paper No. AAS 03-143.] . That means that for the cost of getting to the Earth–Sun L2 point which is rather low, one can travel to a huge number of very interesting points, for a low additional fuel cost, or even for free.

The transfers are so low-energy that they make travel to almost any point in the solar system possible. On the downside, these transfers are very slow, and only useful for automated probes. Nevertheless, they have already been used to transfer spacecraft out of the Earth-Sun L1 point, a useful point for studying the Sun that was used in a number of recent missions, including the Genesis mission [Lo, M. W., et al. 2001. Genesis Mission Design, The Journal of the Astronautical Sciences 49:169-184.] . The Solar and Heliospheric Observatory is here. The network is also relevant to understanding solar system dynamics [Belbruno, E., and B.G. Marsden. 1997. [http://dx.doi.org/10.1086/118359 Resonance Hopping in Comets] . The Astronomical Journal 113:1433-1444] [W.S. Koon, M.W. Lo, J.E. Marsden, and S.D. Ross. 2000. [http://dx.doi.org/10.1063/1.166509 Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics] . Chaos 10:427-469] ; Comet Shoemaker-Levy 9 followed such a trajectory to collide with Jupiter. [Smith, D. L. 2002. [http://pr.caltech.edu/periodicals/EandS/articles/LXV4/exit.html Next Exit 0.5 Million Kilometers] . Engineering and Science LXV(4):6-15] [Ross, S. D. 2003. [http://www.esm.vt.edu/~sdross/papers/ross-barcelona-2002.pdf Statistical theory of interior-exterior transition and collision probabilities for minor bodies in the solar system] , Libration Point Orbits and Applications (Eds. G Gomez, M.W. Lo and J.J. Masdemont), World Scientific, pp. 637-652.]

Further Explanation

In addition to orbits around Lagrange points, the rich dynamics that arise from the gravitational pull of more than one mass yield interesting trajectories, also known as low energy transfers [Conley, C. C. 1968. Low energy transit orbits in the restricted three-body problem, SIAM Journal on Applied Mathematics 16:732-746.] . For example, the gravity environment of the Sun-Earth-Moon system allows spacecraft to travel great distances on very little fuel, albeit on an often circuitous route. Launched in 1978, the ISEE-3 spacecraft was sent on a mission to orbit around one of the Lagrange points [Farquhar, R. W., D. P. Muhonen, C. Newman, and H. Heuberger. 1980. Trajectories and Orbital Maneuvers for the First Libration-Point Satellite, Journal of Guidance and Control 3:549-554.] . The spacecraft was able to maneuver around the Earth's neighborhood using little fuel by taking advantage of the unique gravity environment. After the primary mission was completed, ISEE-3 went on to accomplish other goals, including a flight through the geomagnetic tail and a comet flyby. The mission was subsequently renamed the International Cometary Explorer (ICE).

The first low energy transfer utilizing this network was the rescue of Japan's "Hiten" lunar mission in 1991 [Belbruno, E. 2004. [http://www.pupress.princeton.edu/titles/7687.html Capture Dynamics and Chaotic Motions in Celestial Mechanics: With the Construction of Low Energy Transfers] , Princeton University Press] . Another example of the use of the ITN was NASA's recent Genesis mission, which orbited the Sun-Earth L1 point for over two years collecting material, before being redirected to the L2 Lagrange point, and finally redirected from there back to Earth. Most recently, "SMART-1" of the European Space Agency used another low energy transfer from the ITN. The ITN is based around a series of orbital paths predicted by chaos theory and the restricted three-body problem leading to and from the unstable orbits around the Lagrange points — points in space where the gravity between various bodies balances with the centrifugal force of an object there. For any two bodies in which one body orbits around the other, such as a star/planet or planet/moon system, there are three such points, denoted L1 through L3. For instance, the Earth-Moon L1 point lies on a line between the two, where gravitational forces between them exactly balance with the centrifugal force of an object placed in orbit there. For two bodies whose ratio of masses exceeds 24.96, there are two additional stable points denoted as L4 and L5. These five points have particularly low delta-v requirements, and appear to be the lowest-energy transfers possible, even lower than the common Hohmann transfer orbit that has dominated orbital navigation in the past.

Although the forces balance at these points, the first three points (the ones on the line between a certain large mass (e.g. a star) and a smaller, orbiting mass (e.g. a planet)) are not stable equilibrium points. If a spacecraft placed at the L1 point is given even a slight nudge towards the Moon, for instance, the Moon's gravity will now be greater and the spacecraft will be pulled away from the L1 point. The entire system is in motion, so the spacecraft will not actually hit the Moon, but will travel in a winding path, off into space. There is, however, a semi-stable orbit around each of these points. The orbits for two of the points, L4 and L5, are stable, but the orbits for L1 through L3 are stable only on the order of months.

ee also

*Gravitational slingshot
*Low energy transfers
*Orbital mechanics

ources and notes

External links

* [http://dx.doi.org/10.1511/2006.59.994 "The Interplanetary Transport Network" American Scientist, May-June 2006 (Subscription)]
* [http://www.newscientist.com/article/mg18925441.300.html "Ride the celestial subway" New Scientist, 27 March 2006]
* [http://www.sciencemag.org/content/vol310/issue5751/r-samples.dtl#310/5751/1114a "Tube Route" Science, 18 November 2005]
* [http://sciencenews.org/articles/20050416/bob9.asp "Navigating Celestial Currents" Science News, 18 April 2005]
* [http://pr.caltech.edu/periodicals/EandS/articles/LXV4/exit.html "Next Exit 0.5 Million Kilometers" Engineering and Science, 2002]
* [http://www.spacedaily.com/news/cosmology-05z.html "Mathematics Unites The Heavens And The Atom" Space Daily, 28 September 2005]
* [http://focus.aps.org/story/v9/st31 "Asteroids Lost in Space" Physical Review Focus, 14 June 2002]
* [http://www.esm.vt.edu/~sdross/talks/index.html#els-2004 Interplanetary Transport Network lecture] by Shane D. Ross
* [http://etd.caltech.edu/etd/available/etd-05182004-154045/ PhD thesis] by Shane D. Ross
* [http://www.pupress.princeton.edu/titles/7687.html "Capture Dynamics and Chaotic Motions in Celestial Mechanics: With the Construction of Low Energy Transfers"] - A mathematical analysis of aspects of the ITN, Edward Belbruno
* [http://www.spaceroutes.com/papers/FTM1008.pdf The Dynamical Mechanism of Ballistic Lunar Capture Transfers in the Four-Body Problem from the Perspective of Invariant Manifolds and Hill's Regions] by Edward Belbruno
* [http://www.cds.caltech.edu/~marsden/books/Mission_Design.html "Dynamical Systems, the Three-Body Problem, and Space Mission Design"] , by Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden, Shane D. Ross (book available as PDF). ISBN 978-0-615-24095-4