Interplanetary Transport Network

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This stylized depiction of the ITN is designed to show its often convoluted path through the solar system. The green ribbon represents one path from among the many that are mathematically possible along the surface of the darker green bounding tube. Locations where the ribbon changes direction abruptly represent trajectory changes at Lagrange points, while constricted areas represent locations where objects linger in temporary orbit around a point before continuing on.

The Interplanetary Transport Network (ITN)^[1] 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 even though there is no material object at them.

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^[2]. 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^[3]. 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^[4]. 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 two bodies whose ratio of masses exceeds 24.96, there are two other stable points denoted as L4 and L5. 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. 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 (star) and a smaller, orbiting mass (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 in the order of months.

1 History
2 Commonality with atomic physics
3 See also
4 Sources and notes
5 External links

[edit] 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^[5]. 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 Charles C. Conley and Richard P. McGehee in the 1960s^[6]. Theoretical work by Edward Belbruno in 1994^[7] 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^[8]. That means that for the cost of getting to the Earth–Sun L2 point (Lagrange points L1, L2, and L3 exist for all bodies in orbit of each other; L4 and L5 exist for pairs of bodies with a great enough mass ratio, e.g.: Earth–Moon, Sun-Earth, Sun-Mars etc.) which is rather low, one can travel to a huge number of very interesting points, for low 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^[9]. The Solar and Heliospheric Observatory is here. The network is also relevant to understanding solar system dynamics^[10]^[11]; Comet Shoemaker-Levy 9 followed such a trajectory to collide with Jupiter^[12]^[13].

[edit] Commonality with atomic physics

There is a rough analogy between the dynamical theory of bodies in classical mechanics and a heuristic used in computational chemistry calculations of reaction equilibria and reaction rates^[14]^[15]. Transition states, or intermediates in a chemical reaction, may be identified with regions in the phase space describing the evolution of the reaction. Transitions taking one state to another state are thus rough analogues of trajectories in classical mechanics. This heuristic is a rough one only and many refinements are necessary to obtain satisfactory results. Still, algorithms developed in one context are often usefully applied to the other^[16].

[edit] See also

[edit] Sources and notes

^ Ross, S. D. 2006 The Interplanetary Transport Network. American Scientist 94:230-237.
^ Conley, C. C. 1968. Low energy transit orbits in the restricted three-body problem, SIAM Journal on Applied Mathematics 16:732-746.
^ 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.
^ Belbruno, E. 2004. Capture Dynamics and Chaotic Motions in Celestial Mechanics: With the Construction of Low Energy Transfers, Princeton University Press
^ Marsden, J.E. and S.D. Ross. 2006. New methods in celestial mechanics and mission design. Bull. Amer. Math. Soc. 43:43-73
^ Conley, C. C. 1968. Low energy transit orbits in the restricted three-body problem, SIAM Journal on Applied Mathematics 16:732-746.
^ Belbruno, E. 1994. The Dynamical Mechanism of Ballistic Lunar Capture Transfers in the Four-Body Problem from the Perspective of Invariant Manifolds and Hill's Regions
^ Ross, S.D., W.S. Koon, M.W. Lo and J.E. Marsden. 2003. Design of a Multi-Moon Orbiter. 13th AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puerto Rico. Paper No. AAS 03-143.
^ Lo, M. W., et al. 2001. Genesis Mission Design, The Journal of the Astronautical Sciences 49:169-184.
^ Belbruno, E., and B.G. Marsden. 1997. Resonance Hopping in Comets. The Astronomical Journal 113:1433-1444
^ W.S. Koon, M.W. Lo, J.E. Marsden, and S.D. Ross. 2000. Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. Chaos 10:427-469
^ Smith, D. L. 2002. Next Exit 0.5 Million Kilometers. Engineering and Science LXV(4):6-15
^ Ross, S. D. 2003. 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.
^ Jaffe, C., S.D. Ross, M.W. Lo, J. Marsden, D. Farrelly, and T. Uzer. 2002. Statistical theory of asteroid escape rates. Physical Review Letters, 89(1):011101.
^ National Science Foundation. 2005. Mathematics Unites the Heavens and the Atom. Press Release 05-168
^ American Association for the Advancement of Science, 2005. Tube Route. Science 310(5751):1114.

[edit] External links

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Orbital elements	Inclination ( $i\,\!$ ) • Longitude of the ascending node ( $\Omega\,\!$ ) • Eccentricity ( $e\,\!$ ) • Argument of periapsis ( $\omega\,\!$ ) • Semi-major axis ( $a\,\!$ ) • Mean anomaly at epoch ( $M_o\,\!$ )
Other orbital parameters	True anomaly ( $v\,$ ) • Semi-minor axis ( $b\,$ ) • Linear eccentricity ( $\epsilon\,$ ) • Eccentric anomaly ( $E\,$ ) • Mean longitude ( $L\,$ ) • True longitude ( $l\,$ ) • Orbital period ( $T\,$ )
Orbital maneuvers	Bi-elliptic transfer • Geostationary transfer orbit • Gravitational slingshot • Hohmann transfer orbit • Orbital inclination change • Orbit phasing • Space rendezvous
Other orbital mechanics topics	Apsis • Celestial coordinate system • Delta-v budget • Epoch • Ephemeris • Equatorial coordinate system • Ground track • Interplanetary Transport Network • Kepler's laws of planetary motion • Lagrangian point • List of orbits • n-body problem • Orbit equation • Orbital state vectors • Retrograde and direct motion • Specific orbital energy • Specific relative angular momentum