Interplanetary Transport Network
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 are redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them, despite lacking an object to orbit. While they use little energy, the transport can take a very long time. Shane Ross has said "Due to the long time needed to achieve the low energy transfers between planets, the Interplanetary Superhighway is impractical for transfers such as from Earth to Mars at present."^{[2]}
Contents
History
Interplanetary transfer orbits are solutions to the gravitational "restricted three-body problem", which, for the general case, does not have exact solutions, and is addressed by numerical analysis approximations. However, a small number of exact solutions exist, most notably the five orbits referred to as "Lagrange points", which are orbital solutions for circular orbits in the case when one body is significantly more massive.
The key to discovering the Interplanetary Transport Network was the investigation of the nature of the winding paths near the Earth-Sun and Earth-Moon Lagrange points. They were first investigated by Jules-Henri Poincaré in the 1890s. He noticed that the paths leading to and from any of those points would almost always settle, for a time, on an orbit about that point.^{[3]} There are in fact an infinite number of paths taking one to the point and away from it, and all of which require nearly zero change in energy to reach. When plotted, they form a tube with the orbit about the Lagrange point at one end.
The derivation of these paths traces back to mathematicians Charles C. Conley and Richard P. McGehee in 1968.^{[4]} Hiten, Japan's first lunar probe, was moved into lunar orbit using similar insight into the nature of paths between the Earth and the Moon. Beginning in 1997, Martin Lo, Shane D. Ross, and others wrote a series of papers identifying the mathematical basis that applied the technique to the Genesis solar wind sample return, and to Lunar and Jovian missions. They referred to it as an Interplanetary Superhighway (IPS).^{[5]}
Paths
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 one will eventually end up on one of the outbound paths after spending no energy at all. Edward Belbruno coined the term "weak stability boundary"^{[6]} or "fuzzy boundary"^{[7]} for this effect.
With careful calculation, one can pick which outbound path one wants. This turned out to be useful, as many of these paths lead to some interesting points in space, such as the Earth's Moon or between the Galilean moons of Jupiter.^{[8]} As a result, for the cost of reaching the Earth–Sun L_{2} point, which is rather low energy value, one can travel to a number of very interesting points for a little or no additional fuel cost. But the trip from Earth to Mars or other distant location would likely take thousands of years.
The transfers are so low-energy that they make travel to almost any point in the Solar System possible.^{[citation needed]} On the downside, these transfers are very slow. For trips from Earth to other planets, they are not useful for manned or unmanned probes, as the trip would take many generations. Nevertheless, they have already been used to transfer spacecraft to the Earth–Sun L_{1} point, a useful point for studying the Sun that was employed in a number of recent missions, including the Genesis mission, the first to return solar wind samples to Earth.^{[9]} The network is also relevant to understanding Solar System dynamics;^{[10]}^{[11]} Comet Shoemaker–Levy 9 followed such a trajectory on its collision path with Jupiter.^{[12]}^{[13]}
Further explanation
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 L_{1} through L_{3}. For instance, the Earth–Moon L_{1} 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,^{[14]} there are two additional stable points denoted as L_{4} and L_{5}. 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 Earth–Moon L_{1} 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 L_{1} 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, called a halo orbit. The orbits for two of the points, L_{4} and L_{5}, are stable, but the halo orbits for L_{1} through L_{3} are stable only on the order of months.
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.^{[4]} For example, the gravity environment of the Sun–Earth–Moon system allows spacecraft to travel great distances on very little fuel^{[citation needed]}, albeit on an often circuitous route.
Missions
Launched in 1978, the ISEE-3 spacecraft was sent on a mission to orbit around one of the Lagrange points.^{[15]} 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 using what would later be called the ITN was the rescue of Japan's Hiten lunar mission in 1991.^{[16]} Another example of the use of the ITN was NASA's 2001–2003 Genesis mission, which orbited the Sun–Earth L_{1} point for over two years collecting material, before being redirected to the L_{2} Lagrange point, and finally redirected from there back to Earth. The 2003–2006 SMART-1 of the European Space Agency used another low energy transfer from the ITN. In a more recent example, the Chinese spacecraft Chang'e 2 used the ITN to travel from lunar orbit to the Earth-Sun L_{2} point, then on to fly by the asteroid 4179 Toutatis.
See also
Sources and notes
- ^ Ross, S. D. (2006). "The Interplanetary Transport Network" (PDF). American Scientist. 94: 230–237. doi:10.1511/2006.59.994.
- ^ The Interplanetary Superhighway; Shane Ross; Virginia Tech.
- ^ Marsden, J. E.; Ross, S. D. (2006). "New methods in celestial mechanics and mission design". Bull. Amer. Math. Soc. 43: 43–73. doi:10.1090/S0273-0979-05-01085-2.
- ^ ^{a} ^{b} Conley, C. C. (1968). "Low energy transit orbits in the restricted three-body problem". SIAM Journal on Applied Mathematics. 16: 732–746. doi:10.1137/0116060. JSTOR 2099124.
- ^ Lo, Martin W. and Ross, Shane D. (2001) The Lunar L1 Gateway: Portal to the Stars and Beyond, AIAA Space 2001 Conference, Albuquerque, New Mexico.
- ^ Edward A. Belbruno; John P. Carrico (2000). "Calculation of Weak Stability Boundary Ballistic Lunar Transfer Trajectories" (PDF). AIAA/AAS Astrodynamics Specialist Conference.
- ^ Frank, Adam (September 1994). "Gravity's Rim". Discover. Retrieved 29 August 2017.
- ^ Ross, S.D., W.S. Koon, M.W. Lo and J.E. Marsden (2003) Design of a Multi-Moon Orbiter Archived 2007-01-08 at the Wayback Machine.. 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 Archived 2007-01-08 at the Wayback Machine., Libration Point Orbits and Applications (Eds. G Gomez, M.W. Lo and J.J. Masdemont), World Scientific, pp. 637–652.
- ^ "The Lagrange Points" (PDF)., Neil J. Cornish with input from Jeremy Goodman
- ^ Farquhar, R. W.; Muhonen, D. P.; Newman, C.; Heuberger, H. (1980). "Trajectories and Orbital Maneuvers for the First Libration-Point Satellite". Journal of Guidance and Control. 3: 549–554. Bibcode:1980JGCD....3..549F. doi:10.2514/3.56034.
- ^ Belbruno, E. (2004). Capture Dynamics and Chaotic Motions in Celestial Mechanics: With the Construction of Low Energy Transfers. Princeton University Press. ISBN 9780691094809.
External links
- "The Interplanetary Transport Network" by Shane D. Ross, American Scientist, May–June 2006 (Subscription)
- "Ride the celestial subway" New Scientist, 27 March 2006
- "Tube Route" Science, 18 November 2005
- "Navigating Celestial Currents" Science News, 18 April 2005
- "Next Exit 0.5 Million Kilometers" Engineering and Science, 2002
- "Mathematics Unites The Heavens And The Atom," Space Daily, 28 September 2005
- "Asteroids Lost in Space" Physical Review Focus, 14 June 2002
- Interplanetary Transport Network lecture (YouTube) by Shane D. Ross, 2004
- "Cylindrical manifolds and tube dynamics in the restricted three-body problem" - PhD dissertation by Shane D. Ross
- 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 (2004)
- The Dynamical Mechanism of Ballistic Lunar Capture Transfers in the Four-Body Problem from the Perspective of Invariant Manifolds and Hill's Regions^{[permanent dead link]} by Edward Belbruno
- 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
- 2007-10-08 audio interview with Belbruno on low-energy transfer