A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L1and L2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L1and L2is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L1and the other around L2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold ‘tubes’ associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.
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- Belbruno, E. and Marsden, B.: 1997, ‘Resonance Hopping in comets’, Astr. J. 113(4), 1433-1444.Google Scholar
- Conley, C.: 1968, ‘Low energy transit orbits in the restric ted three-body problem’, SIAM J. Appl. Math. 16, 732-746.Google Scholar
- Howell, K. C., Marchand, B. G. and Lo, M. W.: 2000, ‘Temporary Satellite Capture of Short-Period Jupiter Family Comets from the Perspective of Dynamical Systems’, AAS/AIAA Space Flight Mechanics Meeting, Paper No. 00-155, Clearwater, Florida, U.S.A.Google Scholar
- Koon, W. S., Lo, M. W., Marsden, J. E. and Ross, S. D.: 2000, ‘Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics’, Chaos 10(2), 427-469.Google Scholar
- Llibre, J., Martinez, R. and Simó, C.: 1985, ‘Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem’, J. Differ. Eq. 58, 104-156.Google Scholar
- Lo, M. and Ross, S.: 1997, ‘SURFing the solar system: invariant manifolds and the dynamics of the solar system’, JPL IOM 312/97, 2-4.Google Scholar
- McGehee, R.: 1969, ‘Some Homoclinic Orbits for the Restricted Three Body Problem’, PhD Thesis, University of Wisconsin, Madison, Wisconsin, U.S.A.Google Scholar
- Parker, T. S. and Chua, L. O.: 1989, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York.Google Scholar
- Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.Google Scholar