Binary and triple collisions causing instability in the free-fall three-body problem
- 49 Downloads
Dominant factors for escape after the first triple-encounter are searched for in the three-body problem with zero initial velocities and equal masses. By a global numerical survey on the whole initial-value space, it is found that not only a triple-collision orbit but also a particular family of binary-collision orbits exist in the set of escape orbits. This observation is justified from various viewpoints. Binary-collision orbits experiencing close triple-encounter turn out to be close to isosceles orbits after the encounter and hence lead to escape. Except for a few cases, binary-collision orbits of near-isosceles slingshot also escape.
Unable to display preview. Download preview PDF.
- Agekian, T. A. and Martynova, A. I.: 1973, Vestn. Leningrad Univ., p. 122-126.Google Scholar
- Marchal, C.: 1990, Section 188.8.131.52 of The three-body problem, Elsevier, New York.Google Scholar
- Simó, C. and Martínez, R.: 1988, 'Qualitative study of the planar isosceles three-body problem', Celest. Mech. & Dyn. Astr. 41, 179-251.Google Scholar
- Umehara, H., Tanikawa, K. and Aizawa, Y.: 1995, 'Triple collision and escape in the three-body problem', in: Y. Aizawa, S. Saito and K. Shiraiwa (eds), Dynamical Systems and Chaos, World Scientific, Singapore, Vol. 2, pp. 404-407.Google Scholar
- Umehara, H. and Tanikawa, K.: 1996, 'Dominant roles of binary and triple collisions in the freefall three-body problem', in: J. C. Muzzio, S. Ferraz-Mello and J. Henrard (eds), Chaos in Gravitational N-Body Systems, Kluwer Academic Publishers, Netherlands, pp. 285-290.Google Scholar
- Umehara, H.: 1997, 'The free-fall three-body problem: escape and collision', PhD Thesis, The Graduate University for Advanced Studies, Mitaka, Tokyo, 181-8588 Japan.Google Scholar
- Umehara, H. and Tanikawa, K.: 2000, 'Improvement of the triple-encounter criterion', Publ. Astron. Soc. Japan (submitted).Google Scholar
- Waldvogel, J.: 1973, 'Collision singularities in gravitational problems', in: B. D. Tapley and V. Szebehely (eds), Recent Advances in Dynamical Astronomy, Reidel Publishing Company, Dordrecht, Holland, pp. 21-33.Google Scholar
- Junzo Yoshida: 1997, Private communications.Google Scholar
- Zare, K. and Szebehely, V.: 1995, 'Order out of chaos in the three-body problem: regions of escape', in: Roy and Steves (eds), From Newton to Chaos, Plenum Press, New York, pp. 299-313.Google Scholar