Celestial Mechanics and Dynamical Astronomy

, Volume 76, Issue 3, pp 187–214 | Cite as

Binary and triple collisions causing instability in the free-fall three-body problem

  • Hiroaki Umehara
  • Kiyotaka Tanikawa
Article

Abstract

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.

three-body problem triple collision binary collision escape chaos 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Hiroaki Umehara
    • 1
  • Kiyotaka Tanikawa
    • 2
  1. 1.Communications Research Laboratory, HiraiKashima Space Research CenterKashima, IbarakiJapan
  2. 2.National Astronomical Observatory, MitakaTokyoJapan

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