On the relationship between instability and Lyapunov times for the three-body problem

D. J. Urminsky, D. C. Heggie

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Abstract

In this study we consider the relationship between the survival time and the Lyapunov time for three-body systems. It is shown that the Sitnikov problem exhibits a two-part power-law relationship as demonstrated by Mikkola & Tanikawa for the general three-body problem. Using an approximate Poincare map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the three-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general three-body problem.

Original languageEnglish
Pages (from-to)1051-1059
Number of pages9
JournalMonthly Notices of the Royal Astronomical Society
Volume392
Issue number3
DOIs
Publication statusPublished - 21 Jan 2009

Keywords

  • stellar dynamics
  • celestial mechanics
  • time
  • OUTER ASTEROID BELT
  • ORIGINAL DISTRIBUTION

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