Instabilities in the Sun-Jupiter-Asteroid three body problem

John C. Urschel, Joseph R. Galante

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider dynamics of a Sun-Jupiter-Asteroid system, and, under some simplifying assumptions, show the existence of instabilities in the motions of an asteroid. In particular, we show that an asteroid whose initial orbit is far from the orbit of Mars can be gradually perturbed into one that crosses Mars' orbit. Properly formulated, the motion of the asteroid can be described as a Hamiltonian system with two degrees of freedom, with the dynamics restricted to a "large" open region of the phase space reduced to an exact area preserving map. Instabilities arise in regions where the map has no invariant curves. The method of MacKay and Percival is used to explicitly rule out the existence of these curves, and results of Mather abstractly guarantee the existence of diffusing orbits. We emphasize that finding such diffusing orbits numerically is quite difficult, and is outside the scope of this paper.

Original languageEnglish (US)
Pages (from-to)233-259
Number of pages27
JournalCelestial Mechanics and Dynamical Astronomy
Volume115
Issue number3
DOIs
StatePublished - Mar 2013

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics

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