The three-dimensional motion of Trojan asteroids

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The problem is considered within the framework of the elliptic restricted three-body problem. The asymptotic solution is derived by a three-variable expansion procedure. The variables of the expansion represent three time-scales of the asteroids: the revolution around the Sun, the libration around the triangular Lagrangian points L4, L5, and the motion of the perihelion. The solution is obtained completely in the first order and partly in the second order. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter. As an example for the perturbations of the orbital elements the main perturbations of the eccentricity, the perihelion longitude and the longitude of the ascending node are given. Conditions for the libration of the perihelion are also discussed.

Original languageEnglish
Pages (from-to)141-161
Number of pages21
JournalCelestial Mechanics
Issue number2
Publication statusPublished - Aug 1 1978


ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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