English

Periodic orbits in the restricted four-body problem with two equal masses

Classical Analysis and ODEs 2015-06-05 v1 Earth and Planetary Astrophysics

Abstract

The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral triangle in a rotating coordinate system. A massless fourth body moves under the Newtonian gravitational law due to the three primaries, as in the Restricted three-body problem (R3BP), the fourth mass does not affect the motion of the three primaries. In this paper we explore symmetric periodic orbits of the restricted four-body problem (R4BP) for the case of two equal masses where they satisfy approximately the Routh's critical value.

Keywords

Cite

@article{arxiv.1205.3446,
  title  = {Periodic orbits in the restricted four-body problem with two equal masses},
  author = {Jaime Burgos-García and Joaquín Delgado},
  journal= {arXiv preprint arXiv:1205.3446},
  year   = {2015}
}

Comments

We offer an exhaustive study of each family of periodic orbits and the stability of each of them

R2 v1 2026-06-21T21:04:34.061Z