Some Periodic Solutions of a Four-Body Problem
Abstract
A four-body problem which is a model for the motion of a particle or vehicle in the Sun-Earth-Moon system is obtained by rotating the barycenter B of the two massive bodies in a restricted three-body configuration about a third massive body. It is shown that this problem can be regarded as a perturbation of the restricted three-body problem where the perturbation parameter is the mass of the third body divided by the cubed distance from the third body to B. It is proved that under certain conditions, especially with a restriction on the magnitude of the perturbation parameter, the particle of negligible mass has a periodic motion near each of the libration points of the restricted three-body problem; a method for estimating the restriction on the magnitude of the perturbation parameter is described.
- Publication:
-
Icarus
- Pub Date:
- December 1964
- DOI:
- 10.1016/0019-1035(64)90003-X
- Bibcode:
- 1964Icar....3..423C