The Open Astronomy Journal

2014, 7 : 29-32
Published online 2014 December 31. DOI: 10.2174/1874381101407010029
Publisher ID: TOAAJ-7-29

Quasi-periodic Solutions of a Spiral Type for Photogravitational Restricted Three-Body Problem

Sergey V. Ershkov
Institute for Time Nature Explorations, M.V. Lomonosov's Moscow State University, Leninskie gory, 1-12, Moscow 119991, Russia.

ABSTRACT

A new type of exact solutions for photogravitational restricted three-body problem (a case of spiral motion) is presented here.

A key point is that we obtain the appropriate specific case of spiral motions from the Jacobian-type integral of motion for photogravitational restricted three-body problem (when orbit of small 3-rd body is assumed to be like a spiral).

Besides, we should especially note that there is a proper restriction to the type of spiral orbital motion of small 3-rd body, which could be possible for choosing as the exact solution of equations for photogravitational restricted three-body problem.

The main result, which should be outlined, is that in a case of quasi-planar orbital motion (of the small 3-rd body) the asymptotic expression for component z of motion is proved to be given by the proper elliptical integral.

Keywords:

Photogravitational restricted three-body problem, spiral motion, Jacobian-type integral of motion.