Restricted four-body problem. The case of a central configuration: Libration points and their stability |
| |
Authors: | Yu D Medvedev N I Perov |
| |
Institution: | (1) Institute of Applied Astronomy, Russian Academy of Sciences, nab. Kutuzova 10, St. Petersburg, 191187, Russia;(2) Yaroslavl State Pedagogical University, ul. Respublikanskaya 108, Yaroslavl, 150000, Russia |
| |
Abstract: | We consider the problem of the motion of a zero-mass body in the vicinity of a system of three gravitating bodies forming a central configuration.We study the case where two gravitating bodies of equal mass lie on the same straight line and rotate around the central body with the same angular velocity. Equations for calculating the equilibrium positions in this system have been derived. The stability of the equilibrium points for a system of three gravitating bodies is investigated. We show that, as in the case of libration points for two bodies, the collinear points are unstable; for the triangular points, there exists a ratio of the mass of the central body to the masses of the extreme bodies, 11.720349, at which stability is observed. |
| |
Keywords: | celestial mechanics central configuration libration points positions of libration points stability of libration points |
本文献已被 SpringerLink 等数据库收录! |
|