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Advances in Astronomy
Volume 2015, Article ID 615029, 7 pages
Research Article

Stability of the Moons Orbits in Solar System in the Restricted Three-Body Problem

Institute for Time Nature Explorations, M.V. Lomonosov’s Moscow State University, Leninskie Gory 1-12, Moscow 119991, Russia

Received 1 April 2015; Revised 3 June 2015; Accepted 4 June 2015

Academic Editor: Elmetwally Elabbasy

Copyright © 2015 Sergey V. Ershkov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the equations of motion of three-body problem in a Lagrange form (which means a consideration of relative motions of 3 bodies in regard to each other). Analyzing such a system of equations, we consider in detail the case of moon’s motion of negligible mass around the 2nd of two giant-bodies , (which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. Under assumptions of R3BP, we obtain the equations of motion which describe the relative mutual motion of the centre of mass of 2nd giant-body (planet) and the centre of mass of 3rd body (moon) with additional effective mass placed in that centre of mass , where ξ is the dimensionless dynamical parameter. They should be rotating around their common centre of masses on Kepler’s elliptic orbits. For negligible effective mass it gives the equations of motion which should describe a quasi-elliptic orbit of 3rd body (moon) around the 2nd body (planet) for most of the moons of the planets in Solar System.