Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 251978, 16 pages
Research Article

On the Evection Resonance and Its Connection to the Stability of Outer Satellites

Tadashi Yokoyama,1 Ernesto Vieira Neto,2 Othon Cabo Winter,2 Diogo Merguizo Sanchez,1 and Pedro Ivo de Oliveira Brasil1

1Departamento de Estatística, Matemática Aplicada e Computação (DEMAC), Instituto de Geociências e Ciências Exatas (IGCE), Universidade Estadual Paulista (UNESP), Caixa Postal 178, 13500-970 Rio Claro, SP, Brazil
2Grupo de Dinâmica Orbital e Planetologia, Faculdade de Engenharia de Guaratinguetá (FEG), Universidade Estadual Paulista (UNESP), Campus de Guaratinguetá, Caixa Postal 205, CEP 12516-410 Guaratinguetá, SP, Brazil

Received 15 August 2007; Accepted 6 February 2008

Academic Editor: Jose Balthazar

Copyright © 2008 Tadashi Yokoyama et al. 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.


In terms of stability around the primary, it is widely known that the semimajor axis of the retrograde satellites is much larger than the corresponding semimajor axis of the prograde satellites. Usually this conclusion is obtained numerically, since precise analytical derivation is far from being easy, especially, in the case of two or more disturbers. Following the seminal idea that what is unstable in the restricted three-body problem is also unstable in the general N-body problem, we present a simplified model which allows us to derive interesting resonant configurations. These configurations are responsible for cumulative perturbations which can give birth to strong instability that may cause the ejection of the satellite. Then we obtain, analytically, approximate bounds of the stability of prograde and retrograde satellites. Although we recover quite well previous results of other authors, we comment very briefly some weakness of these bounds.