The effect of Jupiter's mass growth on satellite capture

Retrograde case

¹ Grupo de Dinâmica Orbital & Planetologia, UNESP, CP 205 CEP 12.516-410 Guaratinguetá, SP, Brazil e-mail: ernesto@feg.unesp.br
² Universidade Estadual Paulista, IGCE, DEMAC, CP 178 CEP 13.500-970 Rio Claro, SP, Brazil e-mail: tadashi@ms.rc.unesp.br

Corresponding author: O. C. Winter, ocwinter@feg.unesp.br

Received: 13 June 2003
Accepted: 12 September 2003

Abstract

Gravitational capture can be used to explain the existence of the irregular satellites of giants planets. However, it is only the first step since the gravitational capture is temporary. Therefore, some kind of non-conservative effect is necessary to to turn the temporary capture into a permanent one. In the present work we study the effects of Jupiter mass growth for the permanent capture of retrograde satellites. An analysis of the zero velocity curves at the Lagrangian point L₁ indicates that mass accretion provides an increase of the confinement region (delimited by the zero velocity curve, where particles cannot escape from the planet) favoring permanent captures. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time considering the decrease of M_♃. We considered initial conditions of the particles to be retrograde, at pericenter, in the region 100 R_♃ ≤ a ≤ 400 R_♃ and 0 ≤ e ≤ 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values are an indication of the necessary conditions that could provide capture. An analysis of these results shows that retrograde satellites would be captured as soon as they get inside the Hills' radius and after that they keep migrating toward the planet while it is growing. For the region where the orbits of the four “old” retrograde satellites of Jupiter (Ananke, Carme, Pasiphae and Sinope) are located we found that such satellites could have been permanently captured when Jupiter had between 62% and 93% of its present mass.