Time analysis for temporary gravitational capture

Stable orbits

Grupo de Dinâmica Orbital & Planetologia, UNESP, CP 205, Guaratinguetá, CEP 12500-000, SP, Brazil e-mail: ernesto@feg.unesp.br

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

Received: 20 April 2001
Accepted: 20 August 2001

Abstract

In a previous work, Vieira Neto & Winter ([CITE]) numerically explored the capture times of particles as temporary satellites of Uranus. The study was made in the framework of the spatial, circular, restricted three-body problem. Regions of the initial condition space whose trajectories are apparently stable were determined. The criterion adopted was that the trajectories do not escape from the planet during an integration of 10⁵ years. These regions occur for a wide range of orbital initial inclinations (i). In the present work it is studied the reason for the existence of such stable regions. The stability of the planar retrograde trajectories is due to a family of simple periodic orbits and the associated quasi-periodic orbits that oscillate around them. These planar stable orbits had already been studied (Hénon [CITE]; Huang & Innanen [CITE]). Their results are reviewed using Poincaré surface of sections. The stable non-planar retrograde trajectories, , are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case (). It was not found any periodic orbit out of the plane associated to such quasi-periodic orbits. The largest region of stable prograde trajectories occurs at . Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at .