EDP Sciences
Free access
Volume 377, Number 3, October III 2001
Page(s) 1119 - 1127
Section The solar system
DOI http://dx.doi.org/10.1051/0004-6361:20011165

A&A 377, 1119-1127 (2001)
DOI: 10.1051/0004-6361:20011165

Time analysis for temporary gravitational capture

Stable orbits
O. C. Winter and E. Vieira Neto

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

(Received 20 April 2001 / Accepted 20 August 2001 )

In a previous work, Vieira Neto & Winter (2001) 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 1970; Huang & Innanen 1983). Their results are reviewed using Poincaré surface of sections. The stable non-planar retrograde trajectories, $110^{\rm o}\leq i< 180^{\rm o}$, are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case ( $i=180^{\rm o}$). 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 $i=60^{\rm o}$. Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at $i=120^{\rm o}$.

Key words: planets and satellites: general -- astrometry -- celestial mechanics

Offprint request: O. C. Winter, ocwinter@feg.unesp.br

© ESO 2001