**DPS 2001 meeting, November 2001**

*Session 37. Galilean and Other Outer Planet Satellite Posters*

Displayed, 9:00am Tuesday - 3:00pm Saturday, Highlighted, Friday, November 30, 2001, 9:00-10:30am, French Market Exhibit Hall
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## [37.12] Time Analysis for Temporary Gravitational Capture.Stable Orbits

*O.C. Winter, E. Vieira Neto (UNESP - BRAZIL)*

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 10^{5} 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 and Huang & Inanen,1983).
Their results are reviewed using Poincaré surface of
sections. The stable non-planar retrograde trajectories,
110^{o} < i < 180^{o} are found to be tridimensional
quasi-periodic orbits around the same family of periodic
orbits found for the planar case (i =180^{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^{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^{o} .

Acknowledgments. OCW and EVN thanks Fapesp and OCW also
thanks CNPq for financial support.

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