**DPS Pasadena Meeting 2000, 23-27 October 2000**

*Session 61. Dynamics Posters*

Displayed, 1:00pm, Monday - 1:00pm, Friday, Highlighted Tuesday and Thursday, 3:30-6:30pm, C101-C105, C211
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## [61.05] An Analytical Study of Orbits Around Rotating Nonsymmetric Objects

*O. Olsen (ITA)*

ESA's upcoming Rosetta mission and NASA's NEAR mission have
made it interesting to study orbits around rotating non
symmetric objects. For simplicity, only the C_{20} and
C_{22} parts of the potential are included. The potential
is expanded in a Fourier-series in the Poincare variables. A
canonically invariant perturbation theory as derived by
Deprit, Cel. Mech, 1:12, 1969, is used to derive a secular
theory valid near resonances of the form 2w\approx N\,n,
where N is an integer, w is the angular velocity of the
rotating nucleus and n is the mean motion of the orbiter.
The theory is easily extended to other resonances.

This secular Hamiltonian is used to derive the location of
stable fixed points in the averaged phase space. With the
help of the canonical invariant perturbation theory, the
location of the fixed points in the instantaneous phase
space is recovered. These orbits' long term evolution is
checked by numerical integration of the equations of motion.

The author(s) of this abstract have provided an email address
for comments about the abstract:
oeysteio@astro.uio.no

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