**34th Meeting of the AAS Division on Dynamical Astronomy, May 2003**

* 10 Satellites and Rings*

Oral, Tuesday, May 6, 2003, 3:25-5:10pm,
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## [10.05] Effect of slow variations of parameters for 2 co-orbital satellites and stationary configurations for N co-orbital satellites

*B. Sicardy, S. Renner (Observatoire de Paris), V. Dubois (Universite de Nantes)*

We study the evolution of a test particle co-orbital with a
satellite of mass m_{s} and semi-major axis a_{s}, orbiting
around a planet of mass M_{0}, under the slow evolution of
(1) M_{0}, (2) m_{s} and (3) the variation of the specific
angular momentum of the satellite, J_{s}, caused by a
torque.

We show that the particle motion is distorted (with respect
to the classical horsheshoe and tadpole orbits) in a manner
which is entirely described by dJ_{s}/dt and by m_{s}/(M_{0} +
m_{s}), for any amplitude of the corotation motion.

Adiabatic invariance arguments show that the long term
evolution of the particle motion only depends on the
variation of m_{s}a_{s}.

Generalization can be made when a constant torque is applied
to the particle as well. If this torque exhibits a radial
gradient, however, then the adiabatic invariance of action
is destroyed and the evolution of the system must be studied
case by case.

We finally investigate the stationary configurations of N
co-orbital satellites with unequal masses. We show that if
N is even, a relation between the angular separations of
the co-orbitals must be verified to permit an equilibrium,
with a two-parameter family of possible masses. If N is
odd, then for any angular separations of the co-orbitals,
there is a one-parameter family of masses which allows
equilibrium. The case N=3 can be solved analytically and
will be displayed.

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Bulletin of the American Astronomical Society, **35** #4

© 2003. The American Astronomical Soceity.