Effect of slow variations of parameters for 2 co-orbital satellites and stationary configurations for N co-orbital satellites

Details Effect of slow variations of parameters for 2 co-orbital satellites and stationary configurations for N co-orbital satellites Effect of slow variations of parameters for 2 co-orbital satellites and stationary configurations for N co-orbital satellites

Aug 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003dda....34.1005s&link_type=abstract

American Astronomical Society, DDA meeting #34, #10.05; Bulletin of the American Astronomical Society, Vol. 35, p.1045

Astronomy and Astrophysics

Astronomy

Scientific paper

We study the evolution of a test particle co-orbital with a satellite of mass ms and semi-major axis as, orbiting around a planet of mass M0, under the slow evolution of (1) M0, (2) ms and (3) the variation of the specific angular momentum of the satellite, Js, 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 dJs/dt and by ms/(M_0 + ms), 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 msa_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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