Co-Orbital Motion with Slowly Varying Parameters

Details Co-Orbital Motion with Slowly Varying Parameters Co-Orbital Motion with Slowly Varying Parameters

Aug 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003cemda..86..321s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 86, Issue 4, p. 321-350 (2003).

Astronomy and Astrophysics

Astronomy

1

Scientific paper

We consider the dynamics of a test particle co-orbital with a satellite of mass ms which revolves around a planet of mass M0 >> ms with a mean motion ns and semi-major axis as. We study the long term evolution of the particle motion under slow variations of (1) the mass of the primary, M0, (2) the mass of the satellite, ms and (3) the specific angular momentum of the satellite Js. The particle is not restricted to small harmonic oscillations near L4 or L5, and may have any libration amplitude on tadpole or horseshoe orbits. In a first step, no torque is applied to the particle, so that its motion is described by a Hamiltonian with slowly varying parameters. We show that the torque applied to the satellite, as measured by $\epsilon_{\rm s}=\dot{J}_{\rm s}/(n_{\rm s}J_{\rm s})$ induces an distortion of the phase space which is entirely described by an asymmetry coefficient α = ɛs/μ, where μ = ms/M. The adiabatic invariance of action implies furthermore that the long term evolution of the particle co-orbital motion depends only on the variation of msas with time. Applying a constant torque to the particle, as measured by $\epsilon_{\rm p}=\dot{J}/(n_{\rm s}J_{\rm s})$ is then merely equivalent to replacing α = ɛs/μ by α = (ɛs - ɛp)/μ. However, if the torque acting on the particle exhibits a radial gradient, then the action is no more conserved and the evolution of the particle orbit is no more controlled by msas only. We show that even mild torque gradients can dominate the orbital evolution of the particle, and eventually decide whether the latter will be pulled towards the stable equilibrium points L4 or L5, or driven away from them. Finally, we show that when the co-orbital bodies are two satellites with comparable masses m1 and m2, we can reduce the problem to that of a test particle co-orbital with a satellite of mass m1 + m2. This new problem has then parameters varying at rates which are combinations, with appropriate coefficients, of the changes suffered by each satellite.

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