Mathematics – Probability
Scientific paper
Aug 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994icar..110..239b&link_type=abstract
Icarus (ISSN 0019-1035), vol. 110, no. 2, p. 239-260
Mathematics
Probability
34
Capture Effect, Circular Orbits, Orbital Resonances (Celestial Mechanics), Poynting-Robertson Effect, Radiation Pressure, Three Body Problem, Adiabatic Equations, Drag, Libration, Planetary Mass
Scientific paper
In this paper we discuss the process of resonance trapping, due to radiation pressure and Poynting-Robertson drag, in the frame of the planar circular restricted problem of three bodies. We consider the averaged resonant equations and search for stationary solutions (i.e., librations) which may act as possible capture centers. These solutions are found to exist in all external mean-motion resonances, for a wide range of values of the drag coefficient beta and planetary mass m1. The 1/2, 2/3, and 1/3 commensurabilities are discussed in detail. Particular attention is given to the variation of the parameters of the libration solutions (position and stability) as functions of beta and m1. The analytical results are then compared with numerical simulations of the exact equations. Even though trappings are effectively found in these points, they are temporary: after a few 105 - 106 years the particle suffers a close encounter with the perturber, resulting in an ejection from the resonance. Concerning the orbital evolution from the nonresonant initial conditions to the final librational orbit, we find the averaged system to be adiabatic in general for m1 greater than 10-3 beta. In this interval, the dissipative problem can be approximated by a slowly varying one degree of freedom Hamiltonian system. We apply the formalism of the adiabatic invariant theory and discuss the mechanism and probability of capture in each resonance. Results are once again compared with numerical integrations.
Beauge Christian
Ferraz-Mello Sylvio
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