Capture in Exterior Mean-Motion Resonances Due to Poynting-Robertson Drag

Abstract 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 β and planetary mass m 1 . 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 β and m 1 . 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 10 5 -10 6 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 m 1 > 10 -3 β. 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.