Observatorio Nacional, Brazil
Resonance trapping in the Solar System occurs when a body is subject to a nonconservative force that brings it to a mean motion commensurability with a perturbing planet. For low eccentricities, the second fundamental model for resonance (Henrard & Lemaitre, 1982, Celest. Mech., 30, 197) and extensions to higher orders (Lemaitre, 1984, Celest. Mech. 32, 109) are used to compute trapping probabilities in an adiabatic regime. These models simulate well many problems in celestial mechanics where there is a dissipative effect. However, to arrive at a hamiltonian system, a noncanonical term in the variation of the momentum must be neglected. These terms should appear in a more rigorous treatment for problems in which the nonconservative force yields a secular variation in the eccentricity. Although there is usually little loss in neglecting the noncanonical term in the derivative of the momentum, at least one interesting point is put in evidence when one considers this more complete model, which is a possible explanation for resonance trapping in the case of diverging orbits.
Although we can show examples of such resonance trapping with this improved model, we cannot so far assume that it explains all or even any of the real cases observed in numerical simulations, because we are still dealing with a low eccentricity model, whereas resonance trapping for diverging orbits usually occurs for moderate to high eccentricities. Moreover, these numerical simulations show trappings for cases where there is a moderate close approach to the perturber (Gomes, 1996, Proceedings of the IAU Colloquium No. 150) and it is doubtful whether an average theory can be used for this purpose.