Celletti A., Chierchia L.
Birth of resonances in the spin--orbit problem of celestial mechanics
(711K, Poscript)
ABSTRACT. The behaviour of resonances in the spin-orbit coupling in Celestial
Mechanics is investigated. We introduce a Hamiltonian nearly-integrable
model describing an approximation of the spin-orbit interaction.
A parametric representation of periodic orbits is presented.
We provide explicit formulae to compute the Taylor series
expansion in the perturbing parameter of the function describing this
parametrization. Then we compute approximately the radius of convergence
providing an indication of the stability of the periodic orbit.
This quantity is used to describe the different probabilities of
capture into resonance. In particular, we notice that for low values
of the orbital eccentricity the only significative resonance is the
synchronous one. Higher order resonances (including 1:2, 3:2, 2:1)
appear only as the orbital eccentricity is increased.