 98620 Celletti A., Chierchia L.
 Birth of resonances in the spinorbit problem of celestial mechanics
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Sep 28, 98

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Abstract. The behaviour of resonances in the spinorbit coupling in Celestial
Mechanics is investigated. We introduce a Hamiltonian nearlyintegrable
model describing an approximation of the spinorbit 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.
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