Veronica Danesi

Universit√† degli Studi di Roma “Tor Vergata”

Construction of the Kolmogorov normal form for three-body planetary problems with double Mean-Motion Resonance: the case study of the HD60532 extrasolar system

We investigate the dynamics of the two giant planets in the HD60532 system, which gives an example of extrasolar system in mean-motion resonance. We consider the secular approximation at order one in the masses which results (after the reduction of the constant of motions) in a resonant Hamiltonian with two libration angles. In this framework, the usual algorithms constructing the Kolmogorov normal form approach do not easily apply and we need to perform some untrivial preliminary operations, in order to adapt the method to this kind of problems. In practice, we start from an averaging procedure over the fast angle of libration which provides an integrable approximation of the Hamiltonian. Then we introduce action-angle variables that are adapted to such an integrable approximation. This sequence of preliminary operations brings the Hamiltonian in a suitable form to successfully start the Kolmogorov normalization scheme. This allows us to reconstruct the quasi-periodic motion of the system, with initial conditions that are compatible with the observations.

This work is made in joint collaboration with U. Locatelli and M. Sansottera.

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Construction of the Kolmogorov normal form for three-body planetary problems with double Mean-Motion Resonance: the case study of the HD60532 extrasolar system
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