Dipartimento di Matematica “Tullio LeviCivita”, Università degli Studi di Padova
3D secular dynamics for extrasolar planetary systems: an overview
While averaged models of the planar (2D) planetary 3body problem yield an integrable dynamics, 3D averaged models yield a richinstructure problem associated with a nonintegrable two DOF secular Hamiltonian model. The talk will review some basic results stemming from the analysis of such a 3D secular model for exoplanetary dynamics. The emphasis will be on results obtained by a suitable decomposition of the (Jacobireduced) Hamiltonian under the form H = H_{planar}+ H_{3D}. The term H_planar yields the usual dynamics structured by the nonlinear normal modes associated with apsidal corotation resonances (ACR). The term H_{3D}, instead, leads to a sequence of bifurcations of new periodic orbits which bridge the ACR family with the family of highly inclined circular orbits associated with the Kozai resonance. The talk will review how the structure of the phase space varies by altering a properly chosen parameter (representing, essentially, the increase in mutual inclination), as well as the dependence of phase portraits on the remaining important parameters of the problem, namely the mass ratios of the two planets with respect to the central star and the semimajor axis ratio of the planetary heliocentric orbits (work in collaboration with Rita Mastroianni, UniPD).
Event Timeslots (1)
Tuesday

3D secular dynamics for extrasolar planetary systems: an overview
tmscm