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Abstract: We construct a secular theory of a coplanar system of N-planets not involvedin strong mean motion resonances, and which are far from collision zones.Besides the point-to-point Newtonian mutual interactions, we consider thegeneral relativity corrections to the gravitational potential of the star andthe innermost planet, and also a modification of this potential by thequadrupole moment and tidal distortion of the star. We focus on hierarchicalplanetary systems. A survey regarding model parameters the masses, semi-majoraxes, spin rate of the star reveals a rich and non-trivial dynamics of thesecular system. Our study is focused on its equilibria. Such solutionspredicted by the classic secular theory, which correspond to aligned mode Ior anti-aligned mode II apsides, may be strongly affected by thegravitational corrections. The so called true secular resonance, which is a newfeature of the classic two-planet problem discovered by Michtchenko and Malhotra2004, may appear in other, different regions of the phase space of thegeneralized model. We found bifurcations of mode II which emerge new, yetunknown in the literature, secularly unstable equilibria and a complexstructure of the phase space. These equilibria may imply secularly unstableorbital configurations even for nitially moderate eccentricities. The pointmass gravity corrections can affect the long term-stability in the secular timescale, which may directly depend on the age of the host star through its spinrate. We also analyze the secular dynamics of the upsilon Andromede system inthe realm of the generalized model. Also in this case of the three-planetsystem, new secular equilibria may appear.



Autor: Cezary Migaszewski, Krzysztof Gozdziewski

Fuente: https://arxiv.org/



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