34 research outputs found
The generalized non-conservative model of a 1-planet system - revisited
We study the long-term dynamics of a planetary system composed of a star and
a planet. Both bodies are considered as extended, non-spherical, rotating
objects. There are no assumptions made on the relative angles between the
orbital angular momentum and the spin vectors of the bodies. Thus, we analyze
full, spatial model of the planetary system. Both objects are assumed to be
deformed due to their own rotations, as well as due to the mutual tidal
interactions. The general relativity corrections are considered in terms of the
post-Newtonian approximation. Besides the conservative contributions to the
perturbing forces, there are also taken into account non-conservative effects,
i.e., the dissipation of the mechanical energy. This dissipation is a result of
the tidal perturbation on the velocity field in the internal zones with
non-zero turbulent viscosity (convective zones). Our main goal is to derive the
equations of the orbital motion as well as the equations governing
time-evolution of the spin vectors (angular velocities). We derive the
Lagrangian equations of the second kind for systems which do not conserve the
mechanical energy. Next, the equations of motion are averaged out over all fast
angles with respect to time-scales characteristic for conservative
perturbations. The final equations of motion are then used to study the
dynamics of the non-conservative model over time scales of the order of the age
of the star. We analyze the final state of the system as a function of the
initial conditions. Equilibria states of the averaged system are finally
discussed.Comment: 37 pages, 13 figures, accepted to Celestial Mechanics and Dynamical
Astronom