Keldysh Institute of Applied Mathematics, Moscow, Russia
We examine the rotational motion of an axisymmetric planet with a liquid core in a central gravitational field. We assume, that the planet's center of mass moves about an attracting center in a circular nonevolving orbit. The characteristic rotational velocity of the planet about its center of mass substantially exceeds the orbital angular velocity.
The planet's core is represented as a spherical cavity containing a high-viscosity incompressible fluid. As it was shown by F.L.Chernous'ko(1968), in this case the effect of a liquid core is equivalent to the action on a "frozen" planet of special type of nonconservative torque.
We devote our attention mainly to analyzing the secular changes in the planet's rotational motion. To investigate these phenomena we apply the averaging method. The following qualitative features of the motion evolution are established: the fast rotation of a planet gradually becomes slower and the inclination of its equator to the orbidal plane gradually increases.
The final stage of evolution was studied usine postponed in our group, when Prof.Markeev and Prof.Sokol'skii left KIAM. It will be nice to resume this activity.