Tidal Effects on Rotating Gaseous Ellipsoids Revolving around a Central Massive Object

摘要

A computationally integrable set of ordinary differential equations is derived for a gaseous ellipsoid of uniform density orbiting in the gravitational potential of an extended massive object (represented by the logarithmic potential). Numerical integrations can be conducted in the same mathematical exactitude as in the classical theory of a homogeneous liquid ellipsoid in equilibrium. First, we obtain a series of equilibrium figures moving in a circular orbit and analyze their linear and nonlinear stability. The gaseous ellipsoids that are elongated toward the center are not realized within a critical radial distance from the extended massive object, whereas those elongated along the circular orbit are distributed in the full range of the radial distance.