The authors study the change in shape of the orbit of a satellite sinking (because of dynamical friction) towards the center of a larger galaxy. The galaxy is assumed spherically symmetric with distribution function either isotropic or predominantly radial. The satellite is a softened point mass. The orbit evolution is studied analytically using the Chandrasekhar (1943) approximation for the dynamical friction drag and the epicyclic approximation for the orbit of the satellite, and numerically, by direct integration of an N-body system. Fully self-consistent spherical models have been used for the galaxy.