Tidal Behavior of a Self-Gravitating, Viscoelastic Planet: Analytical Theory for a Multilayered Body

This presentation will give the analytical solution of the equations governing the response of a gravitating stratified planet to an impulse stress. The complete solution is expressed as a sum of Bessel functions of positive and negative orders. Contrary to the usual method of numerical integration of the sets of six-order differential equations, our new method is merely implemented through the inversion of a (6N-3) square matrix, where N is the number of homogeneous layers constituting the body. We will compare the results provided by both methods for various types of planetary bodies such as icy satellite and Mercury, whose internal structure is under the focus of forthcoming space mission. Our method proves to be a straightforward and accurate way to compute Love numbers.