The focus of this thesis is a collection of problems of timely interest in orbital dynamics and interior structure of planetary bodies. The first three chapters are dedicated to understanding the interior structure of close-in, gaseous extrasolar planets (hot Jupiters). In order to resolve a long-standing problem of anomalously large hot Jupiter radii, we proposed a novel magnetohydrodynamic mechanism responsible for inflation. The mechanism relies on the electro-magnetic interactions between fast atmospheric flows and the...