Magnetic induction heating of planetary satellites: Analytical formulae and applications

Calculations of the magnetic induction heating planetary satellites to date have been done using approximate or numerical models. Here we present analytical formulae that may be used for either conducting metallic cores (spheres) water oceans rock mantles (spherical shells). The formula spheres has in classic electromagnetic literature nearly a century, but appears overlooked by astrophysicists. Analogous spherical shells are derived this paper. We apply these calculate alternating fields as seen frame an orbiting satellite. These arise from inclined horizontally displaced dipoles, well eccentric satellite orbits. derive these, making it easy investigate quickly importance many different system configurations. Magnetic our current Solar System unimportant each effects, greater past, exoplanetary systems, other celestial binaries.