Much of the early theoretical work in electricity and magnetism appears to have been the result of applying celestial mechanical principles to electrostatics. Examples include Cavendish's inverse-square law experiment (which had an analogous gravitational statement due to Newton), and Poisson's application of potential theory to electrostatics (in fact, generally, Poisson's work in electrostatics involved using analytical tools developed by himself and e.g. Laplace, Legendre, Lagrange, and Biot, mostly in relation to mechanics, to Coulomb's experiments). Not to mention the relationship between magnetism and the Earth, which almost blends the two together. Considering the existence of a large body of work on gravity and celestial mechanics, it seems like the analytical approach to electricity would have borrowed heavily from it. How much does E&M owe to celestial mechanics and the mathematicians who developed it? Were there many essential developments which were due mostly or entirely to celestial mechanics?