  Analytic expressions that describe Casimir interactions over the entire range
of separations have been limited to planar surfaces. Here we derive analytic
expressions for the classical or high-temperature limit of Casimir interactions
between two spheres (interior and exterior configurations), including the
sphere-plane geometry as a special case, using bispherical coordinates. We
consider both Dirichlet boundary conditions and metallic boundary conditions
described by the Drude model. At short distances, closed-form expansions are
derived from the exact result, displaying an intricate structure of deviations
from the commonly employed proximity force approximation.
