  We apply the proximity force approximation, which is widely used for the
calculation of the Casimir force between bodies with nonplanar boundary
surfaces, to gravitational and Yukawa-type interactions. It is shown that for
the gravitational force in a sphere-plate configuration the general formulation
of the proximity force approximation is well applicable. For a Yukawa-type
interaction we demonstrate the validity of both the general formulation of the
proximity force approximation, and a simple mapping between the sphere-plate
and plate-plate configurations. The claims to the contrary in some recent
literature are thus incorrect. Our results justify the constraints on the
parameters of non-Newtonian gravity previously obtained from the indirect
dynamic measurements of the Casimir pressure.

Quantum Physics