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.
@article{arxiv.0903.1299,
title = {Application of the proximity force approximation to gravitational and Yukawa-type forces},
author = {R. S. Decca and E. Fischbach and G. L. Klimchitskaya and D. E. Krause and D. López and V. M. Mostepanenko},
journal= {arXiv preprint arXiv:0903.1299},
year = {2009}
}