  A compact form for the static Green's function for symmetric loading of an
elastic sphere is derived. The expression captures the singularity in closed
form using standard functions and quickly convergent series. Applications to
problems involving contact between elastic spheres are discussed. An exact
solution for a point load on a sphere is presented and subsequently generalized
for distributed loads. Examples for constant and Hertzian-type distributed
loads are provided, where the latter is also compared to the Hertz contact
theory for identical spheres. The results show that the form of the loading
assumed in Hertz contact theory is valid for contact angles up to about 10
degrees. For larger angles, the actual displacement is smaller and the contact
surface is no longer flat.
