An existence theorem for absolute geodetic singularities

Summary. It is shown that disturbing masses can be found which can give locally rise in the external gravity field of a spherically symmetric earth to singularities both in geodetic and in gravity space coordinates; in this connection the concept of absolute geodetic singularities is introduced. It is also shown that the previous results hold independently of the mass of the disturbing body and for densities of the disturbing mass which can be lower than the mean Earth density. The connection between the geodetic singularity problem and the study and design of gravity gradient compensators for orbital experiments is put into light.