Geodetic singularities in the gravity field of a non-homogeneous planet

Summary. An inverse geodetic singularity problem is considered for a non-homogeneous spherical planet. The singularity condition is expressed in terms of the density distribution and of the geometrical parameters of the configuration; the condition for the density distribution is deduced which gives rise to singularities of parabolic type in the external gravity field of the planet. The structure of the gravity field in the neighbourhood of the singularities is investigated in detail together with the behaviour of the gradients of the disturbances in the geodetic coordinates.