Solution of the inverse problem for the gravitational field from the potential and its five derivatives at one point (Q2461068)

The inverse problem of the gravitational potential is to calculate the mass distribution from a known field in a given volume. The authors obtain a numerical solution of the inverse problem for the gravitational field at a single point using six elements of the field of a point mass, a spherical cap, a differential spherical sector and a vertical segment. The set of six equations contains the potential \(T\), the radial derivatives \(T_R\) and \(T_{RR}\), the projection \(T_S\) of the gravity force onto the tangent to the great circle arc \(S\) and the second order derivatives \(T_{SS}\) and \(T_{SR}\). Unknowns are the body mass, its center depth and the moments of the second, third and fourth orders. This numerical solution has turned out to be more accurate by a factor of ten as compared with solution by three field characteristics for a point mass, a spherical cap and a thin differential spherical sector.