On a linear inverse potential problem with approximate data on the potential field on an approximately given surface

An approximate solution of the linear inverse problem for the Newtonian potential for bodies of constant thickness is constructed. The solution is stable with respect to the error in the data on the potential field given on an inaccurately known surface. The problem is reduced to an integral equation of the first kind, the proof of the stability of the solution is based on the Tikhonov regularization method.