Mother body problem

This chapter is devoted to the following problem. Given an external gravitational field, produced by some body, there arises the question of determining the form and mass density of this body. Similar problems appear in geoprospecting, where one measures the gravitational field on the ground surface and wants to determine the source of this gravitational field located inside the earth. Clearly, the solution of this problem is not unique. For example, it has been well known since the time of Newton that a ball with constant mass density produces the same gravitational field as the same mass concentrated at the center of the ball. © Springer International Publishing AG 2017.