Equations of Motion in General Relativity

Abstract

This paper contains a new derivation of the equations of motion of bodies moving slowly in their (weak) gravitational field, up to terms of the order (v/c)². In contrast to the method developed previously by Einstein and co-workers, in which only the field outside the bodies has been considered, in the present paper a new method is used in which the field outside as well as inside the bodies, and the internal structure of the bodies, is taken into consideration. The equations of motion derived by this new method are identical with those obtained by Einstein and co-workers, but the new method is essentially simpler and the necessary calculations much less lengthy