Dynamics of Particles in a Gravitational Field

Abstract

The dynamics of particles in a gravitational field is investigated using Lagrange mechanics. Dynamic equations are obtained, including the rate of energy and momentum transfer to the gravitational field. The motion of particles in the Schwarzschild field is considered, and in the case of weak gravitation, it is determined the passive gravitational mass of a photon and a material particle under condition of the relationship between the gravitational potential and its velocity α/r<<V²/c². The active gravitational mass is found for the system special case of two identical bodies moving in opposite directions.