ABSTRACT
The center of mass of an isolated system of N bodies interacting only via Newton’s law, moves in space with constant velocity and in a straight line. The sum of the products of the mass on the projection of corresponding sectorial velocities is a constant for an n-body system. One difference exists between Kepler’s law in the case of the two-body problem and the “Kepler law” for an n-body system. From all 6n integrals required for the complete solution of the n-body problem, only ten are obtained – six integrals of motion of the center of mass, three integrals of areas and the integral of energy. It became clear that further progress in the n-body problem would have to be associated with perturbation theory. The virial theorem has a direct relation to n-body systems. This theorem plays an essential role in statistical mechanics and in stellar dynamics, enabling one to obtain the dynamical characteristics of the systems.
