An overview of problems connected with dynamics of finite number of rigid bodies attracting according to the Newton's law of universal gravitations is presented. In this context new form of equations of motion of N rigid bodies is proposed. It is shown that these new, the so called Newton-Euler equations are Hamiltonian and that are possesses a symmetry group. Both these facts are used to perform a Poisson reduction. The new form of equations of motion is used for study problems of the relative equilibria existence.