Following the method developed by Bel, Salas and Sanchez Ron (1973) to solve the equations of predictive mechanics, and the method by Bel and Martin (1975) to obtain the momentum and angular momentum of a system of particles, the author obtains the accelerations, momentum and angular momentum for two gravitating particles to the first order in G. As 'criterial' conditions for the determination of the acceleration he has used the Lorentz invariant equations obtained by Havas and Goldberg, (1962).