A Regularization of the Nonstationary Two-Body Problem Under the Maneff Perturbing Potential

Abstract

Within the framework of classical mechanics, the Maneff model of gravitational potential constitutes a nonrelativistic modification of Newton’s gravitational law which can be successfully used to accurately account for the secular motion of the pericentre of some celestial bodies, at least in the Solar System (e.g. the advance of the perihelion of the inner planets, or the motion of the perigee of the Moon.) We are concerned with the two-body problem as contemplated in classical celestial mechanics, and concentrate on the so-called Gylden systems, say two-body problems with variable Keplerian parameter,μ(t). On such systems, we superimpose perturbing effects emanating from a Maneff-type nonrelativistic gravitational potential, and we intend to arrive at regularized equations of motion for the resulting dynamical system.