Mathematical model of constraint problem of three bodies in noninertial reference system

Abstract

Many problems in the study of the motion of artificial earth satellites involve the introduction of a nonrotating geocentric system of coordinates [i, 3]. Such a system is not an inertial one, principally because of the earth's rotation about the barycenter (center of gravity) of the earth-moon system 9 This gives rise to inertial force perturbations, quite largely affecting high-altitude and particularly geostationary satellites [2]. In accordance with the principle of relativity pertaining to compensation of noninertial reference systems, it is necessary to add d'Alambert inertia forces to the active forces of gravitation. On the basis of the formulation [3, 7] of the boundary-value problem of three bodies, those forces can be determined through reversing the problem of two bodies and correctly accounting for the variability of the elliptical parameters of the orbit in which the perturbing body moves. The boundary-value problem of three bodies, its approximate solutions and integrals were used in earlier studies [4, 6] for calculating the trajectories of artificial cosmic bodies.