Numerical modeling of the trajectories of particles for measuring the gravitational constant on an artificial satellite

Abstract

The results of numerical modeling of the trajectories of motion of a light body (a “particle”) with respect to a heavier body in the orbit of an artificial satellite are presented [1]. Plane circular and elliptic orbits of the heavy body are considered, ignoring the nonsphericity of the gravitational field of the earth, and also plane circular equatorial orbits taking the quadrupole moment of the earth into account. The sensitivity of the trajectories to small variations of the initial conditions and values of the parameters of the gravitational interaction is investigated. It is shown that for the space experiment carried out in [2] to be successful for determining the gravitational constant G and the parameters of the five-force, and to check the principle of equivalence at large distances, the theoretical model of the motion of a “particle/rd must take into account all the perturbations which lead to a displacement of the trajectories of more than 10⁻⁴ mm.