Providing Spacecraft Inspection in the Plane of a Circular Orbit, Taking into Account the Second Zonal Harmonic

Abstract

The problem of providing the inspection motion of one spacecraft (inspector) relative to another spacecraft (reference spacecraft) moving in a circular orbit is being solved. Inspection refers to the motion of the inspector around the reference spacecraft. In unperturbed motion, it is possible to select initial conditions that provide a closed trajectory of the inspector’s motion relative to the reference spacecraft; however, the influence of the Earth’s oblateness from the poles will lead to the evolution of such a trajectory. The paper presents two approaches that make it possible to select the initial parameters of the motion of the reference spacecraft and the inspector, which provide inspection motion taking into account the second zonal harmonic J2 of the Earth’s gravitational potential (oblateness of the Earth from the poles). In this case, the inspector’s motion is considered in the plane of the circular orbit of the reference spacecraft. The first approach is to select the initial positions of the reference spacecraft in its orbit, at which the oblateness of the Earth does not have a significant effect on the relative trajectory of the inspector. This motion of the inspector is close to the unperturbed relative trajectory. Analytical relationships are obtained that allow one to select the necessary motion parameters. The second approach is to select the relative velocity of the inspector, ensuring inspection motion, taking into account the influence of the Earth’s oblateness. This approach based on the equality of the total orbital energies of the inspector and the reference spacecraft.