Analytical determination of motion parameters of the center of mass of an uncooperative orbiter on the basis of measurement information provided by on-board systems of a space robot in a coplanar orbit

An analytical solution to the problem of determining the parameters of motion of an orbiter’s center of mass is presented on the basis on the results of measurements carried out using the optical system of a space robot located in orbit coplanar to that of the orbiter. The “space robot-orbiter” line-of-sight angle and the line-of-sight rate in the moving orbital system of coordinates of the space robot are selected as initial parameters that are measured by the space robot’s on-board optical system. Along with the known orbital parameters of the space robot they are used to solve the problem of determining the parameters of motion of the orbiter’s center of mass. When solving this task, assumptions are introduced concerning the central gravitational field of the Earth, the coplanarity of the orbits of the space robot and of the orbiter, absence of influence of the atmosphere, the moon's attraction and the pressure of the solar wind on the motion of the space robot and of the orbiter, absence of errors in the results of measurements performed by the space robot’s on-board optics. Analytical expressions are obtained to determine the unknown parameters of motion of the orbiter’s center of mass. The results presented can be used to develop methods allowing standalone determination of parameters of the orbit of unknown orbiters using on-board optics of a space robot.