Some Considerations on the Theoretical Determination of the Potential by the Motion of Artificial Satellites in the Plane Case

We consider the determination of the potential from the orbit of a satellite. The potential obtained is not unique because the satellite might describe the same orbit with different forces. The classical problem of determination of orbits has a unique solution, for given initial conditions. The problem is reduced to the planar case with a conservative force. The mathematical results depend on the arbitrary functions of the system of coordinates used.