In this letter, the problem of an energy-conserving spacecraft surveillance system is addressed. It is assumed that the geostationary Earth orbit satellite is equipped with the radar reflector antenna, which provides high accuracy and a high ground resolution of the specified Earth area. Essential properties of Earth monitoring through a radar phase-shift-keyed signal are studied. For a multibeam radar, the algorithm for switching the partial directional tracks is proposed, providing the uniform exposure of the area of interest with the highest possible density of the probing beams for the minimal time under conditions of uniform satellite rotation about the centroidal axis and the constant probing frequency. The numerical example is presented, showing the efficacy of the proposed algorithm.