Mathematical modeling of movement the reflected pulses on the surface of the earthwhen laser ranging spacecraft are in circular orbits

A mathematical model of motion on the Earth-s surface reflected from the spacecraft light pulses, emitted by laser station, is built. The numerical analysis of this model carried out. It is shown that for high altitude near-earth spacecraft the centers of the spots, formed by the reflected light pulses, are moving on the surface of the Earth at a speed not exceeding 2 m/s, while away from laser station, changing in the process of location from 1100 m to 200 m and to 1100 m. For the low orbital spacecraft, this distance is reduced approximately forty times. Therefore, the receiving telescope of the laser station on the fringe of the spot, formed by the reflected light pulse on the surface of the Earth, and the flow electromagnetic energy taken them, obviously less energy flow, in the center of the spot. To increase the value of the received flow of energy proposed receiving telescope to separate from the laser station, make it mobile and move over the surface of the Earth, so the center of each spot, formed by the reflected light pulses, got into the telescope.