Modification of Laser Ranging Equation

The goal of this paper is to discuss the atmospheric turbulence effects on the laser ranging, especially for the lunar laser ranging. Concerning the returned laser photons from the space retroreflector for a laser pulse firing from the ground telescope, the laser beam wander that is caused by the turbulence plays an important role in it. Considering the short-term beam wander and the Gaussian distribution of the laser beam along radial, a new form of the laser ranging equation is given. If the atmospheric tilt, that corresponds to the beam wander, is removed, the returned photon numbers will be increased a factor of 6 to 40, depend on the turbulence