Velocity aberration and atmospheric refraction in satellite laser communication experiments

The effects of satellite velocity aberration and atmospheric refraction on the direction of propagation of lagser radiation reflected from a satellite back to an observer on the earth are examined. A velocity aberration analysis for the two-dimensional case where the satellite passes directly overhead at velocity v is presented to first order in v/c in order to illustrate the method. The equations for the more general threedimensional case are then given to first order in v/c, and it is indicated that higher order treatments are normally unnecessary in typical experimental considerations. Following this, a simple approximate equation giving the atmospheric refraction to an accuracy of a few microradians is developed; it is indicated that greater accuracy is not important because of laser pointing limitations imposed by atmospheric scattering and turbulence. The atmospheric refraction equation depends only on the apparent zenith angle of the satellite reflector relative to the earth-based laser, on the satelli-te altitude, and on the index of refraction of the laser radiation in the atmosphere at the earth's surface. Both of these developments should be useful in the design and interpretation of satellite laser-communication experiments.