Relativistic effects in earth-orbiting Doppler lidar return signals

Frequency shifts of side-ranging lidar signals are calculated to high order in the small quantities (v/c), where v is the velocity of a spacecraft carrying a lidar laser or of an aerosol particle that scatters the radiation back into a detector (c is the speed of light). Frequency shift measurements determine horizontal components of ground velocity of the scattering particle, but measured fractional frequency shifts are large because of the large velocities of the spacecraft and of the rotating earth. Subtractions of large terms cause a loss of significant digits and magnify the effect of relativistic corrections in determination of wind velocity. Spacecraft acceleration is also considered. Calculations are performed in an earth-centered inertial frame, and appropriate transformations are applied giving the velocities of scatterers relative to the ground.