Modeling of Earth's rotation for space based radar

Space-based radars (SBR) by virtue of their motion generate a Doppler frequency component to the clutter return from any point on the Earth as a function of the SBR - Earth geometry. The effect of Earth's rotation around its own axis also adds an additional component to this Doppler frequency. The overall effect of the Earth's rotation on the Doppler turns out to be two correction factors in terms of a crab angle affecting the azimuth angle, and a crab magnitude scaling the Doppler magnitude of the clutter patch. Interestingly, both these quantities depend only on the SBR orbit inclination and its latitude and not on the location of the clutter patch of interest. Further the crab angle has maximum effect for an SBR on a polar orbit that is above the equator. The crab magnitude on the other hand peaks for an SBR on an equatorial orbit. A detailed derivation of these results is presented in this paper.