Abstract: The Doppler shift of SAR satellite is related to the relative motion between the satellite and the target. Based on the orbit mechanics theory the Doppler shift is splited into two parts: one has relation to the yaw angle that the be compensated and the other has nothing to do with it that can only be viewed as noise. First analytical solution for yaw steering is deduced and simplified to fit for real time computing. Then the concept of compensation effect is defined and the yaw steering's compensation effect is estimated by analysing the two parts, at the same time the results of simulation indicate that the method of theoretical estimation is conditionally effective. The relation between compensation effect and the orbit eccentricity or the elevation angle is also discussed. Last a conclusion about the effect of orbit elements and radar parameters on compensation is drawn to support the primary design of SAR satellite.