Orthogonal time frequency space (OTFS) modulation has been widely considered for high-mobility scenarios. Satellite-to-ground communications have recently received much attention as a typical high-mobility scenario and face great challenges due to the high Doppler shift. To enable reliable communications and high spectral efficiency in satellite mobile communications, we evaluate OTFS modulation performance for geostationary Earth orbit and low Earth orbit satellite-to-ground channels at sub-6-GHz and millimeter-wave bands in both lineof-sight and non-line-of-sight cases. The minimum mean squared error with successive detection (MMSE-SD) is used to improve the bit error rate performance. The adaptability of OTFS and the signal detection technologies in satellite-to-ground channels are analyzed. Simulation results confirm the feasibility of applying OTFS modulation to satellite-to-ground communications with high mobility. Because full diversity in the delay-Doppler domain can be explored, different terminal movement velocities do not have a significant impact on the performance of OTFS modulation, and OTFS modulation can achieve better performance compared with classical orthogonal frequency division multiplexing in satellite-to-ground channels. It is found that MMSE-SD can improve the performance of OTFS modulation compared with an MMSE equalizer.