An equatorial mount having a base, a right ascension base, a right ascension shaft, a declination base, a declination shaft, and a mount-rotation mechanism, the declination base rotatable about a right ascension axis relative to the right ascension base, and the declination shaft rotatable about a declination axis relative to the declination axis, wherein the mount-rotation mechanism is engageable and disenagageable from one or the other of the right ascension shaft and the declination shaft, to apply torque between the declination base and that shaft when engaged and to permit relative rotation of the shaft and the declination base when disengaged.