But the traditional RA circle is synchronized with the axle such that as the object moves, the RA reading keeps changing. So you constantly have to re-set the RA circle on the current object before you can move on to find another object. This is the easy way and is the method shown in the manuals that come with most new telescopes. Finding an object in right ascension is very much time-dependent because diurnal movement carries the object across the sky while you re observing. We have to first know the sidereal time, and from this we subtract the right ascension of the intended object to get the hour angle of the object.
Sidereal time is a measure of the Earth s rotation with respect to the equinox, rather than the Sun.
A sidereal day is shorter than a mean solar day by 3min55sec.909. The way astronomers used to determine sidereal time was to set a clock so that it gains roughly 3min56sec per day. The starting point for setting a sidereal clock was derived using the Nautical Almanac. Computing sidereal time is a real pain. However, nowadays there are computer programs that give us the sidereal time directly.