I have a misunderstanding of principles behind using telescopes with equatorial mount (I don't have it yet, only trying to grasp the idea). For example, I would like to watch Betelgeuse in the telescope, steps to do it:
Will Betelgeuse be visible through a telescope all night?
The stars have an apparent movement in the sky like the Sun1: along their path on the sky they move 15° every hour (actually this is an effect of the rotation of the Earth's, a full rotation of 360° in 24h, and Sun and stars remain where they are). Thus in order to keep observing the same object, you need to compensate this rotation and rotate your telescope by 15° per hour around an axis parallel to the Earth's rotational axis.
The equatorial mount is designed such that this can be achieved by only rotating around one axis, the axis of the right ascension or hour angle which is or has to be carefully aligned such that it is parallel to the Earth's rotational axis. This axis usually can be rotated horizontally so that it points North (or South on the southern hemisphere) and its angle to the horizon can be adjusted to match your geographical latitude.
So yes: you constantly have to turn your telescope to keep watching the same object. This can be done by hand for the simpler mounts. They offer a handle to easily rotate it for observation with the eye. For photography you want a motorized mount which can do this tracking automatically.
1 There are differences of about 4 minutes in the solar and sidereal day as Earth moves along its orbit. That's why the summer sky is different from the winter sky. But this difference does not matter at this level.
