[Wavytone]

Granada,

Assuming the earth's rotation is constant (actually it isn't but we will get to that later), the rate at which objects move across the sky is not constant - it is affected by several things:

1. The motion of all objects is affected by atmospheric refraction, which causes them to appear higher in elevation, as a function of elevation. This produces an variable offset in both their apparent hour angle AND declination, and the offset varies as a function of elevation.

2. Atmospheric refraction is in influenced by site altitude, atmospheric pressure, the humidity of the air column along the optical path, hour angle and declination and ultimately its nontrivial to solve this.

if you want a fixed rate, a good approximation is known as the "king rate".

3. The moon moves visibly at a different rate to the stars and requires its own tracking rate (lunar, on most handsets). Basically it does one less orbit per lunar month than the number of days, so the lunar rate is about 3% slower than the nominal sidereal rate.

4. The sun does one less rotation per year so the solar rate is about 0.3% slower than the sidereal rate.

THE REAL SHOWSTOPPERS... however, are...

5. Periodic errors in the gear train,

6. Geometric errors within the mount; ie the angles between the RA and dec axis, and the dec axis and optical axis not being perpendicular, and

7. Flexure within the telescope OTA and mount as it moves. At the level of seconds of arc, most mounts are not much better than a block of Jello - they move and wobble all over the place.

8. Atmospheric effects (scintillation).

These are all to some extent unpredictable but can be measured empirically, ie by measurements.

And yes it is possible to compensate for scintillation - the gear to do it (adaptive optics) is within a few amateur budgets.

THERE IS, however, another way. Thanks to control-system theory, closed-loop feedback can be used to keep a telescope pointing at ANY target regardless of all of the errors above, by using a small telescope equipped with a guide camera ("auto guider") that provides signals to the drive electronics in response to any offset in hour angle or declination.