Assuming I was observing a source at a given right ascension $\alpha_0$ declination $\delta_0$ at a given time $t_0$ under a certain azimuth $A$ and elevation $a$ angle.
If I now change my time to $t_1$ (e.g. 1 hour later), how can I determine which $\alpha_1$ and $\delta_1$ will be observed based on the same azimuth $A$ and altitude $a$ values?
I suppose one way would be to really go the route and transform $(\alpha_0, \delta_0)→(t_0,A, a)→(t_1,A, a)→(\alpha_1, \delta_1)$.
My question is: Is there a simpler, more elegant solution to the problem? Can I rotate $(\alpha_0, \delta_0)$ directly to $(\alpha_1, \delta_1)$? If so, what steps/rotations are necessary for it (and is this supported in astropy?). I have a bigger source list thus, going via azimuth/elevation is a bit time-consuming and I think it should be possible to simply rotate the sky-sphere based on a known earth rotation (expressed through delta time)?
The "source" is an extragalactic radio source -> I do not have to bother about its distance, movement or about refraction etc. Currently, I was only applying a nutation model but maybe this is even unnecessary...