# Position of specific stars in the sky as a function of time

I'm a beginner in astronomy and I'm trying to figure out how to model the positions of stars in the night sky mathematically (ie a function which spits out azimuth and altitude as a function of time). I was wondering if anyone knew of any such function, I understand it would vary with your position on earth.

Furthermore, does anyone know anything about the mathematics of star movements, I'm trying to learn all I can.

Thanks!

• I think you could write a more detailed problem, the correct answer to your question would be probably too long. Typically, a good question has an answer at most a page length. But I am not sure, maybe also yours belongs to them. Good luck! – peterh May 26 '18 at 1:27
• Are you asking about the apparent movement of the stars in the sky (mostly due to the Earth/'s rotation) or are you asking about the much, much smaller proper motions of the stars with respect to one another? Or both? – Mark Olson May 26 '18 at 11:23
• astronomy.stackexchange.com/questions/14492/… is my answer to this, but I'm actually not that happy with it, and hope to rewrite it. Also astronomy.stackexchange.com/questions/8390/… with same caveats. Basically, coordinate transforms in astronomy are rigid rotations and the matrix form is usually the best way to deal with those. – user21 May 26 '18 at 17:32
• Also see Wikipedia: Celestial coordinates for conversion between equatorial and horizontal systems. – Mike G May 26 '18 at 21:57
• Smarte's Spherical Astronomy is archived here, it's in there somewhere, but I can't point to one single page. – uhoh May 27 '18 at 0:53

• 360$^\circ$/24h is the solar rate; the sidereal rate is 1/365 faster. – Mike G May 31 '18 at 18:16