Astronomy question on altitude and azimuth

Question

If I know the current altitude and azimuth of a star and I know my latitude, can I predict the altitude and azimuth of the star up to 1 hour from now. Is there a simple formula?

Answer 1

This isn't really what you'd call a simple formula but I think it would have to be a two-stage calculation in which you determine the star's hour angle and declination as part of the process. You have a spherical triangle ABC with A being your zenith, B being the celestial pole and C the star. The angle at A is the star's azimuth, the arc AB is your co-latitude and the arc AC is the star's co-elevation. You would then determine the angle at B, which is the star's hour angle and the arc BC, which is the star's co-declination. Calculate the increase in the star's hour angle during your required time interval at 15.041 degrees per hour (the sidereal hourly rate) then perform the same calculation in reverse with the new hour angle. There are formulae for the solution of spherical triangles at http://www.rwgrayprojects.com/rbfnotes/t...

An alternative method for small time increases might be to use differential methods to obtain a single formula, but that would probably be more long-winded both to derive and explain.