Alt/AZ to Hour Angle and Declination
Given Latitude, and Alt/AZ coordinates. The Hour Angle and Declination can be computed. Further, given
Greenwich Sidereal Time, the Hour Angle can be converted to Right Ascension. If the Alt/Az coordinates
are from an observation, you will likely need to correct \(h\) for refraction.
$$
\begin{align*}
\tan H &= \frac{-\sin A}{\tan h \cos \phi - \cos A \sin \phi}
\\
\sin \delta &= \sin \phi \sin h + \cos \phi \cos h \cos A
\end{align*}
$$
\(h\) Alt (height)
\(A\) Azimuth
\(\phi\) Latitude
\(\delta\) Declination
\(H\) Hour Angle