Celestial Programming : Sky Path Angle

The angle between the horizon and the path an object takes through the sky. It is assumed the declination is constant. However for slow moving objects like the Sun and planets, the error is generally negligible.

$$ \begin{align*} \tan A = \frac{\cos \delta} {\tan \phi} \sqrt{1 - (\tan \delta \tan \phi)^2} \end{align*} $$
\( A \) is the angle between the path and the horizon, \(\phi\) is latitude, \(\delta\) is the declination.