The Astronomy Learner

A common problem is how to measure distances on a sphere. For our normal, flat, Euclidean space, it is simply a straight line. However, this is not the case on the surface of a sphere. Do to it's curvature, the shortest path from one point to another (geodesic path) is a segment of a great circle. The derivation is short and can be found on WolframMathWorld | Great Circle . The distance is, With $\lambda$=longitude and $\delta$ = latitude $$d = R~\cos^{-1}\left[\cos{\delta_1}\cos{\delta_2}\cos{(\lambda_1-\lambda_2)}+\sin{\delta_1}\sin{\delta_2}\right],$$ the angular change is $d/R$. If you want to use pure sphereical coordinates, make the transformation $\theta=\frac{\pi}{2}-\delta$ and $\phi = \lambda$ If you are only interested in the motion along the lines of latitiude, then that distance is simply $$d= R|\lambda_1-\lambda_2|$$