Distance on the surface of a sphere

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 λ=longitude and δ = latitude d=R cos−1[cosδ1cosδ2cos(λ1−λ2)+sinδ1sinδ2], the angular change is d/R.
  • If you want to use pure sphereical coordinates, make the transformation θ=π2−δ and ϕ=λ
If you are only interested in the motion along the lines of latitiude, then that distance is simply d=R|λ1−λ2|

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