Main article: Great-circle navigation
The concept of the position angle is inherited from nautical navigation on the oceans, where the optimum compass course is the course from a known position s to a target position t with minimum effort. Setting aside the influence of winds and ocean currents, the optimum course is the course of smallest distance between the two positions on the ocean surface. Computing the compass course is known as the inverse geodetic problem.
This article considers only the abstraction of minimizing the distance between s and t traveling on the surface of a sphere with some radius R: In which direction angle p relative to North should the ship steer to reach the target position?