How does one write and thereafter solve the equations to find the points of intersection of two overlapping circles drawn on the surface of a sphere? I am looking for a simple understandable solution that one could enter into a calculator to solve a 2-star sighting celestial navigation problem.
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A circle is the intersection of a plane with the sphere. If two such circles intersect, their planes intersect, and the line of intersection passes through the sphere at your two points. Whether this can be implemented in an understandable manner depends entirely on your background, about which you have given no information. – Will Jagy Mar 19 '14 at 21:26