The intersection of a Loxodrome with a great circle

The intersections of a loxodrome (rhumb line) and a great circle are of interest for some navigational problems, but a closed-form solution cannot be formulated. An algorithm is given for computing approximations to any desired degree of accuracy using Newton's method. By using the equatorial angle phi as an independent variable all solutions can be found rapidly using the modest computational capabilities of a personal computer.<
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