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Inconsistent formulas for meridian distances
It would be nice if quarter_meridian, meridian_direct, and meridian_inverse all used consistent approximations. Instead:
quarter_meridianis accurate ton^16with the coefficient given to full precision.meridian_directis accurate ton^4with the coefficients given approximately, e.g.,1.572916667instead ofCT(151)/CT(96).meridian_inverseis supposed to be accurate ton^5, however then^4contribution toC0and then^5contribution toC2are omitted and the coefficients are given approximately, e.g.-0.729166667instead ofCT(-35)/CT(48).
I recommend that both median_inverse and meridian_direct include terms up to n^6 which is needed to full double precision accuracy for the earth. If these routines used Horner and Clenshaw summation then there would be little cost in making n^6 the minimum order provided.