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See the wikipedia page on great-circle navigation. Following the prescription there, you compute the heading of the great circle at the first point. Then you can compute the intersection of the resulting path with a particular meridian. (This addresses the problem on a sphere. The ellipsoidal problem is a little more involved. A good place to start is ...


I would not be sure about the accuracy of Google Earth aerial photos if it is down to 2.5 foot offset. It might just be a question of not exactly orthogonal photography. What you might need is just an affine transformation to get your photos aligned with theirs.


as whuber said, there are several pages of explanations to get the exact formulas. Though you can find some simplified series on wikipedia. For Wisconsin Transverse Mercator, please also note that implementing the projection is not enough, because you also need to code the datum transform between WGS 84 and NAD 83. My suggestion is to take advantage of ...


Instead of a gnomonic projection, you can use an azimuthal equidistant projection on one of your points as well. See my example workflow here: great circles in QGIS and export in 3857 webmap

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