I tried to get geographical distance between two points by using spherical trigonometry, Mercator and Gnomonic projection.
The detail of 2 points
point A ( 15º 55’ S, 5º 44’ W) , B( 32º 19’ N, 64º 51’ W)
As a result, I got 8262.132km in trigonometry, 8631.378 in Mercator.
But I couldn't understand why the result in Gnomonic is different depending on chosen origin.
Used formula from http://www-history.mcs.st-and.ac.uk/Projects/Hoyer/S3.html
For example, I set (0,0) and (0, 30º W), and difference is more than 6000km!
We know Gnomonic can show the shortest path, but I don't know why the actual calculation is not correct..
How can I calculate geographical distance by Gnomonic well?