# Calculating the geographical distance between two points (especially Gnomonic)

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?

• I know that its straight line segment in gnomonic shows the shortest route. if we can't define the distance, how can this line is the shortest line except for the concept of great circle? – David Oct 27 '19 at 22:03
• Oops. Deleted comment repost: Gnomonic is equiangular from the center point to all other points, but not equidistant. I wouldn't use either for distance calculation. – Vince Oct 27 '19 at 22:41
• As Vince says, Gnomonic is like Mercator in that straight lines show the shortest path, but if you calculate the distance using that path, it's not the actual distance. – mkennedy Oct 29 '19 at 19:44