How to calculate distance from a point to a line segment, on a sphere?

Question

I have a line segment (great circle part) on earth. The line segment is defined by the coordinates of its ends. Obviously, two points define two line segments, so assume I a

Answer 1

I'm basically looking for the same thing right now, except that I strictly speaking don't care about having a segment of a great circle, but rather just want the distance to any point on the full circle.

Two links I am currently investigating:

This page mentions "Cross-track distance", which basically seems to be what you are looking for.

Also, in the following thread on the PostGIS mailing list, the attempt seems to (1) determine the closest point on the great circle with the same formula used for line-distance on a 2D-plane (with PostGIS' line_locate_point), and then (2) calculating the distance between that and the third point on a spheroid. I have no idea if mathematically step (1) is correct, but I would be surprised.

http://postgis.refractions.net/pipermail/postgis-users/2009-July/023903.html

Finally, I just saw that the following linked under "Related":

Distance from Point To Line great circle function not working right.