I have been sailing on a cruiser which has a basic GPS: one can enter the WGS 84 coordinates of a waypoint, and the GPS displays in real time the distance and bearing of the waypoint, something like the one in the image attached.
As a theoretical physicist, there is a question that I have been asking myself for a while: I would like to know how bearing and distance are precisely calculated by the GPS. In particular, given a curve on the WGS84 ellipsoid that joins the current location of the boat (A) to the waypoint (B), one may choose this curve in different ways. For instance, a loxodrome (i) or a geodesic curve on the ellipsoid (ii), i.e., the shortest path between A and B, which would coincide with a great circle in the case where the ellipsoid reduces to a sphere.
In either case, the angle between the curve and the local meridian at A yields a bearing, and the length of the curve a distance. Does the bearing displayed on the GPS screen correspond to choice (i) or (ii), or something else? Or does it depend on the GPS settings, or on the GPS model?
Thank you very much for your help!
PS I am aware that there is little discrepancy between the twos if the distance between the two points is small. Also, I found a related question
on a forum years ago, but there seems to be no definite answer there...