This question has already been asked here, but has not been answered fully. I really want to know the answer, so I ask again.
If we have two points A and B on the surface of a sphere, a geodesic between them, and another point C on the same sphere surface, but not on the geodesic, is there any concept of a "perpendicular" geodesic to AB that passes through C ?
Because I'm not able to describe the problem mathematically (because I don't know what is the exact concept I'm searching for, and I don't have the proper mathematical vocabulary), I'm going to describe the practical problem for which I need this.
A and B are two points on the surface of the Earth with a geodesic between them, C is another point on the surface of the Earth, which does not pass through AB, and I need to calculate the coordinates of D, on the AB geodesic, so that the geodesic distance between C and D is minimized. It is sort of a "shortest distance from point to line" problem applied to geodesics. In 2D geometry D would be the perpendicular foot from C to AB.