Suppose there is a spherical rectangle for which I have the lat, long coordinates for each corner. Additionally this rectangle has a center line for which I know the lat, long coordinates of the start, mid and end point (see image below) If you're given a lat, long of a new point (orange circle) is it possible to find the lat, long of the orthogonal intersection with the center line? I know this is pretty easy using cartesian coordinates. But I'd prefer to stick with geographic coordinates since I need to get a very precise distance measurement.
EDIT: So far the only idea I have is to make a grid referenced to the edges and interpolate between them. I plotted the result and it's a little bit off. I'm using the answer from this question