Suppose you start at a location identified by a set of coordinates (latitude, longitude) on Earth, then move a given distance in a given direction. What is the equation that gives you the coordinates where you end up? I know that at higher altitudes, a distance corresponds to a smaller angle; I would like an equation that works for different altitudes, not just on the Earth's surface.
I have looked at haversine and great circle equations, but I don't think those are the right way to go. The distance traveled in the equation I'd like wouldn't be that big (a mile or two at the most), and this distance is a straight line.