I have a graph in which each node is a geographical point on the surface of the earth, defined by it's latitude / longitude coordinates.
Correct ways to calculate the distance between two such points could be the Haversine Formula for spherical earth models, or Vincenty's inverse problem for spheroidal earth models.
But these are very costly in terms of computational resources, and in A* basically you don't need the absolute values of those results, you only need them for comparison purposes.
In my A* algorithm the heuristic function is the shortest distance between 2 points (defined as the length of the smaller great circle arc between the 2 points in a spherical model), and the actual path between two nodes is a linestring, whose length is calculated basically in the same way, just that you sum distances between consecutive vertices.
d(A, B) is the actual geographical distance between A and B (as latitude / longitude points), the problem basically is to find the most computationally efficient distance estimator
d*(A, B) that satisfies conditions needed for A* to work properly, such as:
d(A, B) < d(C, D)then
d*(A, B) < d*(C, D).
d(A, B) + d(E, F) < d(C, D)then
d*(A, B) + d*(E, F) < d*(C, D)
I even saw in some places that people recommend Euclidean distance for such a case, even though latitude / longitude are angles. It may be the case, but I'm interested if it's "mathematically correct" to assume that it satisfies conditions such as above.