Will geodesics remain the same on an ellipsoidal Earth?

[snoopies622]

I am wondering about writing a computer program that will find the "as the crow flies" distance between any two points on the Earth's surface, assuming that the planet is not a sphere but an ellipsoid.

Question: will the geodesics be the same? My intuition says yes: If I imagine a spherical balloon with a rubber band stretched between two surface points, the rubber band doesn't shift position as I flatten the balloon.

But parameterizing a geodesic on a sphere and seeing if it remains a geodesic while changing the spherical metric to an ellipsoidal one.. Well, that sounds like quite a challenge.

 

[pat_connell]

You would need to use a mathematical model of the Earth as an ellipsoid and use a numerical integration method to solve the geodesic equations. The numerical integration methods available vary depending on the desired accuracy and the computational power available.