An approximation of geodesic circle passing through three points on an ellipsoid

In this paper we present an approximation method for a geodesic circle passing through three points on an oblate ellipsoid. Our method uses a prolate ellipsoid passing through the three points, and the new approximation curve is the intersection of the oblate and prolate ellipsoids, which can be obtained algebraically without iterations. The advantage of our approximation method is that it yields a significantly smaller approximation error. Compared to the plane section curve passing through the three points on the oblate ellipse, our method reduces the approximation error by at least 98 % when the radii of geodesic circles are 100 km similar to 1000 km on the surface of the Earth. We illustrate the results using numerical examples.