On Gauss's Method of Orbit Determination.

摘要

This report presents a statistical version of the Gaussian initial orbit technique. It neglects neither the angular velocity nor the radial velocity terms in the f and g series. More importantly it provides a rigorous, analytically simple result for the radius of convergence of the f and g series. The radius of convergence can be extremely small at periastron, approaching zero as the eccentricity of the orbit approaches unity. The leading term is given by sq. rt. 2 (1-e)(to the 3/2 power)P/(3 pi) as e approaches 1 where P is the orbital period. This implies that initial orbit determination by any procedure which uses the f and g series is a process fraught with the possibility of unknown errors.