Lambert's problem revisited

Two classical forms of the time of flight equation for the two body, two point boundary value problem, known as 'Lambert's problem', are combined to produce an elegant formulation which may serve as the nucleus of an extremely efficient computation algorithm. The time equation is universal (i.e., includes elliptic, parabolic and hyperbolic orbits), is a well-behaved function of a single convenient independent variable, and requires the evaluation of a single hypergeometric function. New recursive identities for hypergeometric functions are developed and effectively exploited to enhance computation speed. Also presented is a 'top-down' continued fraction algorithm, used for efficient evaluation of the hypergeometric function, which avoids the necessity of repeated scaling. This formulation represents a considerable improvement over other methods known to the author.