Lambert's problem revisited

Two classical foms 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 cornputat.- ion algorithm. (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 f or hypergeometric functions are developed and efFectively exploited to enhance computation speed. "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 improve- ment over other methods known to the author, The time equation is universal