VARIABLE EXPANSION POINTS FOR SERIES SOLUTIONS OF THE LAMBERT PROBLEM

Lambert's problem, to find the unique conic trajectory that connects two points in a spherical gravity field in a given time, is represented by a set of transcendental equations due to Lagrange. The associated Lagrange equations for the orbital transfer time of flight may be expressed as series expansions for all cases. Power series solutions have been previously published that reverse the functionality of the Lagrange equations to provide direct expressions for the unknown semi-major axis as an explicit function of the transfer time. In this paper, convergence of the series solutions is achieved for certain problematic cases through the introduction of variable expansion points as a simple function of the input parameters of the problem. The resulting series expression for the transfer time may be reversed to produce convergent series solutions for the unknown semi-major axis over the full domain of interest.