Application of the Lambert Problem to Inverse-Square Gravity

摘要

The Lambert Problem can be solved by employing an iterative procedure that utilizes the Newton-Raphson method. Three candidates for the iteration variable are considered. Equations for an elliptical trajectory in terms of each of the iteration variables are derived. Equations for hyperbolic and parabolic trajectories are then deduced, and it is demonstrated how the type of trajectory can be determined from the given parameters.