Exact Solution to Lambert’s Problem Using Contour Integrals

A novel method for solving Lambert’s problem based around the universal variable formulation is presented. By extending the transfer time function into the complex plane, an exact solution is derived for Lambert’s boundary value problem. This solution is a function of complex contour integrals of the transfer time function that must be approximated numerically. For integrals of this type, the composite trapezoidal rule is exponentially convergent and is used to approximate the solution to a high degree of accuracy for both zero- and [Formula: see text]-revolution Lambert problems. Different families of contours are presented for the cases of hyperbolic, zero-revolution elliptic, and [Formula: see text]-revolution elliptic transfers, and numerical examples are presented for all the cases. Monte Carlo analysis demonstrates a direct tradeoff between accuracy and computation speed based on the number of points used to approximate the integrals. When choosing a number of points with a balanced accuracy to speed, this method demonstrates an exceptionally fast computation speed, faster than all other methods we compare to in this paper.