A fascinating corollary to Lambert's famous problem is developed. By applying this new property of twobody orbits, a simple reformulation of the two-point boundary-value problem is possible. This is accomplished by means of a geometrical transformation of the orbital foci which converts the original problem to one for which the initial point is an apsidal point. The elementary form of Kepler's equation then provides the analytic description of the time of flight. The elements of the original orbit are shown to be simply related to the corresponding elements of the transformed orbit. Finally, a simple iterative method of solving the transformed boundary-value problem using successive substitutions is developed. In most cases of interest, convergence is seen to be quite rapid.

Program to Optimize Simulated Trajectories II (POST2) is used as a basis for an end-toend descent and landing trajectory simulation that is essential in determining design and integration capability and system performance of the lunar descent and landing system and environment models for the Autonomous Landing and Hazard Avoidance Technology (ALHAT) project. The POST2 simulation provides a six degree-of-freedom capability necessary to test, design and operate a descent and landing system for successful lunar landing. This paper presents advances in the development and model-implementation of the POST2 simulation, as well as preliminary system performance analysis, used for the testing and evaluation of ALHAT project system models. Nomenclature

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