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An Elegant Lambert Algorithm for Multiple Revolution Orbits

A simple efficient algorithm to solve the non-unique multiple revolution time-constrained two-body two-point orbital boundary value Lambert's problem is of great interest for spacecraft interception and rendezvous and interplanetary transfer. The multiple revolution transfer orbits permit greater navigational flexibility and result in lower energy orbits than the unique direct transfer orbit. Two algorithms, based on the elegant algorithm for direct orbital transfer developed by R. H. Battin from Gauss' orbit determination method, definitively separate the low and high energy solutions for each complete revolution within the transfer. Both retain the excellent convergence characteristics of the direct transfer method, requiring only one additional iteration to converge to an additional four significant figures and having nearly uniform convergence over a wide range of problems. First the derivation of the direct transfer algorithm is summarized. A simple approximation of the maximum number of complete revolutions that can be made within the given transfer time is suggested. Both the high and low energy algorithms are derived along the lines of the direct transfer algorithm. Tables display the number of iterations required for convergence for a large number of transfer problems, demonstrating the capability of these algorithms. Thesis Supervisor: Dr. Richard H. Battin Title: Adjunct Professor of Aeronautics and Astronautics