2283 AAS 11-263 GPU ACCELERATED LAMBERT SOLUTION METHODS FOR THE ORBITAL TARGETING PROBLEM Sam Wagner * and Bong Wie † Lamberts problem is concerned with the determination of an orbit that con- nects two position vectors within a specified time of flight. It must often be solved millions of times, especially when one is conducting global searches for possible gravity assist missions, which requires fast efficient solutions. The or- bital targeting problem lends itself well to parallel processing, with each depar- ture and arrival combinations being computationally separate. By using the parallel capabilities of modern Graphics Processing Unit (GPU) technology, it is possible to reduce the total run time of the search program by several orders of magnitude. Three methods, have been implemented on a GPU, with run times up to 1100 times faster, when compared to comparable serial FORTRAN verions, at a maximum of almost 20 million solutions per second. Two exam- ple missions, one to asteroid 99942 Apophis and a 200-year Earth to Mars search, have been conducted to evaluate the performance of each method. INTRODUCTION Lambert’s problem is one of most important problems for initial orbital determination and the orbit targeting problem. It has been studied extensively, 1, 2, 3, 4, 5, 6 in order to determine efficient and robust solutions. In this paper only methods based on a universal variable approach will be consid- ered. In general, these solutions work for all types of orbits, hyperbolic, parabolic, and elleptical and are very robust. Each of the methods tested can easily be employed for multi-revolution solutions as well. The initial orbit determination often involves searching millions of launch and arrival combi- nations using Lambert’s solutions. Each of these combinations is completely independent, which means the orbit searching program lends itself well to the use of parallel processing. Using the Portland Groups CUDA FORTRAN capabilities, efficient search program can be developed allow- ing millions of solutions per second. In this paper, three methods, BMW’s universal variable ap- proach, 1 Battin’s solution, 2 and Gooding’s solution to the Lambert equation 5, 6, 7 will be developed for an NVIDIA Tesla c2060 GPU. Two example missions, one to asteroid 99942 Apophis, which has been studied extensively by the Iowa State Asteroid Deflection Research Center (ADRC), 8, 9, 10 and the other for a 200 years search from 1900 to 2100 Earth to Mars transfer. This second example mission was chosen in order to ensure a sufficiently large search for the maximum performance from the GPU. Using GPUs to solve Lambert’s problem will help minimize cost, in terms of both run time and computer resources. ∗ Graduate Research Assistant, Asteroid Deflection Research Center, Aerospace Engineering Department, Iowa State Uni- versity, Ames, IA. † Vance Coffman Endowed Chair Professor, Asteroid Deflection Research Center, Aerospace Engineering Department, Iowa State University, Ames, IA.