As a final project in AE 546 (Aerospace Guidance, Navigation, and Control) at San Diego State University, I implemented and simulated the Apollo powered-descent guidance law in MATLAB for a human-scale Mars landing mission. 

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Powered-descent is a phase of landing on a planetary body, in which the landing vehicle uses thrust vectoring to control its trajectory, and retro-propulsively descend to a designated landing site. The objective of the guidance system is to determine the requisite thrust direction, magnitude, and burn time to achieve the desired terminal conditions. This paper outlines the steps of such process and provides the simulated results of a human-scale Mars landing mission. Several assumptions were made to simplify the analysis; however, a thorough understanding of the fundamentals will allow for the development of more complex scenarios.