A trajectory optimization and rendezvous study of a manned Mars ascent vehicle

The purpose of this study is to describe the ascent flight dynamics and orbital maneuvering requirements of a manned Mars Ascent Vehicle (MAY) within the missionstructure defined by the NASA Design Reference Mission (DRM). The primary task of the MAV is to transport the astronauts and their scientific cargo from the surface of Marsto an orbiting Earth Return Vehicle (ERY), in which the crew will depart Mars orbit and begin their return to Earth. This objective comprises two phases of operation, an ascent from the Martian surface to a parking orbit, and an orbital rendezvous with the waiting ERY, and is critical to the success of a manned Mars mission.In order to accomplish this study two programs were written to model each of the distinct phases of MAV operation. The ascent program uses Pontryagin's MaximumPrinciple to optimize the ascent trajectory and reduce it to a two point boundary value problem. This is then solved by the numerical method of Runge-Kutta integration, withNewton's Method used to guess the unknown initial conditions of the trajectory. Thisprogram finds the optimal trajectory to place the MAY into a parking orbit prior to rendezvous with the ERY, minimizing propellant expended and maximizing useful spacecraft payload.The orbital rendezvous portion of the study involves quantifying the impulsive maneuvers needed to alter the MAY orbit to match its position and velocity with the ERY. This is accomplished through a study of the differential equations of relative position and velocity between the two vehicles. The resulting boundary value problem is solved using the numerical methods of Runge-Kutta integration and Newton's Method,providing the necessary maneuvers to achieve orbital rendezvous.