Optimal lunar orbit insertion from a free return trajectory - Jesick, Mark Christopher (2012)
With the discovery of water ice at the moon's south pole, future human lunar exploration will likely occur at polar sites and, therefore, require high inclination orbits. Also of importance for human missions is the capability to abort if unfavorable circumstances arise. This dissertation addresses both of these concerns by creating an automated, systematic architecture for constructing minimum propellant lunar orbit insertion sequences while ensuring crew safety by maintaining a ballistic Earth return trajectory. To ensure a maneuver-free abort option, the spacecraft is required to depart Earth on a free return trajectory, which is a ballistic Earth-moon-Earth segment that requires no propulsive maneuvers after translunar injection. Because of the need for global lunar access, the required spacecraft plane change at the moon may be large enough that a multi-maneuver sequence offers cost savings. The combination of this orbit insertion sequence with the free return orbit increases the likelihood of a safe Earth return for crew while not compromising the ability to achieve any lunar orbit. A procedure for free return trajectory generation in a simplified Earth-moon system is presented first. With two-body and circular restricted three-body models, the algorithm constructs an initial guess of the translunar injection state and time of flight. Once the initial trajectory is found, a square system of nonlinear equations is solved numerically to target Earth entry interface conditions leading to feasible free return trajectories. No trial and error is required to generate the initial estimate. The automated algorithm is used to generate families of free return orbits for analysis. A targeting and optimization procedure is developed to transfer a spacecraft from a free return trajectory to a closed lunar orbit through a multi-maneuver sequence in the circular restricted three-body model. The initial estimate procedure is automated, and analytical gradients are implemented to facilitate optimization. Cases are examined with minimum time, variable symmetric, and general free returns. The algorithm is then upgraded to include a more realistic solar system model with ephemeris-level dynamics. An impulsive engine model is used before conversion to a finite thrust model. Optimal control theory is applied and the results are compared with the linearly steered thrust model. Trends in the flight time and propellant for various orbit insertion sequences are analyzed. Aerospace Engineering