Recently there is an increase in interest in the Moon as a destination for space missions. This increased interest is in the composition and geography of the Moon as well as using the Moon to travel beyond the Earth to other planets in the solar system. This thesis explores the mechanics behind a lunar mission and the costs and benefits of different approaches. To constrain this problem, the launch criteria are those of Wallops Flight Facility (WFF), which has expressed interest in launching small spacecraft to the Moon for exploration and study of the lunar surface. The flight from the Earth to the Moon and subsequent lunar orbits, referred to hereafter as the mission, is broken up into three different phases: first the launch and parking orbit around the Earth, second the transfer orbit, and finally the lunar capture and orbit.

A launch from WFF constrains the direction of the launch and the possible initial parking orbits. Recently WFF has been offered the use of a Taurus XL launch vehicle whose specifications will be used for all other limitations of the launch and initial parking orbit. The orbit investigated in this part of the mission is a simple circular orbit with limited disturbances. These disturbances are only a major factor for long duration orbits and don't affect the parking orbit significantly.

The transfer orbit from the Earth to the Moon is the most complex and interesting part of the mission. To fully describe the dynamics of the Earth-Moon system a three-body model is used. The model is a restricted three-body problem keeping the Earth and Moon orbiting circularly around the system barycenter. This model allows the spacecraft to experience the influence of the Earth and Moon during the entire transfer orbit, making the simulation more closely related to what will actually happen rather than what a patched conic solution would give. This trajectory is examined using Newtonian, Lagrangian, and Hamiltonian mechanics along with using a rotating and non-rotating frame of reference for the equations of motion. The objective of the transfer orbit is to reduce the time and fuel cost of the mission as well as allow for various insertion angles to the Moon.

The final phase of the mission is the lunar orbit and the analysis also uses a simple two body model similar to the parking orbit. The analysis investigates how the orbits around the Moon evolve and decay and explores more than just circular orbits, but orbits with different eccentricities. The non-uniform lunar gravity field is investigated to accurately model the lunar orbit. These factors give a proper simulation of what happens to the craft for the duration of the lunar orbit. Tracking the changes in the orbit gives a description of where it will be and how much of the lunar surface it can observe without any active changes to the orbit. The analysis allows for either pursuing a long duration sustained orbit or a more interesting orbit that covers more of the lunar surface.

These three phases are numerically simulated using MATLAB, which is a focus of this thesis. In all parts of the mission the simulations are refined and optimized to reduce the time of the simulation. Also this refinement gives a more accurate portrayal of what would really happen in orbit. This reduction in time is necessary to allow for many different orbits and scenarios to be investigated without using an unreasonable amount of time.