Bringing your Analogue past into our Digital future

This project was carried out to look into the uses of the Jacobi integral equation in trajectory plotting. In order to carry out this study first a review of past works in the area of trajectory plotting was carried out. Second a method of utilizing the equation was created and from this a computer program designed and built to plot a trajectory between the earth and the moon. The purpose of this program was to demonstrate that the Jacobi equation could be used in trajectory plotting and was to provide data on the energy requirements of the mission. The main data found by this report was the position of the L1 point between x=0.836920 and 0.836990 The value of the Jacobi constant C that will allow travel between the Earth and the Moon was also found to be Ct =3.187. It was found that using the Jacobi equation as a starting point trajectories could be found which required little to no energy. This would allow a spacecraft to travel from Earth to the Moon. From these findings the potential uses of this method were looked into and future predictions made as to how this method could be utilized. Finally the limitations of this particular program were highlighted and then improvements were suggested. Overall this study into the Jacobi equation brought to light a host of alternative low energy trajectory methods which could be used for a variety of future spacecraft missions.