Combinations of Low Energy Trajectories for a Lunar L 2 mission Thesis Report by A .

To learn more about the origin of the universe, scientist wish to make measurements in the lowfrequency radio wave region. Such measurements suffer greatly from disturbances by man-made signals. Therefore, missions are proposed which use the Moon as a shield from these disturbances, by making use of the Earth-Moon L Lagrange point, a point in space behind the Moon in which spacecraft can remain stable with respect to the Earth and the Moon. Especially missions using large numbers of small satellites are considered valuable, because such groups could together work as an antenna with a very large aperture, which is beneficial for low-frequency measurements. This research explores the use of low energy trajectories for a mission to the Earth-Moon L point. Low energy trajectories are found in the circular restricted three body problem, originating in the vicinity of the Lagrange points. They may be divided into four classes: The periodic ellipse around the Lagrange point, asymptotic trajectories spiralling into or out of this ellipse, non-transit trajectories which stay either on the main body’s side of the Lagrange point or stay on the other side, and the transit trajectories which move from one side of the Lagrange point to the other. Although low energy trajectories have been researched for 50 years and used in missions such as Hiten and Genesis, there has hardly been research on the use of low energy trajectories for a mission to the Earth-Moon L point. This leads to the following research question: What is the optimal configuration for a low energy transfer for a small satellite mission from an Earth-orbit to a lunar L orbit, when allowing for ballistic and non-ballistic transfers? The research assumes that the launcher vehicle will inject the small satellite into the transfer trajectory. The design of the mission transfer trajectory using low energy trajectories can be performed with different approaches. Each approach uses a combination of the low energy trajectory categories. Four configurations are considered: 1. The standard approach found in literature, which uses a non-transit trajectory in the Sun-Earth system coupled at the vertical Poincaré cut through the Earth with an asymptotic trajectory approaching the Earth-Moon L in the Earth-Moon system. 2. An approach with three asymptotic trajectories, which first travels to the Sun-Earth L point, then back in the direction of Earth, to be coupled to a final segment in the Earth-Moon system to arrive at the Earth-Moon L point. 3. An approach that uses the same segments as the standard approach, but that allows the location of the link between segments to be at any point instead of only on the vertical Poincaré cut. 4. An approach which allows up to six linked trajectories and has no restriction on the classes of low energy trajectories used or the location of their links. These four low energy transfer configurations were compared to answer the research question. The first comparison is made based on ΔV. Here we see that the third approach is most efficient with a ΔV below 10 m/s (standard approach: 30 m/s). The second comparison, on transfer time, also shows that the third approach is the most efficient, with a total transfer time of approximately 120 days (standard approach: 140 days). Third, we look at the scheduling restrictions: How much does ΔV increase when the moment of launch changes. Clearly optimal here is the second approach, which allows for a stationkeeping orbit around the Sun-Earth L point. Lastly, we look at the location of orbit insertion. Insertion near to the Earth means that the launcher requires less ΔV, which is beneficial for total mission cost. Again, the third approach performs best, with a starting point at a distance of 11,790 km from the Earth. It can then be concluded that the third approach is the optimal configuration for a low energy transfer for a small satellite mission from an Earth-orbit to a lunar L orbit. However, when additional mission objectives can be performed at the Sun-Earth L , the second approach might be a good alternative. In general, this research has shown that significant improvements over the standard approach found in literature are possible.