Study on the viability of transfer trajectories to the stability region around L4 and L5 Lagrange Points in the Earth-Sun system

Abstract

In the present thesis a study is done regarding the viability and optimization of trajectories to get to the stability region around Lagrange points L4 and L5 from the Earth, specifically from periodic orbits around Lagrange points L1 and L2, in the frame of the circular restricted three-body problem of the Earth-Sun system. The trajectory of a spacecraft inside this stability region around L4 and L5 does not leave it for 1000 years or more and without the necessity of any maneuver, i.e. without fuel consumption. Furthermore, this region offers good positions to observe the Sun, and with that to be able to understand and predict the behaviour of possible space weather events, such as solar flares or coronal mass ejections. This is the set of reasons why this stability region is of scientific interest, so that the objective of the present thesis is to study how to get there in the most optimal way possible. Therefore, the unstable invariant manifolds that arise from the periodic orbits around L1 and L2 are the paths to consider as starting points for the transfer trajectories up to L4 and L5, as they take advantage of the dynamic nature of the circular restricted three-body problem. Once the stability region, the types of trajectories around L4 and L5 and the unstable invariant manifolds have been defined, it has been found that it is possible to reach L4 and L5 with a delta-V budget to perform the impulsive maneuvers of around 260 m/s, with times of flight between 8.5 and 9 years. However, it is possible to decrease the time of flight if the delta-V budget is increased, achieving 6-year transfers with delta-V budgets of around 400 m/s or 4-year transfers with delta-V budgets of around 550 m/s. These results show that there is a large variety of trajectories to choose to get to the equilibrium points L4 and L5, all them comparable, in flight times as well as in delta-V budget, to both current and past interplanetary missions. Therefore, it has been seen that there are lots of reasonable possibilities to send a satellite or a set of missions to these stability regions, in order to carry out observations of the Sun and research about space weather without needing to perform station-keeping maneuvers such as in L1 and L2 during the mission period.