Lagrange Points: Asteroids and SOHO

Lagrange points are gravitational locations in a two body orbital system (like Sun and Earth, Earth and Moon, etc.) where small objects can semi-stably orbit. There are five Lagrange points in any one of these systems. L1, L2, and L3 are located in the line containing the two major bodies. L4 and L5 are located 60 degrees ahead and 60 degrees behind (respectively) in the smaller major body's orbit. Trojan asteroids such as Earth's own 2020-XL5 was analyzed in an attempt to investigate it’s long-term orbital behavior. We wanted to answer two questions. Why did it switch from L4 to L5? And, why do trojan asteroids prefer a particular Lagrange point over the other? In the interest of time, we altered the scope of the project to focus on SOHO, a solar observatory orbiting L1 (a Lagrange point requiring orbit adjustments). We then investigated its motion and the station keeping maneuvers required to keep it in orbit.