What are Lagrange points and how do they work in the context of celestial mechanics?

Lagrange points are specific locations in space where the gravitational forces of two large bodies, such as a planet and a moon, balance out the centrifugal force of a smaller body, like a spacecraft. There are five Lagrange points in the Earth-Sun system, labeled L1 to L5. These points are stable and allow objects to orbit in a synchronized manner with the larger bodies, making them useful for spacecraft to conserve fuel and stay in position for extended periods of time.