My question Does the Sun influence the stability of the Lagrangian points in the Earth-Moon system? Apparently the concept of Lagrangian points works both in the Earth-Moon system and the Earth-Sun system. However, In the Earth-Moon system the Sun, as a third body, has a big influence on the two body Earth-Moon system. In the Earth-Sun system there is no significant third body. Is there a difference in which the Lagrangian point concept works in the two systems?