The Restricted three - The Restricted three-body problem As...

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The Restricted three-body problem As lambda decreases further the crossover point L 2 turns into a neck. (Note this curve is not the trajectory of a vehicle or body - it merely defines the boundary to where m can go.) Eventually as lambda gets smaller the case of curves C with subscript lambda and 2 is reached where inner and outer circles meet, initially at point L 3 . By curves C with subscript lB>. By curves C with subscript lambda and 3 the "necks" are open at both ends and only the shaded areas are "not allowed" (energetically) to the body. These regions shrink as lambda gets smaller, and eventually end up as points L 4 and L 5 . Fo lambda less than this limiting value nothing can be plotted, and the body m has so much energy it can move freely anywhere in the system. Small lambda means large initial energy. L 1 , L 2 , L 3 , L 4 and L 5 are known as the Lagrangian points . The points L 4 and L 5 form equilateral triangles with m 1 and m 2 .
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