Force map of the Lagrange points

[Joe]

Space can (if you want to anyway) be thought of as a somewhat flat surface with low spots caused by gravity. While not really accurate, the analogy works for thinking. The isobars shown in the image can be thought of as topographical lines (again if you want to).

Envision setting a sphere on our imaginary space plane. The sphere will roll downhill. No space is truly "flat", it all leans to some degree into a low. The degree of "steepness" will indicate whether the sphere will very slowly drift across a huge empty area, or get wickedly yanked into a black hole.

The Lagrange points are areas of space where the contour of the surface is such that a sphere could rest there without rolling toward a low. The gravity pulls equally in all directions.

The unstable points are the ones where something could stay, but the coutour drops off steeply nearby. If the object gets bumped, see ya. The stable ones are more like plateau areas. Objects would need more of a shove to get them to move to the sloping areas.