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The first three Lagrangian points are technically stable only in the plane perpendicular to the line between the two bodies. This can be seen most easily by considering the L1
point. A test mass displaced perpendicularly from the central line
would feel a force pulling it back towards the equilibrium point. This
is because the lateral components of the two masses' gravity would add
to produce this force, whereas the components along the axis between
them would balance out. However, if an object located at the L1
point drifted closer to one of the masses, the gravitational attraction
it felt from that mass would be greater, and it would be pulled closer.
(The pattern is very similar to that of tidal forces.)
In contrast to the collinear libration points, the triangular points (L4 and L5) are stable equilibria (cf. attractor), provided the ratio of the masses M1/M2
is > 24.96. This is the case for the Sun/Earth and Earth/Moon
systems, though by a smaller margin in the latter. When a body at these
points is perturbed, it moves away from the point, but the Coriolis effect then acts, and bends the object's path into a stable, kidney beanâshaped orbit around the point (as seen in the rotating frame of reference).
