Lagrange points

In the restricted three-body problem — two massive bodies in circular orbit plus one massless test particle — there are exactly five points where the test particle can remain stationary in the rotating frame. Three (L1, L2, L3) lie on the line connecting the two massive bodies and are unstable equilibria (saddle points of the effective potential). Two (L4, L5) form equilateral triangles with the two bodies and are stable — the Coriolis force in the rotating frame provides a restoring mechanism despite the potential being a local maximum.

Joseph-Louis Lagrange discovered these points in 1772 while studying the three-body problem analytically. L1 (between Sun and Earth) hosts the SOHO solar observatory. L2 (beyond Earth from the Sun) hosts the James Webb Space Telescope. L4 and L5 of the Sun-Jupiter system are home to the Trojan asteroids — over 12,000 known objects librating around these stable points. The concept extends to any two-body system: Earth-Moon Lagrange points are candidates for future space stations.