Lagrange Points
Five Equilibria in Every Two-Body System
Mass ratio
50 : 1
L-points
5 total
Stable
L4, L5
Unstable
L1, L2, L3
L4/L5 angle
±60°
Triangle type
Equilateral
Lagrange points arise where the gravitational pull of two large bodies and the centrifugal force of the rotating system exactly cancel. An object placed at one requires no thrust to maintain its position.
L4 and L5 are stable because any small displacement creates a restoring force — the Coriolis effect nudges the object back, causing it to trace slow ellipses called libration orbits.
L1, L2, and L3 are saddle points. A displacement along the axis leads away from equilibrium. Spacecraft stationed there require periodic stationkeeping burns.
Between the two bodies
Solar observation (SOHO, DSCOVR)
Gravity from both bodies balances. Ideal for monitoring the primary, but any perturbation causes drift.
Beyond the smaller body
Deep space telescopes (JWST, Herschel)
Always in the shadow of the secondary. Cold and stable enough for infrared instruments.
Beyond the larger body, hidden
Theoretically none — always out of view
The least useful point. Perpetually blocked by the primary and slowly perturbed by other bodies.
60° ahead of secondary
Trojan asteroids, long-term debris
Forms an equilateral triangle with both bodies. Objects here librate slowly and remain for billions of years.
60° behind secondary
Trojan asteroids, proposed space stations
Mirror of L4. Jupiter's Trojans share this point with thousands of asteroids. Proposed for future colonies.