Lagrange Point Stability Explorer

Lagrange points represent locations in space where the gravitational forces of two massive bodies balance the centripetal force required for a small object to orbit with them. Statically, L1, L2, and L3 are unstable saddle points, requiring active station-keeping. L4 and L5 are stable due to the Coriolis force, forming gravitational wells that accumulate orbital debris, known as Trojan asteroids. This stability occurs only if the mass ratio of the two primary bodies exceeds 24.96.

Imagine watching from a merry-go-round that turns along with the two bodies, so the Lagrange point sits perfectly still. This tool gives a test particle a tiny push (ε) plus a small sideways speed, then traces where it goes. At a stable point the path curls into slow loops that never wander far; at an unstable one the distance keeps doubling until the particle escapes. Try a nudge at L4 versus one at L1 to feel the difference.

The collinear points here are unstable — yet that very flaw is exactly why spacecraft love them. Because a saddle point has an escape direction, a probe can drift away along it using almost no fuel, riding invisible tubes called the Interplanetary Transport Network. NASA's Genesis mission surfed these low-energy pathways through the Sun-Earth L1 and L2 points, trading speed for enormous fuel savings.