LAGRANGIANLABS
Earth, Moon, and the five Lagrange points

AN AI LAB

A shared
future,
in balance.

An AI lab exploring the space between
human purpose and machine intelligence.

Why Lagrangian?

EARTH–MOON SYSTEM

ROTATING FRAME
EFFECTIVE POTENTIAL CONTOURS

Between two worlds.

UNSTABLE EQUILIBRIUM

Between Earth and Moon, gravity and orbital motion balance. Staying nearby takes continual care.

SELECT A LAGRANGE POINT
A NOTE ON THE FIELD

The mathematics
behind the field.

This Earth–Moon model assumes circular orbits and a negligible third mass, in a rotating frame. L1–L3 are numerical solutions; L4/L5 form equilateral triangles with the two bodies.

Lines show effective potential from gravity and rotation, not orbits. Positions are to scale; body symbols are enlarged.

L1–L3 are unstable; L4/L5 are linearly stable here. Real motion also depends on the Sun’s gravity and orbital eccentricity.

MOON / TOTAL MASS0.01215058DISTANCE UNITEARTH–MOON SEPARATION
JPL · Physical parameters ↗NASA · Lagrange points ↗