00 · IN THREE MINUTES

The answer in three steps

  1. 1The two main bodies and a small object are viewed in a rotating frame.
  2. 2At five solutions, gravitational and inertial terms allow the geometry to repeat.
  3. 3L4 and L5 can be stable under the right mass ratio; L1, L2 and L3 are unstable and usually need station-keeping.

01 · BALANCE DOES NOT MEAN ZERO FORCE

Balance does not mean zero force

At a , gravity is still acting. The useful balance is between the two bodies' gravity and the motion required for the small object to rotate with the system.

02 · THREE POINTS SIT ON ONE LINE

Three points sit on one line

L1 lies between the main bodies, L2 beyond the smaller body and L3 beyond the larger one. They are valuable observing regions but small errors grow, so spacecraft orbit around them and make corrections.

FIG. 02 · INTERACTIVEHow the evidence fits together

A conceptual model: the geometry shows relationships, not measured scale.

1

Balance does not mean zero force

At a Lagrange point, gravity is still acting. The useful balance is between the two bodies' gravity and the motion required for the small object to rotate with the system.

rotating frame
A conceptual model: the geometry shows relationships, not measured scale.

03 · TWO POINTS FORM TRIANGLES

Two points form triangles

L4 and L5 lead and trail the smaller body by about 60 degrees. When the mass ratio is favourable, nearby motion can remain bounded, which is why asteroids can collect in Trojan populations.

04 · WEBB DOES NOT PARK AT A DOT

Webb does not park at a dot

The James Webb Space Telescope follows a large halo-like orbit around the Sun-Earth L2 region. That geometry keeps the Sun, Earth and Moon on one side of its sunshield while preserving communications.

05 · THE IDEAL MODEL HAS LIMITS

The ideal model has limits

The textbook solution treats the third object as negligible and starts with circular orbits. Real systems include additional bodies, radiation pressure, eccentricity and navigation errors.

06 · SOURCES AND EVIDENCE

Sources and evidence

The explanation follows the evidence chain below. Links open the original source.

  1. 01
    What Is a Lagrange Point?

    Supports a specific claim or evidence boundary used in this article.

    INSTITUTIONAL EXPLAINER ↗
  2. 02
    What are Lagrange points?

    Supports a specific claim or evidence boundary used in this article.

    INSTITUTIONAL EXPLAINER ↗
  3. 03
    Webb's Orbit at Sun-Earth L2

    Supports a specific claim or evidence boundary used in this article.

    OFFICIAL DATA / TECHNICAL REPORT ↗
CHANGE LOG28 Aug 2026 · First five-language edition; claims, evidence boundaries and visual model checked.