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When to Use the Lagrange Point Stability (L1-L5) 3D Explorer

Last reviewed: 2026-08-04

Open the Lagrange Point Stability 3D Explorer when you want a real numerical answer to why L1, L2, and L3 always drift away while L4 and L5 hold only below Routh's critical mass ratio, about 0.0385.

Sessions this explorer fits

Students learning why three of the five Lagrange points are always unstable and two are conditionally stable, teachers contrasting real named systems - Sun-Earth, Sun-Jupiter, Earth-Moon, Pluto-Charon - on one mass-ratio slider, and readers who want to see a genuine Runge-Kutta integration decide which of five nudged test points escape and which stay bounded all get a direct answer here.

Sessions this explorer does not fit

Sessions this page does not fit are simply locating where the five Sun-Earth Lagrange points sit and which real spacecraft fly near them, which is on the Lagrange Points 3D Explorer; or a general-purpose figure-8 orbit sandbox with no Lagrange points at all, which is on the Three-Body Problem 3D Explorer. Walk through the controls in the step-by-step guide.

← Back to Space 3D

Last updated: Aug 4, 2026

Reviewed by the Free Tool Online editorial team · Tested in the current versions of Chrome, Firefox, Safari, and Edge before publishing. No account is needed to use any tool. Report a bug - we triage within 72 hours. · Last refreshed April 2026.

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