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For Engineers · Lagrange Points

Lagrange Points for a habitable zone

Built for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed. Simulate a habitable zone live below — adjust the inputs and watch it respond, right in your browser.

Lagrange PointsLive

restricted three-body problem

Controls

Presets

Mass ratio μ

Show effective potential

In a two-body system, five points let a small object stay fixed in the rotating frame. L1-L3 sit on the line through the two masses (unstable); L4 and L5 lead and trail the secondary by 60° and are stable for μ below 0.0385 — where Jupiter's Trojan asteroids live. JWST orbits the Sun-Earth L2.

▶ Run in Python

Data Inspector

μ = m₂/(m₁+m₂)0.150

L4/L5 stable?no

Points5

Governing equation

Ω (x, y) = \frac{1}{2} (x^{2} + y^{2}) + \frac{1 - μ}{r _{1}} + \frac{μ}{r _{2}}, μ = 0.150

Reading this result: At μ=0.150 the masses are too comparable: even L4 and L5 turn unstable, so every Lagrange point here needs active station-keeping to hold a spacecraft in place.

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Frequently asked questions

Is this good for engineers?: Yes — this version of "Lagrange Points for a habitable zone" is framed for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.