Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Students · Lagrange Points

Lagrange Points for a gravity assist

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a gravity assist 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.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Lagrange Points

Lagrange Points for a planet orbit Lagrange Points for a binary star Lagrange Points for a black hole Lagrange Points for a galaxy rotation Lagrange Points for a comet path Lagrange Points for a solar eclipse Lagrange Points for a supernova Lagrange Points for a star's life

Frequently asked questions

Is this good for students?: Yes — this version of "Lagrange Points for a gravity assist" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.