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Lagrange Points

About this simulation

This simulation plots the effective potential of two masses orbiting each other and marks the five Lagrange points. Students set the mass ratio from 5 to 200, choose where to start the test body (near L4, L5, L2 or L1), toggle the potential surface and relaunch the body. Readouts show the ratio, the distances to L1 and L2, and whether L4 and L5 are stable. It lets teachers show saddle points versus stable points, and why telescopes and Trojan asteroids sit where they do.

What students can explore

  • Start the Test body near L4 and watch whether it stays close to the point.
  • Choose Near L1 or Near L2 and press Relaunch test body to see it drift away.
  • Slide Mass ratio below 25 and watch the L4 / L5 stable readout change.
  • Raise the mass ratio and read how the distances to L1 and L2 change.
  • Toggle Potential surface off to see only the orbit paths.

Learning objectives

  1. 1Identify the five Lagrange points in a two-body system.
  2. 2Distinguish unstable points L1, L2 and L3 from the stable points L4 and L5.
  3. 3State that L4 and L5 are stable when the mass ratio is above about 25.
  4. 4Give real examples such as telescopes at L2 and Trojan asteroids.

Questions teachers ask

Is the Lagrange points simulation free to use?

Yes. It is completely free and runs in any modern web browser, including on interactive whiteboards, tablets, Chromebooks and phones. There is nothing to install and no sign-up or account is needed.

What is a Lagrange point?

It is a place in a system of two orbiting masses where a small object can stay in step with them, because gravity from both bodies and the rotation of the system balance out.

Which Lagrange points are stable?

L4 and L5, forming equilateral triangles with the two masses, are stable when the heavier mass is more than 24.96 times the lighter. L1, L2 and L3 are unstable, like a ball on a saddle.

How do I use the Lagrange points simulation?

Pick a start point for the test body, press Relaunch, and watch what happens. Then change the mass ratio and compare the stable and unstable cases.

Embed this simulation

Drop it into your LMS, blog, or class site — free.

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