Three-Body Problem Simulation

Two bodies moving under gravity have an exact solution: each traces a conic section, and you can write down where they will be at any future moment. Three bodies obey the very same law and have no such general solution. Special cases exist — the figure-eight choreography and Lagrange's triangle are both real, exact orbits — but they are fragile: change one mass slightly and the motion never repeats. Students can change body 1 mass and body 2 mass and compare what happens. Use it for math inquiry with High School on a projector or student device.

Standards: Common Core CCSS.MATH.CONTENT.HSF.IF.B.4, CCSS.MATH.CONTENT.HSF.IF.C.7

• Run the figure-eight, then raise one mass by a few percent and watch the pattern break
• Compare the energy readout with the paths: the orbits become unpredictable while the total energy does not
• Set up the Lagrange triangle and check that all three separations stay equal as it turns
• Use the Sun-planet-moon setup to see why a hierarchy of orbits stays stable when a crowded system does not

1. 1Predict how changing body 1 mass will affect the pull between 1 and 2, then test the prediction.
2. 2Use evidence from the live calculation and visual to explain the result.

Questions teachers ask