Three-body problem and N-body gravity simulation
Two bodies under gravity have a neat solution: ellipses. Add a third and there is no general formula at all. The three-body problem has been open since Newton, and most of its solutions are chaotic.
Interactive, free and runs in your browser. Part of the Frontier Physics simulations.
What you will see
Bodies attract each other with Newtonian gravity, leaving glowing trails. Presets show a famous stable figure-of-eight orbit where three equal masses chase each other, a binary pair with a probe passing by, and a chaotic four-body system that never repeats.
Try this
- Start the figure-of-eight and watch how precisely it repeats.
- Run the chaotic preset twice and see how differently it unfolds.
- Watch the probe in the binary preset gain speed as it slingshots past.
Common misconception
Chaotic does not mean random. The motion is completely determined by Newton’s laws; it is unpredictable in practice because tiny differences in the starting positions grow exponentially.
Exam-style question
Why can a two-body orbit be written down exactly but a general three-body orbit cannot?
Two bodies reduce to one body orbiting the centre of mass, which has enough conserved quantities (energy and angular momentum) to solve completely. With three bodies there are not enough conserved quantities to pin down the motion, so in general there is no closed-form solution and the orbits are chaotic.
Key equations
F = G m₁m₂ / r²v_circ = √(GM / r)
Curriculum
IB Physics E.5, enrichment: astrophysics and cosmology.