Empirical Earth · The Sky — Sun, Moon & Stars

The three-body problem

The claim

“The three-body problem has no solution, so the model can’t predict the system.”

What is measured

Spacecraft are steered to other planets with Newton’s gravity to the kilometer across hundreds of millions of km. It is the same physics that pulls Earth into a sphere.

What would show this is wrong

planetary positions straying from Newtonian / relativistic three-body predictions.

Sources

  1. The three-body problem & ephemerides. H. Poincaré (1890, non-integrability); Chenciner & Montgomery (2000, figure-eight orbit, Annals of Mathematics); JPL Development Ephemeris DE440 (NASA/J link
  2. Apophis 2029 — a gravity prediction you can check. Radar and optical tracking fix asteroid (99942) Apophis’s closest approach at ~31,600 km above the surface on 13 April 2029 (inside the geo link
  3. Exact periodic three-body orbits keep being found. The general problem has no closed-form solution, but Euler (1767) and Lagrange (1772) found special ones, Moore found the figure-eight chor link
The full entry, with the working →

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