Kepler Problem
The Kepler problem describes the motion of a body in a central gravitational field, with Hamiltonian
\[H(q, p) = \frac{1}{2} \| p \|^2 - \frac{\mu}{\| q \|} ,\]
a classic integrable, super-integrable Hamiltonian system (conserving energy, angular momentum and the Laplace–Runge–Lenz vector).
This system is documented for completeness but is not yet provided as a problem type in GeometricProblems.jl. For a related gravitational example, see the Three Body Problem.