Turing completeness of the n-body problem

Determine whether the Newtonian n-body problem in celestial mechanics is Turing complete for some n > 2 and for some choices of masses, in the sense that its Hamiltonian flow can simulate a universal Turing machine via an orbit reachability encoding.

Background

Through the Reeb–Beltrami correspondence, certain mechanical systems (including celestial mechanics on positive energy levels) can be interpreted as steady Euler flows on suitable Riemannian manifolds. The paper discusses universal computation in hydrodynamics and notes a lack of prior analysis on the computational power of the Newtonian n-body problem.

This question asks whether, for some number of bodies greater than two and appropriate mass choices, the n-body Hamiltonian dynamics can encode computations of a universal Turing machine, thereby exhibiting undecidable trajectory properties.