The ancient idea of crystal spheres, which probably goes back to the classical Greeks, adn probably back to the dawn of human thought, has taken on a new form in the fact that all known orbits (of any kind) are now known to be due solely to the spherical symmetry of spacetime, encapsulated in one simple orbital theorem
nr = r / m = integral dr = r + mu
and the Frobenius Theorem of mathematics. The classical and renaissance idea of the sphere as encapsulating perfection takes on a new meaning. The fact that the constant of integration mu is -2MG / c squared is deduced by experimental obsrevation of orbits by satellites and telescopes, which can give very precise data. Even in binary pulsars, where a very tiny perturbation a / r is needed, the symmetry of spacetime is still spherical.