  In spherical symmetry with radial coordinate $r$, classical Newtonian
gravitation supports circular orbits and, for $-1/r$ and $r^2$ potentials only,
closed elliptical orbits [1]. Various families of elliptical orbits can be
thought of as arising from the action of perturbations on corresponding
circular orbits. We show that one elliptical orbit in each family is singled
out because its focal length is equal to the radius of the corresponding
unperturbed circular orbit. The eccentricity of this special orbit is related
to the famous irrational number known as the golden ratio. So inanimate
Newtonian gravitation appears to exhibit (but not prefer) the golden ratio
which has been previously identified mostly in settings within the animate
world.
