  We apply Feynman's principle, ``The same equations have the same solutions'',
to Kepler's problem and show that Newton's dynamics in a properly curved 3-D
space is identical with that described by Einstein's theory in the 3-D optical
geometry of Schwarzschild's spacetime. For this reason, rather unexpectedly,
Newton's formulae for Kepler's problem, in the case of nearly circular motion
in a static, spherically spherical gravitational potential accurately describe
strong field general relativistic effects, in particular vanishing of the
radial epicyclic frequency at the marginally stable orbit.
