  In 1687 Isaac Newton published PHILOSOPHI\AE \ NATURALIS PRINCIPIA
MATHEMATICA, where the classical analytic dynamics was formulated. But Newton
also formulated a discrete dynamics, which is the central difference algorithm,
known as the Verlet algorithm. In fact Newton used the central difference to
derive his second law. The central difference algorithm is used in computer
simulations,where almost all Molecular Dynamics simulations are performed with
the Verlet algorithm or other reformulations of the central difference
algorithm. Here we show, that the discrete dynamics obtained by Newtons
algorithm for Kepler's equation has the same solutions as the analytic
dynamics. The discrete positions of a celestial body are located on an ellipse,
which is the exact solution for a shadow Hamiltonian nearby the Hamiltonian for
the analytic solution.
