  Here we review the understanding of the classical hydrogen atom in classical
electromagnetic zero-point radiation, and emphasize the importance of special
relativity. The crucial missing ingredient in earlier calculational attempts
(both numerical and analytic) is the use of valid approximations to the full
relativistic analysis. It is pointed out that the nonrelativistic time Fourier
expansion coefficients given by Landau and Lifshitz are in error as the
electromagnetic description of a charged particle in a Coulomb potential, and,
because of this error, Marshall and Claverie's conclusion regarding the failure
of radiation balance is invalid. Rather, using Marshall and Claverie's
calculations, but restricted to lowest nonvanishing order in the orbital
eccentricity (where the nonrelativistic orbit is a valid approximation to the
fully relativistic electromagnetic orbit) radiation balance for classical
electromagnetic zero-point radiation is shown to hold at the fundamental
frequencies and associated first overtones.
