  Classical radiation equilibrium (the blackbody problem) is investigated by
the use of an analogy. Scaling symmetries are noted for systems of classical
charged particles moving in circular orbits in central potentials V(r)=-k/r^n
when the particles are held in uniform circular motion against radiative
collapse by a circularly polarized incident plane wave. Only in the case of a
Coulomb potential n=1 with fixed charge e is there a unique scale-invariant
spectrum of radiation versus frequency (analogous to zero-point radiation)
obtained from the stable scattering arrangement. These results suggest that
non-electromagnetic potentials are not appropriate for discussions of classical
radiation equilibrium.
