Solar System planetary tests of \dot c/c
  Analytical and numerical calculations show that a putative temporal variation
of the speed of light c, with the meaning of space-time structure constant
c_ST, assumed to be linear over timescales of about one century, would induce a
secular precession of the longitude of the pericenter \varpi of a test particle
orbiting a spherically symmetric body. By comparing such a predicted effect to
the corrections \Delta\dot\varpi to the usual Newtonian/Einsteinian perihelion
precessions of the inner planets of the Solar System, recently estimated by
E.V. Pitjeva by fitting about one century of modern astronomical observations
with the standard dynamical force models of the EPM epehemerides, we obtained
\dot c/c =(0.5 +/- 2)\times 10^-7 yr^-1. Moreover, the possibility that \dot
c/c\neq 0 over the last century is ruled out at 3-12\sigma level by taking the
ratios of the perihelia for different pairs of planets. Our results are
independent of any measurement of the variations of other fundamental constants
which may be explained by a variation of $c$ itself (with the meaning of
electromagnetic constant c_EM). It will be important to repeat such tests if
and when other teams of astronomers will estimate their own corrections to the
standard Newtonian/Einsteinian planetary perihelion precessions.
