Transiting planets as a precision clock to constrain the time variation
  of the gravitational constant
  Analysis of transit times in exoplanetary systems accurately provides an
instantaneous orbital period, $P(t)$, of their member planets. A long-term
monitoring of those transiting planetary systems puts limits on the variability
of $P(t)$, which are translated into the constraints on the time variation of
the gravitational constant $G$. We apply this analysis to $10$ transiting
systems observed by the Kepler spacecraft, and find that $\Delta G/G\lesssim
5\times10^{-6}$ for 2009-2013, or $\dot{G}/G \lesssim
10^{-6}\,\mathrm{yr}^{-1}$ if $\dot{G}$ is constant. While the derived limit is
weaker than those from other analyses, it is complementary to them and can be
improved by analyzing numerous transiting systems that are continuously
monitored.
