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.