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Analysis of transit times in exoplanetary systems accurately provides aninstantaneous orbital period, $P(t)$, of their member planets. A long-termmonitoring of those transiting planetary systems puts limits on the variabilityof $P(t)$, which are translated into the constraints on the time variation ofthe gravitational constant $G$. We apply this analysis to $10$ transitingsystems observed by the Kepler spacecraft, and find that $\Delta G/G\lesssim5\times10^{-6}$ for 2009-2013, or $\dot{G}/G \lesssim10^{-6}\,\mathrm{yr}^{-1}$ if $\dot{G}$ is constant. While the derived limit isweaker than those from other analyses, it is complementary to them and can beimproved by analyzing numerous transiting systems that are continuouslymonitored.

Transiting planets as a precision clock to constrain the time variation of the gravitational constant