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. 
Kento Masuda and Yasushi Suto
gr-qc astro-ph.CO astro-ph.EP