We present nine newly observed transits of TrES-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. A Markov-Chain Monte-Carlo analysis was used to determine the planet-star radius ratio and inclination of the system, which were found to be Rp/Rstar=0.1664^{+0.0011}_{-0.0018} and i = 81.73^{+0.13}_{-0.04} respectively, consistent with previous results. The central transit times and uncertainties were also calculated, using a residual-permutation algorithm as an independent check on the errors. A re-analysis of eight previously published TrES-3 light curves was conducted to determine the transit times and uncertainties using consistent techniques. Whilst the transit times were not found to be in agreement with a linear ephemeris, giving chi^2 = 35.07 for 15 degrees of freedom, we interpret this to be the result of systematics in the light curves rather than a real transit timing variation. This is because the light curves that show the largest deviation from a constant period either have relatively little out-of-transit coverage, or have clear systematics. A new ephemeris was calculated using the transit times, and was found to be T_c(0) = 2454632.62610 +- 0.00006 HJD and P = 1.3061864 +- 0.0000005 days. The transit times were then used to place upper mass limits as a function of the period ratio of a potential perturbing planet, showing that our data are sufficiently sensitive to have probed for sub-Earth mass planets in both interior and exterior 2:1 resonances, assuming the additional planet is in an initially circular orbit.
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