  Context: We are testing the Brans-Dicke class of scalar tensor theories with
planetary ephemerides. Aims: In this work, we apply our recently proposed
Bayesian methodology to the Brans-Dicke case, with an emphasis on the issue of
the strong equivalence principle (SEP). Methods: We use an MCMC approach
coupled to full consistent planetary ephemeris construction (from point-mass
body integration to observational fit) and compare the posterior distributions
obtained with and without the introduction of potential violations of the SEP.
Results: We observe a shift in the confidence levels of the posteriors
obtained. We interpret this shift as marginal evidence suggesting that the
effect of violation of the SEP can no longer be assumed to be negligible in
planetary ephemerides with the current data. We also notably report that the
constraint on the Brans-Dicke parameter with planetary ephemerides is getting
closer to the figure reported from the Cassini spacecraft alone, but also to
the constraints from pulsars. We anticipate that data from future spacecraft
missions, such as BepiColombo, will significantly enhance the constraints based
on planetary ephemerides.
