  Does the Solar System and, more generally, a gravitationally bound system
follow the cosmic expansion law ? Is there a cosmological influence on the
dynamics or optics in such systems ? The general relativity theory provides an
unique and unambiguous answer, as a solution of Einstein equations with a local
source in addition to the cosmic fluid, and obeying the correct (cosmological)
limiting conditions. This solution has no analytic expression. A Taylor
development of its metric allows a complete treatment of dynamics and optics in
gravitationally bound systems, up to the size of galaxy clusters, taking into
account both local and cosmological effects. In the solar System, this provides
an estimation of the (non zero) cosmological influence on the Pioneer probe: it
fails to account for the " Pioneer effect " by about 10 orders of magnitude. We
criticize contradictory claims on this topic.
