  It is suggested a metric ansatz to describe local matter in an expanding
universe, hence interpolating between the Schwarzschild metric at small spatial
scales and the FLRW metric at large spatial scales. This is acomplished
maintaining space-time free of singularities except for the Schwarzschild mass
pole at the origin as opposed to metrics already considered in the literature
with the same purpose, namely the McVittie metric. The modified Newton law is
analyzed and the static orbit solutions computed. It is concluded that the
effects of expantion in the solar system are negligible, however depending on
the metric parameter value, at galactic scales there is a significant deviation
from the General Relativity Newton law which may contribute to dark matter
effects allowing for a flattening of galaxy rotation curves.
