  We apply recent results in the theory of PDE, specifically in problems with
two different time scales, on Einstein's equations near their Newtonian limit.
The results imply a justification to Postnewtonian approximations when
initialization procedures to different orders are made on the initial data. We
determine up to what order initialization is needed in order to detect the
contribution to the quadrupole moment due to the slow motion of a massive body
as distinct from initial data contributions to fast solutions and prove that
such initialization is compatible with the constraint equations. Using the
results mentioned the first Postnewtonian equations and their solutions in
terms of Green functions are presented in order to indicate how to proceed in
calculations with this approach.
