  As it is well known, the $0-0$ component of the Schwarzschild space can be
obtained by the requirement that the geodesic of slowly moving particles match
the Newtonian equation. Given this result, we show here that the remaining
components can be obtained by requiring that the inside of a Newtonian ball of
dust matched at a free falling radius with the external space determines that
space to be Schwarzschild, if no pathologies exist. Also we are able to
determine that the constant of integration that appears in the Newtonian
Cosmology coincides with the spacial curvature of the FLRW metric.
