  Using a representation of spatial infinity based in the properties of
conformal geodesics, the first terms of an expansion for the Bondi mass for the
development of time symmetric, conformally flat initial data are calculated. As
it is to be expected, the Bondi mass agrees with the ADM at the sets where null
infinity ``touches'' spatial infinity. The second term in the expansion is
proportional to the sum of the squared norms of the Newman-Penrose constants of
the spacetime. In base of this result it is argued that these constants may
provide a measure of the incoming radiation contained in the spacetime. This is
illustrated by means of the Misner and Brill-Lindquist data sets.
