  How does one compute the Bondi mass on an arbitrary cut of null-infinity
$\scri$ when it is not presented in a Bondi system? What then is the correct
definition of the mass aspect? How does one normalise an asymptotic translation
computed on a cut which is not equipped with the unit-sphere metric? These are
questions which need to be answered if one wants to calculate the Bondi-Sachs
energy-momentum these quantities for a space-time which has been determined
numerically. Under such conditions there is not much control over the
presentation of $\scri$ so that most of the available formulations of the Bondi
energy-momentum simply do not apply. The purpose of this article is to provide
the necessary background for a manifestly conformally invariant and gauge
independent formulation of the Bondi energy-momentum. To this end we introduce
a conformally invariant version of the GHP formalism to rephrase all the
well-known formulae. This leads us to natural definitions for the space of
asymptotic translations with its Lorentzian metric, for the Bondi news and the
mass-aspect. A major role in these developments is played by the
"co-curvature", a naturally appearing quantity closely related to the Gau{\ss}
curvature on a cut of $\scri$.
