  This is the first of two papers devoted to the asymptotic structure of
space-time in the presence of a non-negative cosmological constant $\Lambda$.
This first paper is concerned with the case of $\Lambda =0$. Our approach is
fully based on the tidal nature of the gravitational field and therefore on the
`tidal energies' built with the Weyl curvature. In particular, we use the
(radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at
infinity to provide a novel characterisation of radiation escaping from, or
entering into, the space-time. Our new criterion is easy to implement and shown
to be fully equivalent to the classical one based on the news tensor. One of
its virtues is that its formulation can be easily adapted to the case with
$\Lambda>0$ covered in the second paper. We derive the general
energy-momentum-loss formulae including the matter terms and all factors
associated to the choices of arbitrary foliation and of super-translation. We
also revisit and present a full reformulation of the traditional peeling
behaviour with a neat geometrical construction that leads, in particular, to an
asymptotic alignment of the supermomenta in accordance with the radiation
criterion.
