  The properties of a dilute granular gas in the homogeneous cooling state are
mapped to those of a stationary state by means of a change in the time scale
that does not involve any internal property of the system. The new
representation is closely related with a general property of the granular
temperature in the long time limit. The physical and practical implications of
the mapping are discussed. In particular, simulation results obtained by the
direct simulation Monte Carlo method applied to the scaled dynamics are
reported. This includes ensemble averages and also the velocity autocorrelation
function, as well as the self-diffusion coefficient obtained from the latter by
means of the Green-Kubo representation. In all cases, the obtained results are
compared with theoretical predictions.
