  The time dependence of deviations from the Gaussian state in a freely cooling
homogeneous system of smooth inelastically colliding spheres is investigated by
kinetic theory. We determine the full time dependence of the coefficients of an
expansion around the Gaussian state in Generalized Laguerre polynomials.
Approximating this system of equations to sixth order, we find that the
asymptotic state, where the mean energy T follows Haff's law with time
independent cooling rate, is reached within a few collisions per particle.
Two-dimensional molecular dynamics simulations confirm our results and show
exponential behavior in the high-energy tails.
