  We study the Yamabe flow starting from an asymptotically flat manifold
$(M^n,g_0)$. We show that the flow converges to an asymptotically flat, scalar
flat metric in a weighted global sense if $Y(M,[g_0])>0$, and show that the
flow does not converge otherwise. If the scalar curvature is nonnegative and
integrable, then the ADM mass at time infinity drops by the limit of the total
scalar curvature along the flow.
