  In this paper, we study the limiting behavior of the Brown-York mass and
Hawking mass along nearly round surfaces at infinity of an asymptotically flat
manifold. Nearly round surfaces can be defined in an intrinsic way. Our results
show that the ADM mass of an asymptotically flat 3-manifold can be approximated
by some geometric invariants of a family of nearly round surfaces which
approach to infinity of the manifold.
