  In this paper, we establish that a four-dimensional static vacuum
asymptotically flat spacetime containing a massive particle sphere is isometric
to the Schwarzschild spacetime. Our results expand upon existing uniqueness
theorems for static vacuum asymptotically flat spacetimes, which focus on
scenarios featuring event horizons or photon spheres. Similarly to the
uniqueness theorems concerning photon spheres or event horizons, only a single
massive particle sphere is sufficient to obtain a unique solution. However, in
contrast to previous theorems, our result leads to the existence of an entire
spacetime foliation sliced by a set of massive particle spheres spanning
various energies.
