  Frequently, the quantitative effect of the large-scale cosmological expansion
on local systems is studied in the light of Newtonian approach, and the General
Relativity Theory is neglected. We, however, analyze the influence of
cosmological expansion on small systems in the light of Post-Newtonian
approximation. The equations show the product Hc=6.99*10^-10 ms^-2, and it so
happens that the magnitude of this acceleration is very close the apparently
anomalous acceleration of the Pioneer 10 and 11 spacecraft. Furthermore, we
obtain the new radius at which the acceleration due to the cosmological
expansion has the same magnitude as the two-body attraction, and the classical
critical radius is obtained when the Schwarzschild radius approaches zero (for
example, the Solar System).
