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Frequently, the quantitative effect of the large-scale cosmological expansionon local systems is studied in the light of Newtonian approach, and the GeneralRelativity Theory is neglected. We, however, analyze the influence ofcosmological expansion on small systems in the light of Post-Newtonianapproximation. The equations show the product Hc=6.99*10^-10 ms^-2, and it sohappens that the magnitude of this acceleration is very close the apparentlyanomalous acceleration of the Pioneer 10 and 11 spacecraft. Furthermore, weobtain the new radius at which the acceleration due to the cosmologicalexpansion has the same magnitude as the two-body attraction, and the classicalcritical radius is obtained when the Schwarzschild radius approaches zero (forexample, the Solar System).

The effect of the cosmological expansion on local systems: Post-Newtonian approximation