Solar system effects in Schwarzschild--de Sitter spacetime

Abstract

The Schwarzschild--de Sitter space--time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant $\Lambda$. Based on this space--time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, Perihelion shift, geodetic or de Sitter precession, as well as the influence of $\Lambda$ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For $\Lambda=\Lambda_0 \sim 10^{-52} {\rm m}^{-2}$ the cosmological constant plays no role for all of these effects, while a value of $\Lambda \sim - 10^{-37} {\rm m}^{-2}$, if hypothetically held responsible for the Pioneer anomaly, is not compatible with the Perihelion shift.