Solar system effects in Schwarzschild–de Sitter space–time

Abstract

The Schwarzschild–de Sitter space–time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant Λ. 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 Λ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For Λ=Λ0∼10−52 m−2 the cosmological constant plays no role for all of these effects, while a value of Λ∼−10−37 m−2, if hypothetically held responsible for the Pioneer anomaly, is not compatible with the perihelion shift.