Interplanetary Measures Can Not Bound the Cosmological Constant

Abstract

The effect of a cosmological constant on the precession of the line of apsides is O(Λc^2 r^3/GM) which is 3(H_\circ P)^2/8π^2 \approx 10^{-23} for a vacuum-dominated Universe with Hubble constant H_\circ = 65 km/sec/Mpc and for the orbital period P = 88 days of Mercury. This is unmeasurably small, so planetary perturbations cannot be used to limit the cosmological constant, contrary to the suggestion by Cardona & Tejeiro (1998).