2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33821The effect of the expanding universe on planetary motion is considered to first order in the Hubble constant H. Orbital elements are shown to be unaffected, but there is a small change in the connection between planetary proper time and coordinate time. This can produce an apparent anomalous acceleration in velocities inferred from echo-ranging, but the effect is too small by many orders of magnitude to account for the Pioneer 10/11 anomaly.10 pages, 1 figureGeneral Relativity and Quantum Cosmologytext