2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111180We give a rigorous derivation of the general-relativistic formula for the two-way Doppler tracking of a spacecraft in Friedmann-Lemaitre-Robertson-Walker and in McVittie spacetimes. The leading order corrections of the so-determined acceleration to the Newtonian acceleration are due to special-relativistic effects and cosmological expansion. The latter, although linear in the Hubble constant, is negligible in typical applications within the Solar System.10 pages, 1 figure. Journal versionGeneral Relativity and Quantum CosmologyAstrophysicsSpace Physicstext