On Doppler tracking in cosmological spacetimes
Matteo Carrera, Domenico Giulini
TL;DR
This paper rigorously derives the general-relativistic Doppler tracking formula for spacecraft in cosmological spacetimes, highlighting the negligible impact of cosmological expansion on Solar System measurements.
Contribution
It provides a precise derivation of Doppler tracking formulas in Friedmann-Lemaitre-Robertson-Walker and McVittie spacetimes, including relativistic and cosmological corrections.
Findings
Cosmological expansion effects are negligible in Solar System Doppler measurements.
Relativistic effects contribute to the leading order corrections.
The derivation clarifies the impact of cosmology on spacecraft tracking.
Abstract
We 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.
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