On Doppler tracking in cosmological spacetimes

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.

10 pages, 1 figure. Journal version

References in corpus (7)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Study of the anomalous acceleration of Pioneer 10 and 11
• Lorentz Covariant Theory of Light Propagation in Gravitational Fields of Arbitrary-Moving Bodies
• Solar system effects in Schwarzschild--de Sitter spacetime
• Independent Confirmation of the Pioneer 10 Anomalous Acceleration
• On the influence of the global cosmological expansion on the local dynamics in the Solar System
• The "Pioneer effect" as a manifestation of the cosmic expansion in the solar system

Cited by in corpus (12)

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• Influence of global cosmological expansion on local dynamics and kinematics
• Making sense of the bizarre behaviour of horizons in the McVittie spacetime
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• Local gravitational physics of the Hubble expansion
• Cosmology in the Solar System: Pioneer effect is not cosmological
• Does cosmological expansion affect local physics?
• Influence of cosmological expansion in local experiments
• Constraining an Expanding Locally Anisotropic metric from the Pioneer anomaly
• A note on the computation of geometrically defined relative velocities
• Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
• An algorithm for computing geometric relative velocities through Fermi and observational coordinates