Relativistic satellite astrometry: the stellar radial velocity

¹ Dipartimento di Fisica “Galileo Galilei”Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
e-mail: defelice@pd.infn.it; preti@pd.infn.it; crosta@to.astro.it; vecchiato@to.astro.it
² INFN, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
³ Osservatorio Astronomico di Torino, strada Osservatorio 20, 10125 Pino Torinese (TO), Italy

Received: 12 July 2010
Accepted: 6 January 2011

Abstract

We present a general-relativistic analysis that allows the stellar radial velocities to be determined from a suitable implementation of the spectroscopic data with the astrometric ones shortly to be provided by new generations of astrometric satellites at μarcsec levels of accuracy at least. This analysis leads to an enhancement of the c^-1 Doppler-shift formula presently planned for the Gaia mission to an all-inclusive, general-relativistic formula at the c^-3 level, consistently with the expected accuracy. From this formula, which is shown to provide relevant corrections already at the c^-2 level to a previously proposed one, we are then able to derive the explicit expression for the stellar radial velocity in terms of the spectroscopic and astrometric data, thereby accounting for all the necessary relativistic corrections up to and including the c^-3 level.