A Practical Relativistic Model for Microarcsecond Astrometry in Space

Abstract

This paper is devoted to a practical model for relativistic reduction of positional observations with an accuracy of 1 µas which is expected to be attained in the future space astrometry missions. All relativistic effects which are caused by the gravitational field of the Solar system and which are of practical importance for this accuracy level are thoroughly calculated and discussed. The model includes relativistic modeling of the motion of observer, modeling of relativistic aberration and gravitational light deflection as well as a relativistic treatment of parallax and proper motion suitable for the accuracy of 1 µas. The model is formulated both for remote sources (stars, quasars, etc.) and for Solar system objects (asteroids, etc.). The suggested model is formulated within the framework of Parametrized Post-Newtonian Formalism with parameters β and γ. However, for general relativity (β = γ = 1) the model is fully compatible with the IAU Resolutions (2000) on relativity in celestial mechanics, astrometry and metrology. The model is presented in a form suitable for implementation in a software system for data processing or simulation. The changes which should be applied to the model to attain the accuracy of 0.1 µas are reviewed. Potentially important relativistic effects caused by additional gravitational fields which are generated outside of the Solar system are also briefly discussed. Subject headings: astrometry, reference systems, relativity• the 3-dimensional coordinate quantities ("3-vectors") referred to the spatial axes of the corresponding reference system are set in boldface: a = a i ;• the absolute value (Euclidean norm) of a "3-vector" a is denoted as |a| and can be computed as |a| = (a 1 a 1 + a 2 a 2 + a 3 a 3 ) 1/2 ;

The astrometric core solution for theGaiamission

“…The formulation adopted for Gaia (Klioner 2003(Klioner , 2004) is based on the parametrized post-Newtonian (PPN) version of the relativistic framework adopted in 2000 by the International Astronomical Union (IAU); see Soffel et al (2003). In this section only some key concepts from this formulation are introduced.…”

“…The reference epoch t ep is preferably chosen to be near the mid-time of the mission in order to minimize statistical correlations between the position and proper motion parameters. The transformation between the kinematic and the astrometric parameters is non-trivial (Klioner 2003), mainly as a consequence of the practical need to neglect most of the lightpropagation time t − t * between the emission of the light at the source (t * ) and its reception at Gaia (t). This interval is typically many years and its value, and rate of change (which depends on the radial velocity of the source), will in general not be known with sufficient accuracy to allow modelling of the motion of the source directly in terms of its kinematic parameters according to Eq.…”

“…The transformation fromū i (t) to the observable (proper) direction u i (t) involves taking into account gravitational light deflection by solar-system bodies and the Lorentz transformation A78, page 4 of 47 to the co-moving frame of the observer (stellar aberration); the relevant formulae are given by Klioner (2003). This transformation therefore depends also on the global parameters g, for example the PPN parameter γ which measures the strength of the gravitational light deflection.…”

GaiaData Release 1

“…Various components of the model are gathered in the Gaia relativity model (GREM; Klioner 2003Klioner , 2004. The primary coordinate system used for the astrometric processing of Gaia data is the Barycentric Celestial Reference System (BCRS; Soffel et al 2003).…”

Gaia-like astrometry and gravitational waves

“…In our approximation we can neglect the light deflection due to solar system and consider that u = −k, where k is the coordinate vector from the source to the observer at the moment of observation t as calculated by the relativistic astrometric model (e.g. Gaia Relativity Model (GREM) [20,21]) from the source parameters and the position of the observer x obs = x obs (t). Both source parameters and x obs are defined in the underlying relativistic reference system called Barycentric Celestial Reference System (BCRS) and described e.g.…”