3.1.5 Relativistic model
Author(s): Sergei Klioner
Section 3.1.3 gives an overview of the
set of relativistic reference systems used in Gaia data processing.
The Barycentric Celestial Reference System (BCRS) is used to model the
motion of celestial bodies both inside and outside the solar-system.
From the relativistic point of view, the Gaia catalogue is the model of
Universe expressed in the BCRS. All astrometric parameters —
parallaxes (distances), proper motions, positions — are defined in
the BCRS coordinates. The goal of the relativistic model — called Gaia Relativity
Model (GREM) — is to compute (predict) the observed CoMRS direction towards a source given its
parameters in BCRS. The details of the model can be found in
Klioner (2003a, 2004); Klioner and Peip (2003); Klioner and Zschocke (2010); Zschocke and Klioner (2011).
Using the standard model of stellar motion described in Section 3.1.4
the astrometric parameters of a source
are used to compute the coordinate BCRS direction from the location
of Gaia at the moment of observation to the source
. This direction has to be transformed into the
observed direction with respect to CoMRS.
The transformation essentially consists of two steps. First, the light
propagation from the source to the location of Gaia is modelled in the
BCRS in full details required to reach the required numerical accuracy
of about 0.1 as. In this process, the influence of the
gravitational field of the solar-system is taken into account. This
includes the gravitational light-bending due to the Sun, the major
planets and the Moon. More deflecting bodies are readily available and
can be used for special purposes (e.g. special processing of the data
close to Jupiter foreseen in the future). Both post-Newtonian and
post-post-Newtonian effects are calculated. In this process special
care was given to the relation between the analytical order of
smallness of the effects and their numerical magnitude
(Klioner and Zschocke 2010). In particular, only the so-called
enhanced post-post-Newtonian effects, which can exceed 1 as in
some special observational configurations, are taken into account.
For observations close to the giant planets the effects of their
quadrupole gravitational fields are taken into account in the
post-Newtonian approximation. The effective computation of the rather
complicated quadrupole deflection of light represents a separate
problem (Zschocke and Klioner 2011). To speed up the computations of
the model, the post-Newtonian formula for the quadrupole deflection
was simplified as much as possible to give the required numerical
accuracy of at least 0.1 as for the realistic observational
configuration in Gaia. Besides that, a very efficient criterion was
found allowing one to decide if the actual calculation of the
quadrupole deflection is needed. The criterion allows one to estimate
the quadrupole deflection using only three multiplications.
The non-stationarity of the gravitational field (in particular, due to
translational motion of the solar-system bodies) is also properly
taken into account
(Klioner 2003a, b; Klioner and Peip 2003, and references therein).
No attempt is made to account for effects of the gravitational field
outside the solar-system. This plays a role only in cases when its
influence is variable on time scales comparable with the duration of
observations, e.g. in various gravitational lensing phenomena.
The second step is to compute the observed direction in
CoMRS from the computed BCRS direction of light propagation at the
location of Gaia at the moment of observation (Klioner (2003a, Section
5) and Klioner (2004, Section
VI)). Technically, the transformation
represents a closed-form Lorentz transformation with the velocity of
Gaia as seen by an fictitious observer that is co-located with Gaia at
the moment of observation, but having zero BCRS velocity. One can show
that that “observed” velocity is the BCRS velocity of Gaia multiplied by a factor depending on the
gravitational potential at the location of Gaia.
Besides astrometric parameters of the sources, GREM requires several kinds of auxiliary data:
-
–
Gaia spatial ephemeris (BCRS position and velocity of Gaia for any moment of time covered by observations;
Section 3.2.3);
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–
Gaia time ephemeris (the relation between the readings of the Gaia on-board clock and TCB; Section 3.1.6);
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–
Solar-system ephemeris; the INPOP10e ephemeris (Fienga et al. 2016) parametrized by TCB is
used in the Gaia data processing (see Section 3.2.1);
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–
Various astronomical and physical constants; this includes the TCB-compatible constants used in INPOP10e (masses of all major bodies of the solar-system, etc.).