Gaia Data Release 1 Documentation release 0
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in the post-Newtonian approximation. The e ffective computation of the rather complicated quadrupole deflection of light represents a separate problem (Zschocke & 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 µas for the realistic observational configuration in Gaia. Besides that, a very e fficient 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 & Peip 2003, and references therein). No attempt is made to account for e ffects 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 u 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 v is the BCRS velocity of Gaia v 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); – Gaia time ephemeris (the relation between the readings of the Gaia on-board clock and TCB; Sec- tion 3.1.6); – Solar-system ephemeris; the INPOP10e ephemeris (Fienga et al. 2016) parametrized by TCB is used in the Gaia data processing (see Section 3.2.1.1); – Various astronomical and physical constants; this includes the constants used in INPOP10e (masses of all major bodies of the solar-system, etc.). 3.1.6 Time scales Author(s): Sergei Klioner As explained in Section 3.1.3, Gaia data processing uses the rigorous relativistic definitions of reference systems including time scales as their integral parts. The coordinate time of BCRS — TCB (So ffel et al. 2003) — is used throughout data processing and parametrizes the final Gaia catalogue. Another important technical time coordinate used in Gaia data processing is the On-Board Mission Timeline (OBMT). OBMT represents the readings of the on-board Gaia atomic clock plus a constant chosen for each con- tinuous time interval between Gaia clock resets in such a way that OBMT remains increasing with physical time. Strictly speaking, OBMT is not a time scale since it is not necessarily continuous. OBMT is a purely technical time coordinate that is however unique for any event on board of Gaia. Although the raw observations of Gaia are parametrized by OBMT, for various purposes (e.g. interrogating the solar-system and Gaia ephemerides), OBMT should be related to TCB. This is done by creating the Gaia time ephemeris — a model of Gaia’s clock fitted to 157 the special time synchronization data — the one-way time transfer from Gaia to the ESA ground stations (Klioner 2015). 3.1.7 Transformations of astrometric data and error propagation Author(s): Lennart Lindegren Only the transformation to galactic coordinates is covered here. Epoch transformation is covered by Section 4.3.2. 3.1.7.1 Galactic coordinates The positions and proper motions of non-solar system objects derived from Gaia observations are expressed in the International Celestial Reference System (ICRS). This is an inertial (non-rotating) reference system, which since 1998 replaces the various earlier celestial reference frames (referred to by names such as FK5, FK4, J2000, B1950, equinox and equator of 1950.0, etc.). For galactic research it is often desirable to use galactic coordinates instead of ICRS. Unfortunately there is no accurate transformation from ICRS to galactic coordinate sanctioned by the IAU. (The existing IAU resolution from 1958 defines the galactic axes with reference to the equatorial B1950 system, which cannot be accurately transformed to the ICRS; see Murray 1989.) We therefore adopt the same definition as was used in the Hipparcos Catalogue (Vol. 1, Sect. 1.5.3 of ESA 1997). According to this, the ICRS coordinates of the north galactic pole are (α G , δ G ) = (192.85948 ◦ , +27.12825 ◦ ) and the galactic longitude of the first intersection of the galactic plane with the equator is l Ω = 32.93192 ◦ . 3.1.7.1.1 Transformation of position Transformation of astronomical spherical coordinates (α, δ in ICRS; l and b in the galactic system) and of the corresponding proper motions (µ α∗ , µ δ and µ l∗ , µ b , respectively) is best done by using vectors and matrix algebra (see Ch. 4 in van Altena 2012). A given point on the celestial sphere is then represented by a unit vector, whose components in the two systems are r ICRS = X ICRS Y ICRS Z ICRS = cos α cos δ sin α cos δ sin δ (3.7) and r Gal = X Gal Y Gal Z Gal = cos l cos b sin l cos b sin b . (3.8) In terms of these column matrices the transformation from ICRS to the galactic system is obtained through the matrix multiplication r Gal = A G r ICRS , (3.9) where A G = R z (−l Ω )R x (90 ◦ − δ G )R z (α G + 90 ◦ ) (3.10) = −0.0548755604162154 −0.8734370902348850 −0.4838350155487132 +0.4941094278755837 −0.4448296299600112 +0.7469822444972189 −0.8676661490190047 −0.1980763734312015 +0.4559837761750669 (3.11) 158 Yüklə 5,01 Kb. Dostları ilə paylaş:
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