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The fundamental astronomical reference systems for space missions and the expansion of the universe. Michael Soffel & Sergei Klioner TU Dresden. IAU-2000 Resolution B1.3. Definition of BCRS ( t, x ) with t = x 0 = TCB,
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The fundamental astronomical reference systems for space missions and the expansion of the universe Michael Soffel & Sergei Klioner TU Dresden
IAU-2000 Resolution B1.3 Definition of BCRS (t, x) with t = x0 = TCB, spatial coordinates x and metric tensor g • post-Newtonian metric in harmonic coordinates determined by potentials w, w i
Equations of translational motion • The equations of translational motion • (e.g. of a satellite) in the BCRS • The equations coincide with the well-known Einstein-Infeld-Hoffmann (EIH) • equations in the corresponding point-mass limit LeVerrier
The GCRS is adopted by the International Astronomical Union (2000) to model physical processes in the vicinity of the Earth: A: The gravitational field of external bodies is represented only in the form of a relativistic tidal potential. B: The internal gravitational field of the Earth coincides with the gravitational field of a corresponding isolated Earth. Geocentric Celestial Reference System internal + inertial + tidal external potentials
internal + inertial + tidal external potentials The version of the GCRS for a massless observer: A: The gravitational field of external bodies is represented only in the form of a relativistic tidal potential. Local reference system of an observer observer • Modelling of any local phenomena: • observation, • attitude, • local physics (if necessary)
BCRS-metric is asymptotically flat; ignores cosmological effects, fine for the solar-system dynamics and local geometrical optics
One might continue with a hierarchy of systems • GCRS (geocentric celestial reference system) • BCRS (barycentric) • GaCRS (galactic) • LoGrCRS (local group) etc. • each systems contains tidal forces due to • system below; dynamical time scales grow if we go • down the list -> renormalization of constants (sec- aber) • BUT: • expansion of the universe has to be taken into account
Tidal forces from the next 100 stars: their quadrupole moment can be represented by two fictitious bodies: BCRS for a non-isolated system
The cosmological principle (CP): on very large scales the universe is homogeneous and isotropic The Robertson-Walker metric follows from the CP
Consequences of the RW-metric for astrometry: - cosmic redshift - various distances that differ from each other: parallax distance luminosity distance angular diameter distance proper motion distance
Is the CP valid? • Clearly for the dark (vacuum) energy • For ordinary matter: likely on very large scales
-10 solar-system: 2 x 10 Mpc : our galaxy: 0.03 Mpc the local group: 1 - 3 Mpc
The local supercluster: 20 - 30 Mpc
dimensions of great wall: 150 x 70 x 5 Mpc distance 100 Mpc
Anisotropies in the CMBR WMAP-data
-4 / < 10 for R > 1000 (Mpc/h) (O.Lahav, 2000)
The CP for ordinary matter seems to be valid for scales R > R with R 400 h Mpc inhom -1 inhom
The WMAP-data leads to the present (cosmological) standard model: Age(universe) = 13.7 billion years Lum = 0.04 dark = 0.23 = 0.73 (dark vacuum energy) H0 = (71 +/- 4) km/s/Mpc
In a first step we considered only the effect of the vacuum energy (the cosmological constant ) !
(local Schwarzschild-de Sitter)
The -terms lead to a cosmic tidal acceleration in the BCRS proportial to barycentric distance r effects for the solar-system: completely negligible only at cosmic distances, i.e. for objects with non-vanishing cosmic redshift they play a role
Further studies: • transformation of the RW-metric to ‚local • coordinates‘ • construction of a local metric for a barycenter in motion • w.r.t. the cosmic energy distribution • - cosmic effects: orders of magnitude
According to the Equivalence Principle local Minkowski coordinates exist everywhere take x = 0 (geodesic) as origin of a local Minkowskian system without terms from local physics we can transform the RW-metric to:
‘ Construction of a local metric for a barycenter in motion w.r.t. the cosmic energy distribution
Cosmic effects: orders of magnitude • Quasi-Newtonian cosmic tidal acceleration at Pluto‘s orbit • 2 x 10**(-23) m/s**2away from Sun • (Pioneer anomaly: 8.7 x 10**(-10) m/s**2 towards Sun) • perturbations of planetary osculating elements: e.g., • perihelion prec of Pluto‘s orbit: 10**(-5) microas/cen • 4-acceleration of barycenter due to motion of • solar-system in the g-field of -Cen • solar-system in the g-field of the Milky-Way • Milky-Way in the g-field of the Virgo cluster • < 10**(-19) m/s**2
The problem of ‚ordinary cosmic matter‘ The local expansion hypothesis: the cosmic expansion occurs on all length scales, i.e., also locally If true: how does the expansion influence local physics ? question has a very long history (McVittie 1933; Järnefelt 1940, 1942; Dicke et al., 1964; Gautreau 1984; Cooperstock et al., 1998)
The local expansion hypothesis: the cosmic expansion induced by ordinary (visible and dark) matter occurs on all length scales, i.e., also locally Is that true? Obviously this is true for the -part
Validity of the local expansion hypothesis: unclear The Einstein-Straus solution ( = 0) LEH might be wrong
Conclusions If one is interested in cosmology, position vectors or radial coordinates of remote objects (e.g., quasars) the present BCRS is not sufficient the expansion of the universe has to be considered modification of the BCRS and matching to the cosmic R-W metric becomes necessary