Kein Folientitel

1
The fundamental astronomical reference systems
for space missions and the expansion of the
universe
Michael Soffel Sergei Klioner TU
Dresden
2
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

3
IAU -2000 Resolutions BCRS (t, x) with metric
tensor
4
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
5
Geocentric Celestial Reference System
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.
internal inertial tidal external potentials
6
Local reference system of an observer
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.
observer

• Modelling of any local phenomena
• 
  observation,
• 
  attitude,
• 
  local physics (if necessary)

7
BCRS-metric is asymptotically flat ignores
cosmological effects, fine for the solar-system
dynamics and local geometrical optics
8

• 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 -gt renormalization of constants
  (sec- aber)
• BUT
• expansion of the universe has to be taken into
  account

9
BCRS for a non-isolated system
Tidal forces from the next 100 stars their
quadrupole moment can be represented by two
fictitious bodies
Body 1 Body 2
Mass 1.67 Msun 0.19 MSun
Distance 1 pc 1 pc
? 221.56 285.11
? -60.92 13.91
10
The cosmological principle (CP) on very large
scales the universe is homogeneous and
isotropic The Robertson-Walker metric follows
from the CP
11
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
12
Is the CP valid?

• Clearly for the dark (vacuum) energy
• For ordinary matter likely on very large scales

13
-10
solar-system 2 x 10 Mpc
our galaxy 0.03 Mpc
the local group 1 - 3 Mpc
14
The local supercluster 20 - 30 Mpc
15
dimensions of great wall 150 x 70 x 5
Mpc distance 100 Mpc
16
Anisotropies in the CMBR WMAP-data
17
-4
??/? lt 10 for R gt 1000 (Mpc/h)
(O.Lahav, 2000)
18
The CP for ordinary matter seems to be valid for
scales R gt R with R ? 400 h Mpc
inhom
-1
inhom
19
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
20
(No Transcript)
21
In a first step we considered only the effect of
the vacuum energy (the cosmological constant ?)
!
22

23

(local Schwarzschild-de Sitter)
24
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
25

• 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

26
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
27

• Transformation of the RW-metric to local
  coordinates

28
Construction of a local metric for a barycenter
in motion w.r.t. the cosmic energy distribution

29
Cosmic effects orders of magnitude

• Quasi-Newtonian cosmic tidal acceleration at
  Plutos orbit
• 2 x 10(-23) m/s2
  away from Sun
• (Pioneer anomaly 8.7 x 10(-10) m/s2 towards
  Sun)
• perturbations of planetary osculating elements
  e.g.,
• perihelion prec of Plutos 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
• lt 10(-19) m/s2

30
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)
31
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
32
Validity of the local expansion hypothesis
unclear
The Einstein-Straus solution (? 0) LEH might
be wrong
33
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
34
THE END