Cosmic influences upon the basic reference system for GAIA

Michael Soffel & Sergei Klioner

TU Dresden

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

IAU-2000 Resolution B1.3

...cw2

1g

...wc4

g

...cw2

cw2

1g

2ijij

i3i0

4

2

200

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

The cosmological principle (CP):

on very large scales the universe is homogeneousand isotropic

The Robertson-Walker metric follows from the CP

Consequences of the RW-metricfor 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

Anisotropies in the CMBR

WMAP-data

/ < 10

for

R > 1000 (Mpc/h)

-4

(O.Lahav, 2000)

The WMAP-data leads to the present(cosmological) standard model:

Age(universe) = 13.7 billion years

Lum = 0.04dark = 0.23 = 0.73 (dark vacuum energy)

H0 = (71 +/- 4) km/s/Mpc

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 tosystem below; dynamical time scales grow if we godown the list -> renormalization of constants (sec- aber)

BUT: expansion of the universe has to be taken into account

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°

40 AUaX 17 24 10 /aX m s

In a first step we considered only the effect of thevacuum energy (the cosmological constant )

...c

'w21g

...wc4

g

...cw2

cw2

1g

2ijij

i3i0

4

2

200

!

Various 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

- transformation of the Schwarzschild de Sitter metric to LOCAL isotropic coordinates - cosmic effects: orders of magnitude

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

(localSchwarzschild-de Sitter)

Cosmic effects: orders of magnitude

• Quasi-Newtonian cosmic tidal acceleration at Pluto‘s orbit 2 x 10**(-23) m/s**2 away 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

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

THE END