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**Session 87 - Star Parameters.**

*Oral session, Thursday, June 13*

*Old Madison, *

## [87.03] Determination of Binary Parameters from the Precision Doppler Measurements by Using the Relativistic Doppler Effect

*S. M. Kopeikin (NAO of Japan and ASC/FIAN, Moscow, Russia), L. M. Ozernoy (CSI/GMU and GSFC/NASA)*
The determination of transverse velocities from precision Doppler
measurements implementing the relativistic Doppler effect (Ozernoy 1995, 1996)
is elaborated in detail using relativistic theory of astronomical reference
frames (Kopeikin
1988, Brumberg amp; Kopeikin 1989) so as to determine the parameters of binary
systems. Six reference frames are introduced: (i) proper frame of the emitting
star, (ii) barycentric frame of the binary, (iii) barycentric frame of the
Galaxy, (iv) barycentric frame of the Solar system, (v) geocentric
frame, and (vi) proper coordinate system of observer at the Earth. We apply
successive Lorentz transformations and the relativistic equation of light
propagation to establish the exact treatment of Doppler effect both
in special and general relativity theories. As a result, the Doppler
shift is presented as a sum of linear in c^-1 terms, which include the
ordinary
Doppler effect and its variation due to the radial acceleration of the
emitting star, and (2) terms proportional to c^-2, which include the
contributions from the quadratic Doppler effect, orbital motion of the
star around the binary's barycenter, orbital motion of the Earth
and the related modulation of the source's velocity, and finally
redshifts due to gravitational fields of the binary, Galaxy, and the Solar
system. After parameterization of the binary's orbit we are able to
identify new observational effects along with those binary parameters which
can be extracted by using the precision Doppler measurements.

References:

Brumberg, V.A. amp; Kopeikin, S.M. 1989, Nuovo Cim. B103, 63

Kopeikin, S.M. 1988, Cel. Mech., 44, 87

Ozernoy, L.M. 1995, BAAS 27, 1449

Ozernoy, L.M. 1996, Mon. Not. R.A.S. (in press)

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