THE SOLUTION OF EARTH ORIENTATION PARAMETERS BY OPTICAL ASTROMETRY, 
1899.7-1992.0, solution OA00. 
 
Jan Vondrak, Astronomical Institute 
Bocni II, 141 31 Praha 4, Czech Republic 
e-mail: vondrak@ig.cas.cz 
 
This is an updated version of our previous solution of 1997, with 
slightly more observed data used and a different approach to 
observatories where more instruments were active. 
 
The observations of latitude and universal time variations made at 33 
observatories all over the world with 47 instruments of different types 
are used to derive Earth Orientation Parameters (EOP) in the interval 
1899.7-1992.0.  To this end, all available results (latitude, universal 
time, star altitude) based on individual star or star pair observations 
(that were originally referred to local star catalogs) are re-reduced to 
the HIPPARCOS Catalogue and the present IAU standards. In cases when two 
or more instruments of the same type were active at an observatory 
(Mizusawa, Poltava, Pulkovo, Richmond, Shanghai and Washington), the 
observations were merged into a single series with the estimated steps 
removed. 
 
The apparent places of the observed stars are calculated using relevant 
parts of the IERS Conventions (1996).  About four thousand different 
Hipparcos stars were observed throughout the interval in question. 
Special care is devoted to double and/or multiple stars whose proper 
motions (and sometimes also positions) are corrected in order to be 
consistent with the other observations.  These corrections are derived 
from the trends in the residuals of the respective star observations. 
They are applied only when sufficiently long series of ground-based 
observations are available and the corrections themselves are 
statistically significant; about twenty per cent of the observed 
Hipparcos stars are corrected.  Additional corrections are also applied 
before the solution is made, such as the secular motions of the 
instruments (due to plate tectonics, using the geophysical model NNR 
NUVEL1), certain instrumental constants (plate scale, micrometer value), 
deformations of the apparent almucantar (due to anomalous refraction), 
oceanic tide-loading effects in the direction of the local verticals of 
the observatories.  Short-periodic zonal tide variations in the speed of 
rotation of the Earth (due to deformations of the solid Earth) are 
removed from the observed values of universal time but they are added 
back to the values of UT1-TAI estimated from the solution. 
 
From more than four million observations, almost thirty thousand unknown 
parameters are estimated in a single least-squares solution with 
constraints.  Such a large system of linear equations is solved using a 
modified Cholesky decomposition of the sparse matrix of normal 
equations, taking into account their specific form.  The estimated 
parameters comprise polar motion (i.e. motion of the spin axis in 
terrestrial reference frame) and celestial pole offsets (motion of the 
same axis in celestial reference frame), at five-day intervals in the 
whole time span.  After 1956, when the International Atomic Time scale 
(TAI) became available, the differences between universal time UT1 and 
TAI are also determined, again at five-day intervals . In addition to 
these, combinations of Love numbers Lambda = 1 + k - l (governing the 
solid Earth tidal variations of the local verticals) are estimated, 
together with the small corrections of station coordinates and the 
seasonal effects in latitude/longitude (i.e. a constant, secular trend, 
semi-annual and annual terms) at each observatory.  The latter are 
mutually tied by 18 constraints (these are meant to fix the terrestrial 
reference frame to the one defined by initially chosen station 
coordinates and to reduce the systematic deviations of individual 
instruments due to seasonal effects of refraction). 
 
 
References: 
 
Vondrak J.:  1991, Calculation of the new series of the Earth 
orientation parameters in the Hipparcos reference frame, Bull. Astron. 
Inst. Czechosl. 29, 97-103. 
 
Vondrak J., Ron C., Pesek I., Cepek A.:  1995, New global solution of 
Earth orientation parameters from optical astrometry in 1900-1990, 
Astron. Astrophys. 297, 899-906. 
 
Vondrak J., Ron C., Pesek I., Cepek A.:  1997, Hipparcos Catalogue:  A 
reference frame for Earth orientation in 1899.7-1992.0, Proc. Hipparcos 
Venice '97, ESA SP-402, 95-100. 
 
Vondrak J., Pesek I., Ron C., Cepek A.:  1998, Earth orientation 
parameters 1899.7-1992.0 in the ICRS based on the Hipparcos reference 
frame, Publ. Astron. Inst. Acad. Sci. Czech R. No. 87, 1-56. 
 
Vondrak J., Ron C.: 2000, Survey of observational techniques and 
Hipparcos reanalysis, In: Dick S., McCarthy D., Luzum B.: Polar motion: 
Historical and scientific problems, Astron. Soc. Pacific Conf. Ser. 208, 
239-250.