A global analysis method for astrolabe observations

Abstract

In a previous paper (Chollet & Najid 1992), we gave the general principles of a new global method to analyze the astrolabe observations. The fundamental equation was obtained from the classical one in which the corrections to the star positions at the observational epoch are replaced by developments that contain the corrections to the star positions for the epoch of the catalogue, the proper motions, as well as the corrections to the precession and nutation constants. This computation gives us a new equation in which the coefficients contain only two variable parameters the azimuth and the sidereal time. The method proposed here consists in regarding the whole programme of star observations as only one group. All the possible values of the azimuth and also of the sidereal time are obtained and, in this case the column vectors of the coefficients are quite orthogonal, and the matirx of the normal equations is practically diagonal. The only problem which remains, is due to the variations of the apparent position of the station. These effects are removed by using the parameters of the Earth rotation given by the Bureau International de l'Huere (BIH) and connected to the International Earth Rotation Service (IERS) system by the Central Bureau of the IERS. Now, the new corrected unknowns are related to the mean position of the astrolabe, in the IERS system. The method to obtain absolute declinations follows the form of the preceding relations. The same error multiplied by different but known constants, affects the declination of each star, but also the latitude and zenith distance determinations. From this results, it is possible to find the well known result (Krejnin 1968) concerning the determinations of absolute declinations. But the comparison between the direct measurement and the result obtained from stellar observations will also give the systematic error in declination and latitude. The last important result is that the corrections to the precession and nutation constants appear in the equations without any perturbation due to the catalogue errors. This fact was seen in the past (Guinot 1970) but not used. The method given here does not use sophisticated methods to analyse the observational data obtained by astrolabes. Our purpose was preferably to combine and to correct the data. This method was elaborated to analyze the observations of the future automatic astrolabes. It has been tested on the series of observations obtained at Paris Observatory. <Although the observations are visual ones, the results are satisfying. &The coordinates of stars of the FK 4 catalogue are obtained with errors near 0.01 arcsec, as well as the proper motions for which the errors are about 0.005 arcsec/year. The observational data will be re-reduced in the FK 5 system in a near future before doing the same analysis using the future Hipparcos catalogue.