Ulugh Beg, Prince of Stars

Who was Ulugh Beg? A prince who governed a province in the central Asian empire built by his grandfather Tamerlane. Above all, he was a scholar who founded the Samarkand astronomical observatory, whose work predated that of the best astronomers in Europe one and a half centuries later.

The combination of ground-based astrometric compilation catalogues with the HIPPARCOS Catalogue I. Single-star mode

The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, with the results of the ESA Astrometric Satellite HIPPARCOS produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the HIPPARCOS observations alone. In the combination of the basic FK5 with the HIPPARCOS Catalogue (i.e., in the FK6), the gain in accuracy is about a factor of two for the proper motions of single stars. The use of the GC still improves the accuracy of the proper motions by a factor of about 1.2. We derive and describe in detail how to combine a ground-based compilation catalogue with HIPPARCOS. Our analytic approach is helpful for understanding the principles of the combination method. In real applications we use a numerical approach which avoids some (minor) approximations made in the analytic approach. We give a numerical example of our combination method and present an overall error budget for the combination of the ground-based data for the basic FK5 stars and for the GC stars with the HIPPARCOS observations. In the present paper we describe the single-star mode of our combination method. This mode is appropriate for truly single stars or for stars which can be treated like single stars. The specific handling of binaries will be discussed in subsequent papers.

Photometric Cross-Calibration of the SDSS Stripe 82 Standard Stars catalogue with Gaia EDR3, and Comparison with Pan-STARRS1, DES, CFIS and GALEX catalogues

We extend the SDSS Stripe 82 Standard Stars Catalog with post-2007 SDSS imaging data. This improved version lists averaged SDSS ugriz photometry for nearly a million stars brighter than r~22 mag. With 2-3x more measurements per star, random errors are 1.4-1.7x smaller than in the original catalog, and about 3x smaller than for individual SDSS runs. Random errors in the new catalog are ~< 0.01 mag for stars brighter than 20.0, 21.0, 21.0, 20.5, and 19.0 mag in u, g, r, i, and z-bands, respectively. We achieve this error threshold by using the Gaia Early Data Release 3 (EDR3) Gmag photometry to derive gray photometric zeropoint corrections, as functions of R.A. and Declination, for the SDSS catalog, and use the Gaia BP-RP colour to derive corrections in the ugiz bands, relative to the r-band. The quality of the recalibrated photometry, tested against Pan-STARRS1, DES, CFIS and GALEX surveys, indicates spatial variations of photometric zeropoints <=0.01 mag (RMS), with typical values of 3-7 millimag in the R.A., and 1-2 millimag in the Declination directions, except for <~6 millimag scatter in the u-band. We also report a few minor photometric problems with other surveys considered here, including a magnitude-dependent ~0.01 mag bias between 16 < G_Gaia < 20 in the Gaia EDR3. Our new, publicly available catalog offers robust calibration of ugriz photometry below 1% level, and will be helpful during the commissioning of the Vera C. Rubin Observatory Legacy Survey of Space and Time.

The combination of ground-based astrometric compilation catalogues with the HIPPARCOS Catalogue. II. Long-term predictions and short-term predictions

The combination of ground-based astrometric compilation catalogues, such as the FK5 or the GC, with the results of the ESA Astrometric Satellite HIPPARCOS produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the HIPPARCOS observations alone. In Paper I (Wielen et al. 1999, A&A 347, 1046) we have presented a method of combination for single stars (SI mode). The present Paper II derives a combination method which is appropriate for an ensemble of apparently single-stars which contains undetected astrometric binaries. In this case the quasi-instantaneously measured HIPPARCOS proper motions and positions are affected by cosmic errors, caused by the orbital motions of the photo-centers of the undetected binaries with respect to their center-of-mass. In contrast, the ground-based data are mean values obtained from a long period of observation. We derive a linear long-term prediction (LTP mode) for epochs far from the HIPPARCOS epoch T_H ~ 1991.25, and a linear short-term prediction (STP mode) for epochs close to T_H. The most accurate prediction for a position at an arbitrary epoch is provided by a smooth, non-linear transition from the STP solution to the LTP solution. We present an example for the application of our method, and we discuss the error budget of our method for the FK6 (a combination of the FK5 with HIPPARCOS) and for the combination catalog GC+HIP. For the basic fundamental stars, the accuracy of the FK6 proper motions in the LTP mode is better than that of the HIPPARCOS proper motions (taking here the cosmic errors into account) by a factor of more than 4.

The star catalogue of Wilhelm IV, Landgraf von Hessen-Kassel: Accuracy of the catalogue and of the measurements

We analyse a manuscript star catalogue by Wilhem IV, Landgraf von Hessen-Kassel, from 1586. From measurements of altitudes and of angles between stars, given in the catalogue, we find that the measurement accuracy averages 26 arcsec for eight fundamental stars, compared to 49 arcsec of the measurements by Brahe. The computation in converting altitudes to declinations and angles between stars to celestial position is very accurate, with errors negligible with respect to the measurement errors. Due to an offset in the position of the vernal equinox the positional error of the catalogue is slightly worse than that of Brahes catalogue, but when correction is made for the offset -- which was known to 17th century astronomers -- the catalogue is more accurate than that of Brahe by a factor two. We provide machine-readable Tables of the catalogue.