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Register a new userThe star catalogue of Wilhelm IV, Landgraf von Hessen-Kassel
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Near the end of the 16th century Wilhelm IV, Landgraf von Hessen-Kassel, set up an observatory with the main goal to increase the accuracy of stellar positions primarily for use in astrology and for calendar purposes. A new star catalogue was compiled from measurements of altitudes and angles between stars and a print ready version was prepared listing measurements as well as equatorial and ecliptic coordinates of stellar positions. Unfortunately, this catalogue appeared in print not before 1666, long after the dissemination of Brahes catalogue. With the data given in the manuscript we are able to analyze the accuracy of measurements and computations. The measurements and the computations are very accurate, thanks to the instrument maker and mathematician Jost Burgi. The star catalogue is more accurate by a factor two than the later catalogue of Tycho Brahe.
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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.
Historical star magnitudes from catalogues by Ptolemy (137 AD), as-Sufi (964) and Tycho Brahe (1602/27) are converted to the Johnson V-mag scale and compared to modern day values from the HIPPARCOS catalogue. The deviations (or errors) are tested for dependencies on three different observational influences. The relation between historical and modern magnitudes is found to be linear in all three catalogues as it had previously been shown for the Almagest data by Hearnshaw (1999). A slight dependency on the colour index (B-V) is shown throughout the data sets and as-Sufis as well as Brahes data also give fainter values for stars of lower culmination height (indicating extinction). In all three catalogues, a stars estimated magnitude is influenced by the brightness of its immediate surroundings. After correction for the three effects, the remaining variance within the magnitude errors can be considered as approximate accuracy of the pre-telescopic magnitude estimates. The final converted and corrected magnitudes are available via the Vizier catalogue access tool (Ochsenbein, Bauer, & Marcout, 2000).
The exploration of interstellar space will require autonomous navigation systems that do not rely on tracking from the Earth. Here I develop a method to determine the 3D position and 3D velocity of a spacecraft in deep space using a star catalogue. As a spacecraft moves away from the Sun, the observed positions and velocities of the stars will change relative to those in a Earth-based catalogue due to parallax and aberration. By measuring just the angular distances between pairs of stars, and comparing these to the catalogue, we can infer the coordinates of the spacecraft via an iterative forward-modelling process. I perform simulations with existing star catalogues to demonstrate the method and to compute its performance. Using the 20 nearest stars and a modest angular distance measurement accuracy of 1, the position and velocity of a spacecraft light years from the Sun moving at relativistic speeds can be determined to within 3 au and 2 km/s respectively. These accuracies improve linearly with the measurement accuracy, e.g. with angles measured to 1 mas the navigation accuracy is 1000 times better. Performance can also be improved using more stars, or by including onboard measurements of the stars radial velocities, as these too are affected by the spacecrafts position and motion.
Before atomic timekeeping, clocks were set to the skies. But starting in 1972, radio signals began broadcasting atomic seconds and leap seconds have occasionally been added to that stream of atomic seconds to keep the signals synchronized with the actual rotation of Earth. Such adjustments were considered necessary because Earths rotation is less regular than atomic timekeeping. In January 2012, a United Nations-affiliated organization could permanently break this link by redefining Coordinated Universal Time. To understand the importance of this potential change, its important to understand the history of human timekeeping.
We present a catalogue of ALMA flux density measurements of 754 calibrators observed between August 2012 and September 2017, for a total of 16,263 observations in different bands and epochs. The flux densities were measured reprocessing the ALMA images generated in the framework of the ALMACAL project, with a new code developed by the Italian node of the European ALMA Regional Centre. A search in the online databases yielded redshift measurements for 589 sources ($sim$78 per cent of the total). Almost all sources are flat-spectrum, based on their low-frequency spectral index, and have properties consistent with being blazars of different types. To illustrate the properties of the sample we show the redshift and flux density distributions as well as the distributions of the number of observations of individual sources and of time spans in the source frame for sources observed in bands 3 (84$-$116 GHz) and 6 (211$-$275 GHz). As examples of the scientific investigations allowed by the catalogue we briefly discuss the variability properties of our sources in ALMA bands 3 and 6 and the frequency spectra between the effective frequencies of these bands. We find that the median variability index steadily increases with the source-frame time lag increasing from 100 to 800 days, and that the frequency spectra of BL Lacs are significantly flatter than those of flat-spectrum radio quasars. We also show the global spectral energy distributions of our sources over 17 orders of magnitude in frequency.
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