Constellation simulation
The map of the selected constellation is generated from data stored in astronomical catalogue HIPPARCOS, astronomical database SIMBAD or astronomical catalogues CNS5 and Gaia EDR3.
To display it, a conversion of celestial coordinates (α – Right Ascension, δ – Declination) to a Cartesian coordinate system (X, Y) on the tangent plane of the sky, known as the gnomonic projection, is used.
For the constellation boundaries, the catalog VI/49 from the SIMBAD database, referred to the J2000.0 epoch, was used. The lines between bright stars within the constellation correspond to the 'Western sky culture' version used in Stellarium, which is the official scheme of the International Astronomical Union (IAU) used by astronomers worldwide. The colours used to shade the star discs correspond to the color scheme outlined in the Digital color codes of stars by Harre and Heller (2021), mostly employing color codes that correspond to the center of the range of their spectral class.
Only stars with designations (star name, Greek letter or number, and constellation abbreviation), accounting for approximately 8.5% of the HIPPARCOS catalogue, and having an observed apparent magnitude in the visible part of the electromagnetic spectrum (according to the Vmag column in the HIPPARCOS catalogue) less than 6 mag are displayed. The Right Ascension and Declination of stars are in the ICRS system (International Celestial Reference System) adopted by the IAU. For the HIPPARCOS catalogue, it is for the J1991.25 epoch (subsequently recalculated to the J2000.0 epoch for display purposes), while for the SIMBAD database, it directly uses the J2000.0 epoch. For the CNS5 and Gaia EDR3 catalogues, it corresponds to the epoch range from 2015.0 to 2017.2 (recalculated to the J2000.0 epoch for display purposes).
The size of the star disc corresponds to its observed apparent magnitude in the visible part of the electromagnetic spectrum (column Vmag in the HIPPARCOS catalog, column MagV in the SIMBAD database). The time shift takes into account the star's proper motion in Right Ascension (pmRA column) and Declination (pmDE column), calculating the new position of the star, and the star disc is displayed in green. Radial velocity of the star is not considered, as it only has a negligible impact on observed apparent magnitude (an average change of 0.1 mag). Gravitational interactions with other objects in the Galaxy are also not taken into account, as it involves an N-body problem that is not easily analytically solvable. Additionally, the change in the coordinate system due to precession is not considered; everything is displayed for the J2000.0 equinox. In the case of a nonzero time shift, it is possible to choose to display lines (also in green) between shifted bright stars or to display the proper motions of all stars, not just those connected.
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