This dialogue enables you to enter the RA and Dec of any point in the sky for any epoch. The two coordinates can each be entered in either of two ways. The RA can either be given as hours, minutes and seconds or as degrees. The Dec can either be integral degrees, arc minutes and arc seconds or as decimal degrees. The "Convert" button then converts to the other style. If RA hours is blank the conversion will be from degrees to h-m-s. If RA degrees is blank the conversion will be the other way. Similarly for Dec.
If you set the epoch for the coordinates you can then use the "Change epoch" button. That will ask for another epoch (optionally beginning* with B or J: the latter is assumed if neither is given) and then change the coordinates for the Earth's precession. If the proper motion fields are non-zero (ie, for a star) the proper motion will be applied first.
You can simplify the entry of numerical data by instead entering the name of a star or deep-sky object in the top field and then clicking the "Get data" button. This accesses the Simbad service at the Centre de Données Stellaires (CDS), in Strasbourg, to try to recognise the name. If it is recognised, the other fields in the dialogue will be populated automatically. A text area at the bottom of the dialogue gives confirmation of what Simbad sent back (normally an XML VOTable, which may be selected and copied: it contains a large amount of other information). Error messages can also appear in the text area.
NB: Take note of the units for proper motion reported in the text area. Those units are extracted from Simbad's response. In tests the units have always been arcsec/yr but we are not sure whether that will always be the case. Different units would make the epoch change incorrect. Also be careful that some sources quote proper motion in RA in units of seconds (s) per year rather than arcseconds (") per year; there is a factor of 15 difference!
The calculation scheme is the rigorous method given in Chapter 21 (Precession) of Jean Meeus: "Astronomical Algorithms", 2nd edition (corrected August 2009), Willmann-Bell Inc. This is more accurate than the approximate precession formulas given in the BAA Handbook.
Jean Meeus provided the following additional information about the valid range of epochs.
The accumulated precession angles are expressed through canonical polynomials which are valid only for a limited time span. In addition, the IAU 1976 precession rate is known to be imperfect. The absolute accuracy of the present formulation is
Consequently, outside the time span from 1200 BC to AD 3900, the error may be larger than 10 arcseconds, and hence it would be best not to go outside that interval.
The IAU changed the standard for epochs in 1984. Before that Besselian (tropical) years were used, of measured length 365.2421988 days. After 1984 Julian years of exactly 365.25 days are used. Hence the letters B and J. More details are given by Jean Meeus in Chapter 21 of Astronomical Algorithms (2nd edition).