Astronomical Images : Problem 7: Measuring a comet's parallax

Johannes Regiomontanus

Astronomical Images

<p style='text-align: justify;'>Johannes Regiomontanus died in 1475, leaving behind a printing press, instruments and a library containing printed books and manuscripts. Most of the library was bought by Bernhard Walther (1430-1504), the merchant-astronomer at Nuremberg and then ended up in the possession of Willibald Pirckheimer (1470-1530), the patrician friend of Albrecht Duerer. Pirckheimer sold on several of Regiomontanus's works to Johannes Schoener (1477-1547), who taught mathematics at the gymnasium in Nuremberg. Regiomontanus's work on comets, which was listed in his own printing advertisement, was first edited and published by Schoener in 1531 as <i>Sixteen Problems on the Magnitude, Longitude and True Position of Comets</i>. It was printed again, with several other works of Regiomontanus in 1544. Regiomontanus's seventh problem is to derive the comet's apparent latitude and declination from the altitude, azimuth and time of observation. ABHZ: meridian circle ALB: eastern half of horizon O: apparent position of the comet Z: zenith H: north pole of the World Circle centred on H: Arctic circle K: pole of the ecliptic Arc ZO (known: complement of altitude observed) (a) Angle OZH (known from azimuth observed) (b) Angle OHZ (known from time of observation) (c) ZH: complement of terrestrial latitude of point of observation The task is to find: OH: complement of the comet's apparent declination OK: complement of the comet's apparent latitude For triangle OZH: ZO (a), angle OZH (b), angle OHZ (c) are known Thus, derive OH, which is the complement of the comet's apparent declination (d) For triangle OHK: HK is the maximum declination of the Sun Angle ZHK: determined by right ascension (e) Angle OHK = angle ZHK (e) + angle ZHO (c) Arc OH (d) Thus, derive: OK: complement of the comet's apparent latitude Angle HKO: distance of the comet's apparent place in the ecliptic from the beginning of Cancer OH: complement of the comet's apparent declination Angle ZHO: known by observation Regiomontanus notes that though pole K of the ecliptic may be located in different places on the Arctic circle, it will still be possible to derive angle OHK, however, sometimes it will be necessary to subtract angle ZHK from angle OHZ.</p>