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Astronomical Images : Problem 8: 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. The eighth problem is to investigate the comet's parallax in the altitude circle in another way. Here in the woodcut, one reader has correctly annotated the diagram as follows: G: <i>verus locus</i>, O: <i>visus locus</i>, K: <i>polus eclipticae</i>, H: <i>polus mundi</i>, AEC: <i>ecliptica</i>, BED: <i>horizon</i>. ABCD: meridian circle BED: eastern half of the horizon AEC: half of the ecliptic G: true place of the comet O: apparent place of the comet Z: zenith H: north pole of the World with the Arctic circle around it K: north pole of the ecliptic HK and angle ZHK are known because the position of K is known with respect to the meridian [see problem 7] KL, KM: great circle quadrants cutting through G and O L: true place of the comet in the ecliptic LM: comet's parallax in longitude (known from problem 5) From LM, angle GKO [incorrectly printed as 'GOK' in text] is known from problem 5 (a) HO: construction line The aim is to obtain GO, the comet's parallax in the altitude circle. In triangle OHZ: Arc ZO is known from observation Angle OHZ is known by an instrument ZH is known because it is the complement of the pole's altitude Thus, (i) arc HO, (ii) angle ZOH, (iii) angle ZHO will be known. In triangle OHK: HO is known from (i) HK is known from problem 7 Angle OHK = angle ZHK (known from problem 7) + angle ZHO (iii) Thus, (iv) angle HOK and (v) arc OK, which is the complement of the apparent latitude, become known. In triangle GOK: Angle GOK = angle ZOH (ii) ' angle HOK (iv) Angle GKO is known from (a) OK is known from (v) Thus arc GO is known, which is what was sought. Furthermore arc GK is known, and thus also GL, which is the comet's true latitude from the ecliptic. If arc GK is a quadrant, the comet's true place is in the ecliptic without latitude.</p>


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