Astronomical Images : Problem 13: 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 task of problem thirteen is to compare the diameter of the body of the comet to the Earth's radius, using the apparent diameter measured in problem twelve and the comet's distance from the Earth in relation to the Earth's diameter, established in problem ten. CD: the comet as a sphere with B as its centre A: the centre of vision AC and AD: tangents drawn from points C and D respectively to the centre of vision, A. Angle CAD: the angle under which the comet itself is seen The arc (CD) that subtends angle CAD is the apparent diameter of the comet, which is known from problem 12; thus angle CAD can be derived, as can its half, BAC. For triangle ABC: BC is perpendicular to AC, thus the proportion of AB to BC can be known [in modern parlance: sin CAB = BC / AB] From problem 10, AB is known with respect to the Earth's radius Thus the proportion of the comet's radius to the Earth's radius is established.</p>