Astronomical Images : Problem 1: 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 first problem is a preamble in that it defines the basic terms and outlines the basic approach. The circle ABCD is defined as a great circle with respect to which the size of the Earth would be negligible. Its centre is E. HL represents the sphere of the Earth, where H is the observer on the surface of the Earth. The Earth's radius, EH is extended on both sides and intersects with ABCD at point A at the top and at point D at the bottom. Thus A is the point directly overhead (the zenith). The centre of the comet is G (which is not on the line AD), and two lines are extended through it from points E and H, to intersect with the great circle at B and C. B is the true place of the comet. C is its apparent place. If radius EK is drawn parallel to line HC, point K is indiscernibly removed from point C, because the size of the Earth is negligible with respect to ABCD. So C and K may be taken for each other. If the comet appears at point C to the eye at H, K can be known because angle AHC (taken by an instrument) is equal to angle AEK. Since the vertex of AEK is at the centre of the circle ABCD, the ratio of the arc AK to the whole circumference ABCD can be known. Since A is given, K will thus be known. BC is the parallax, but BK can also be called the parallax since it will differ 'insensibly' from BC. Regiomontanus points out that his approximation can be helpful and is indeed used in the tenth problem. The parallax will be minimum when the comet is on the meridian circle and there will be no parallax when the comet is directly overhead.</p>