Astronomical Images : Problem 9: Measuring a comet's parallax

Johannes Regiomontanus

Astronomical Images

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 Sixteen Problems on the Magnitude, Longitude and True Position of Comets. It was printed again, with several other works of Regiomontanus in 1544. Regiomontanus's ninth problem is to determine the apparent position of the comet 'simply'; that is, from the distance between the comet and two known fixed stars. A: one of the fixed stars B: the other fixed star C: the comet DG: portion of the ecliptic H: pole of the ecliptic HD, HE and HG are great circle quadrants drawn from the pole to the ecliptic through points A, B and C respectively D and E are known (azimuths of fixed stars A and B) (a) AD and BE are known (altitudes of fixed stars A and B) (b) AB, AC, BC: great circle arcs The task is to derive G, the comet's apparent place, and GC, the comet's apparent latitude. In triangle AHB: DE is known (from a), as is angle DHE or angle AHB (1), which is defined by DE AH and BH are known because they are complements of AD and BE, which are known (from b) Thus, derive arc AB (which is the distance between the two fixed stars) (2) and angle BAH (3) In triangle ABC: AC and BC are determined by observation AB is derived (from 2) Thus, derive angle BAC (4) In triangle HAC: AH and is known (complement of AD) AC is determined by observation Angle HAC = angle BAH (from 3) ' angle BAC (from 4) Thus derive AHC, which determines DG, and given that D is known, G, the comet's apparent position, is known. Also derive arc HC, whose complement is GC, the comet's latitude. Regiomontanus seems pleased with this procedure and recommends his book, De triangulis omnimodis.