Astronomical Images : Problem 3: 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 third problem is to find the parallax of the comet at a non-meridian observation when the other observation is at the meridian. Again the diagram needs to be corrected. The point at which the extension of arc AKLE joins the meridian circle (ABH) should be C not G, which normally designates the comet. OZ: apparent distance of the comet from directly overhead, known through instrumental observation (a) ABCD: meridian circle BED: eastern half of horizon AEC: half of the equator Z: zenith H: north pole of the World G: the true position of the comet before meridian O: the apparent position of the comet before meridian GHZ: time between two observations, known (b) ZH: complement of the latitude of the place of observation, known. (c) BZM: azimuth, known (d) Find GO. With respect to triangle GHZ Angle GZH = BZH (180°) ' angle BZM (d) ZH is known (c) ZHG is known (b) Thus, derive GZ (1) GO = ZO (a) ' GZ (1) At the end of this problem, Regiomontanus also suggests adjusting for the comet's proper motion by taking the proper motion of one day, and adjusting it to the time interval between the two observations (thus assuming a uniform proper motion).</p>