Astronomical Images : Problem 15: 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. Problem fifteen is to inquire learnedly the length of the comet's tail. Regiomontanus assumes (with Aristotle) that the comet's tail has the same substance as the body, but because it is more rarefied, light shines through it and because it is lighter, the tail extends above. ABCD: a great circle in relation to which the size of the Earth HL is negligible E: centre of the Earth G: comet H: centre of vision of the observer B: true position of the comet C: apparent position of the comet EK is drawn parallel to HC BC: parallax of the comet BK differs insensibly from BC [see problem 1] Thus angles BEK and EGH are known N is the end of the tail, placed somewhere on GB [though on the woodcut, N appears as if on line HB] A line is drawn from H to N [though in the woodcut, it looks as if N coincides with B and that the line from H ends at B] Angle GHN: measured with an instrument [see problem 12] In triangle GHN: Angle GHN is known by measurement Angle NGH may be derived from angle EGH HG can be derived in relation to EH, the Earth's radius, according to problem 10 Thus GN may be derived relative to the Earth's radius.</p>