Astronomical Images : Measuring the apparent diameters of the Sun and the Moon using eclipses

Daniel Santbech

Astronomical Images

<p style='text-align: justify;'>Daniel Santbech's <i>Problemata</i> is a miscellaneous work in mixed mathematics, including astronomy, gnomonics, perspective, surveying, gunnery and navigation. The unifying element in such a wide range of disciplines is the instrument called the geometric quadrant. According to Lynn Thorndike, Santbech showed appreciation both for specific aspects of Copernicus's work, such as lunar theory, and for the <i>Prutenic Tables</i>, but he ignored cosmological issues. Copernicus is mentioned many times. Virtually nothing is known about Santbech, apart from the fact that he published, in addition to this work, an edition of Regiomontanus's <i>De triangulis</i> (Basel, 1561). The title-page calls Santbech '<i>Noviomagus</i>', and this is generally interpreted as meaning 'of Nijmegen', but Andreas Kleinert reports that Santbech could be from Speyer of Neumagen, a small town near Trier. The volume included a dedicatory letter by Santbech to '<i>Domino Joanni Ludovico a Windeck</i>', dated 1561. The existence of a 1542 Basel edition is disputed by Ernst Zinner. The figures in this edition seem to have been copied from Oronce Fine's <i>Protomathesis</i>. This woodcut of the lunar eclipse shows the body of the Sun in two positions, A (to the left) and Ï? (in the middle); IKL is the Earth, and the Moon is shown at two positions m and n, on a circumference touching the black area, which indicates the shadow cast by the Earth. When the Sun is farther away from the Earth (at position A), it casts a larger shadow cone, IRQX, than when it is closer to Earth (at position Ï?), casting a shadow cone IPOX. The duration of the lunar eclipse will thus be longer in the first case than in the latter case. Santbech's point here is to illustrate the fact that the Sun's distance (as well as the Moon's distance) to the Earth affects the duration of the lunar eclipse. These are important parameters to take into account, since from the time of Aristarchus eclipses had been used to measure the relative diameters of the Sun and the Moon, which in turn could be used to calculate their relative distances.</p>