Building a Model Astrolabe Dominic Ford Published in the Journal of the British Astronomical Association, February 2012. Supplementary materials available for download: http://dcford.org.uk/astrolabe/index.html Submitted: October 2010. Accepted: December 2010. Abstract This paper presents a hands-on introduction to the medieval astro- labe, based around a working model which can be constructed from photocopies of the supplied figures. As well as describing how to as- semble the model, I also provide a brief explanation of how each of its various parts might be used. The printed version of this paper in- cludes only the parts needed to build a single model prepared for use at latitudes around 52◦N, but an accompanying electronic file archive includes equivalent images which can be used to build models prepared for use at any other latitude. The vector graphics scripts used to gen- erate the models are also available for download, allowing customised astrolabes to be made. Introduction For nearly two thousand years, from the time of Hipparchus (c. 190–120 BCE) until the turn of the seventeenth century, the astrolabe was the most sophisticated astronomical instrument in widespread use. Yet today this complex instrument is rarely seen, and those interested in learning about it may even have some difficulty finding a specimen to play with. Ornately carved brass reproductions are available from several telescope dealers, but with substantial price tags attached. These price tags are historically au- thentic: medieval astrolabes were often made from high-cost materials and arXiv:1202.2005v1 [astro-ph.IM] 7 Feb 2012 intricately decorated, becoming expensive items of beauty as well as practi- cal observing instruments. But for the amateur astronomer who is looking for a toy with which to muse over past observing practice, a simpler alter- native may be preferable. In 1975–1976, Sigmund Eisner contributed a series of three papers (Eisner, 1975, 1976a,b) to the Journal of the British Astronomical Association enti- tled Building Chaucer’s Astrolabe. In them, he described how a cardboard astrolabe might be built, using as a model the instrument described by the 1 2 English poet Geoffrey Chaucer (c. 1343–1400) in his Treatise on the As- trolabe (Chaucer, 1391). Though the task described is a time-consuming exercise in geometry, it gives a rewarding insight, not only into how as- trolabes were used, but also into their detailed construction and workings. With the advent of computerised vector graphics, it has become possible to automate much of the delicate geometric construction work that Eis- ner describes. This paper describes the result of implementing a slightly modified version of Eisner’s instructions in a computerised vector graphics scripting language called PyXPlot1, the interpreter for which is available for free download under the GNU General Public License (GPL)2. The various parts of the resulting model are shown on subsequent pages; a later section will describe how they should be cut out and assembled. As an alternative to working with photocopies of the printed version of this paper, these fig- ures are also available in computer printable PDF format from the electronic file archive which accompanies this paper; this can be downloaded from the author’s website at http://dcford.org.uk/astrolabe/index.html. As well as the figures printed here, which are prepared specifically for use at latitudes around 52◦N, these archives also contain equivalent figures which may be used to build astrolabes prepared for use at other latitudes. In addition, they include the full PyXPlot scripts used to generate the model, which may be distributed freely under the GPL or modified to produce custom astrolabes. The astrolabe An astrolabe typically takes the form of a disc, often made of wood or brass, around 10–20 centimetres in diameter and a few millimetres thick. An eyelet protrudes from one side of the disc, through which a ring is connected as a handle. The body of this disc is called the mother, and one of its sides is designated as its front and the other as its back. Two freely rotating pointers are mounted on a central pivot, one on each side of the mother. The pointer on the back of the mother, known as the alidade, is used as a line along which to sight celestial or terrestrial objects when making approximate measurements of their altitudes. The front side of the instrument as a whole can be roughly described as a more sophisticated sibling of the modern planisphere, providing a way of predicting the altitudes and azimuths of celestial objects at any given time. Beyond this rather loose description, astrolabes were historically built to many diverse designs. The emergence of the astrolabe as a single instru- ment began with the bringing together of two forerunners in Greece in the second century BC: the dioptra – an instrument for sighting the altitudes 1http://www.pyxplot.org.uk/ (available for Linux/MacOS X only) 2http://www.gnu.org/licenses/gpl-2.0.html iue1 h ako h ohro h astrolabe. the of mother the of back The 1: Figure 3 0 4 0 0 2 5 0 0 1 0 3 1 0 0 6 2 6 0 2 0 0 1 S C O R a P A I 3 R O 7 B 0 I b L 0 0 3 0 1 O B T E C R O 1 R 0 N S E 2 0 O 0 1 0 2 A B 8 V M 0 G 3 3 0 E 1 0 E I M T T 2 B 0 ` P 1 T 2 0 E E 2 A S R O 0 0 R 0 3 2 1 G 0 0 1 I 1 1 2 1 0 R U 0 I 0 0 9 S 3 2 V 0 0 R E B N O O T 1 c C V 0 3 O E 3 3 0 3 2 3 M 0 0 0 B R E D E e k u 3 R L M T 0 B a E l r e S t 1 a i 1 M n h C 0 c U E 0 D i 1 A 2 E C 0 8 T 0 M E n G d d 1 M P 0 g A C r U 0 1 3 e E f E P 2 4 B w y S A 0 M r 0 R E 0 e o 2 B 1 0 2 g R I e C 0 E ORIENS c r S 8 2 T O 12 R D t a G 3 S o e R m 4 1 7 p O U 1 8 i y 2 h N n 0 0 E 0 3 r i c G e UMBRA c 0 U 0 a 3 5 1 L n 4 UMBRA J U F 1 1 S c 1 A M o A 0 r N d d 1 RECTA . 0 U 4 2 3 g 2 A 0 J A a Y 1 6 3 1 2 A g 0 0 8 R L g 0 0 0 0 M 0 n N . g Y U 3 e 6 12 0 y U s J 0 r Y 2 A a 1 L 8 A 2 3 VERSA R M U 0 Q 1 F Y 4 J . 0 1 E U t _ 5 1 OCCIDENS 0 0 B p 0 A 0 0 P g a 3 1 R 2 R R e 7 0 o B U . 0 E I 3 ly U A n 1 c h 3 C S R a o r 0 N 2 2 Y p J E 2 e 0 a e N A 0 C 4 1 U 20 F J J E 1 0 0 0 2 o e E M s a d N 8 ep e 0 8 0 B A h B 0 1 U 1 J R RC 3 U 2 10 H George A 0 0 Y 1 1 R A 3 3 2 M 3 3 0 Y 2 0 AP 0 P 8 RIL 20 I 31 ^ 9 0 S 10 2 0 1 C 1 10 0 I 0 E 0 20 3 N S 0 I 2 0 1 M 2 f 2 0 Y E 0 M 3 0 A G A R 3 1 M 8 0 2 0 C 1 0 2 0 0 H 1 1 0 A P RIL 3 0 AR ] 0 0 IES US 3 7 TAUR 1 0 0 0 2 0 2 0 3 0 1 0 6 1 0 5 0 2 0 3 0 4 0 3 4 of celestial bodies – and planispheric projections which could be used to represent the celestial sphere on a flat surface. Together, they formed a single instrument which could simultaneously measure or predict the posi- tions of celestial objects as required, becoming what might be described as an analogue celestial calculator. This powerful hybrid instrument spread to the Byzantine, Islamic and Persian worlds over subsequent centuries, evolv- ing variously along the way. Some of the products of this evolution – for example, linear and spherical astrolabes – do not even fit within the delib- erately loose description above, though they retain a common raison d’ˆetre. Another product, the mariner’s astrolabe, emerged as a similar but distinct instrument, simplified and optimised for use on the deck of a rolling ship in the determination of latitude at sea.