THE PLANISPHERIC ASTROLABE ------------------------ John Pazmino NYSkies Astronomy Inc www.nyskies.org email@example.com 2009 May 30 initial 2013 July 4 current
Introduction ---------- I went on 2009 May 22 to the Metropolitan Museum of Art for the talk 'Astrolabes' by Dr Bruce Chandler of College of Staten Island. The event was a memorial to Dr David Pingree, the historian of science who worked with Chandler and who died a few years ago. Dr Chandler described the use and function of the instrument, its origins and history, and where to see good specimina. I do not offer here a thoro summary of his talk, but point out a few items about astrolabes that sometimes get lost in the usual treatment for home astronomers. The Museum has a small set of astrolabes, three being laid out for display and inspection for this talk. The largest collection in the US is at the Adler Planetarium, Chicago IL. Many Europe musea have sizable collections, as well.
Home astronomy ------------ At some point in his development, every home astronomer comes across the astrolabe and wants, oh, like, really WANTS one. Good competent information about astrolabes was tough to come by in the early decades of the 20th century. Most details came from entries in encyclopediae or rare magazine articles. In fact the most common book reprinted time and time again was by, erm, Chaucer. Yes, THAT Chaucer who wrote the Canterbury Tales and other early British poetry. No, I'm NOT making this up!! As ridiculous as this sounds, Chaucer's book, really a long letter to his sun, explains in good detail how to use an astrolabe which he sent to his son as a growing-up gift. The letter is broken off, as if not completed. Maybe the last part was torn off and lost to us. It's in mediaeval English, so be open-minded about the grammar, spelling, and vocabulary. Other works tended to be articles in journals describing a particular instrument from a museum collection. They were hardly ever noticed to the home astronomer except by chance reference by a colleague. Then you had to ask for the article at the central branch of your town's library or a large college. Sadly, many explanations in mainstream astronomy litterature were inept, plain wrong, or mythical. Taking such writings naively, the astrolabe was at times some magical device to predict all kinds of astronomy activity: sunspot cycles, meteor showers, planet alignments, future comets. It didn't and it absolutely could not. Once you learned that the astrolabe was built on the stereographic mapping scheme, you could glean details from geometry books. Many had a section on astrolabes as a use of the stereographic projection. The motivation to have an astrolabe was mainly to solve skywatching problems that were otherwise hideously tedious to work out. When does Antares clear my trees at altitude 15 degrees so I can see its occultation on June 6th? When does nightfall come on May 30th? Does Venus set too soon after the Sun to see her in a dark sky? How long does it take Altair to cross from rising to 140 degree azimuth, going then behind my house? During what hours can the Sun shine on my window that faces azimuth 30 degrees? Other uses were for illustrating assorted concepts of astronomy. How does sidereal time work? What is heliacal rising? Why are some stars semperpatent and others semperlatent? How does day length vary with season? What is the correlation between Moon phase and Moon location in the sky? Textbooks with static pictures never really did the job well. There were other resources for doing these problems, like the sun tables published for photographers and a real starglobe. But there was really nothing all in one that handled the entire range of home astronomy problems. The allure of the astrolabe was that you hopefully could have a mechanical device that simulated a starglobe in a flat portable form. Why not go and get a regular starglobe? It's a bit surprising but starglobes, suitable for working out astronomy problems, were at sale far more so than today. The trouble was they were expensive, builky, not at all portable. You wanted in the worst way some gadget to fit in your attache' case with your other stargazing gear and take with you.
Some history ---------- The groundwork for the astrolabe came from classical Greece, where the stereographic mapping system was invented. Ptolemaeus refined the stereogrpahic system and used it in his geography books. He seems to know about the astrolabe but we have no evidence that he ever actually made or otherwise had one. We have other classical writings about this system, with its use for solving astronomy problems that otherwise required a starglobe. All apparently relate to doing a fresh geomteric calculation for each situation, with no inkling that a mechanical device could do the work. In fact, this is precisa mente what an astrolabe is, a 2D model of the 3D celestial sphere. No one knows when the first physical astrolabes were made. There are writings describing an astrolabe from the 400s AD with no proof of a real specimen. The oldest specimina in musea date from about 1,000AD but their mature build suggests they were in general use from many decades earlier. It seems that they were first made in the Islamic regions and came to Europe by the reviving trade and commerce of the Middle Ages. Once there, they spread rapidly thruout the continent and acquired the flavor of each country. Their design was similar across all craftsmen, also suggesting that the astrolabe matured long before they were commonly available. The prime customers were navigators and astronomers, also scholars and astrologers. They needed a means of quickly, if approximately, working out their spherical geometry problems. This was specially the case given the monstrous methods of maths in force at that time. Astrolabes continued in wide use into the late 18th century. By then the demands for accuracy exceded the capability of the astrolabe's mechanics. Also, almanacs were better compiled and published for easy reference and clocks were more widely available to individuals. Never the less, the instrument was still presented as a rite of passage to graduating students or newly married husbands. By the 20th century, most of the important situations that the astrolabe could tackle were largely forgotten. Else the astronomer went thru the specific massive maths to work on them. By the late 20th century the ardor to acquire an astrolabe was severely slaked with the arrival of calculettes and then home computers. These instruments cut thru the maths and showed pleasing graphics in simulation of the sky. In time their programs evolved into computer-based planetaria, of which there are a wide diversity today. There's even computer simulations of a classical astrolabe! They present a picture of the instrument on screen and you manipulate it with mouse or keyboard. The programs allow setting any latitude, date, epoch, depth of star field, and other parameters. The settings can be saved to keep your personalized instrument.
Brass --- The theory and principles of the astrolabe were worked out at least as early as the classical Greek era. The realization of the instrument came much later, in the Dark Ages. The device requires a construction material not found among the usual materials of the classical world. None of the seven base metals were suitable, nor ws wood and stone. There ws one excellent metal, but it was precious and scarce. It was used for gadgets and trinkets of the upper class, It turns out that when copper, one of the seven original primary metal to the Greeks and Romans, is mined in the Mediterranean region, the metal is a more or less pure element. It had a couple percent of impurities like tin, zinc, aluminum but thee were too small to significantly affect the properties of copper. Copper mined in the mountains of the Middle East had ten to twenty percent of other metals as an alloy. It was utterly unknown to the metal workers why their 'copper' had extra properties that made it superior to plain copper. The alloy was a traded item for the western world. We have artifacts from all over the ancient world made of what we know call in English 'brass'. The copper from the Middle East amounts to a naturally-occurring brass. Ignorance of the alloy nature of the new material, the Greeks named it 'orochalkos', 'mountain copper'. The Romans called it 'aes' as a variation of bronze, the well-known alloy of copper and tin. They also called it 'orochalcum' from the Greeks. While an ideal metal for mechanical devices like the astrolabe, brass was just too costly and rare for wide use as such. During the Dark Ages the Middle East metal crafters discovered that they can make the brass by cooking plain copper in fumes from certain minerals. These minerals had a high content of zinc, an element not yet isolated in pure form. Production of brass increased and the price declined. Astrolabes and other instruments and tools were manufactured and traded. In about the 12th century the element zinc was extracted at mines in northern India, allowing for a more controlled manufacture of the alloy as a deliberate mix of copper and zinc. Brass then, with the expansion of western society, became a commodity and found many new uses besides mechanical devices. It was used for, as examples, locks, clocks, musical instruments, decoration, hand tools, garment fittings. We can credit the Middle East with the discovery and invention of modern brass. It is an other beneficial contributions to humankind like those in general astronomy, mathematics, geography, medicine.
Your own astrolabe ---------------- Today you can fetch cut-out astrolabes from websites. Set your latitude and other parms in the request screen and the master sheets are compiled for you. Print, cut, assemble them, and, voila!, you got an astrolabe. Not a durable one, being made of only paper, but a truly functional one. Occasionally, a museum publishes a cut-out book replicating an instrument in its collection. With care in cutting, specially for the rete, you acquire a functional device. Bear in mind, it is a duplicate of a antique device, so it does not give correct results for the 21st century. If you want a 'real' astrolabe, made of metal or heavy plastic with gorgeous inscriptions all over it, there are a couple firms that can make one for you. It is for contemporary star positions and solar system motions, so it has a practical function for today. It may be either a modern or an antique style.
The instrument ------------ Fundamentally, an astrolabe is a 2-dimensional analog model of the celestial sphere. It maps the sky and ground onto planes. Manipulating these planes simulates the behavior of the real celestial sphere, enabling you to solve assorted problems and to demonstrate many concepts for home astronomy. The usual construction was from brass, an easily worked metal of mature experience and known behavior. Sometimes it has silver inlays as ornament. Lettering was inscribed directly on the metal. Workmanship varied among makers from careful and advanced to rather crude. The better made devices were more expensive, made on order for wealthy customers. The cheaper ones were stocked for walk-in customers at the studio. The astrolabe is the first scientific precision instrument to attract a public appeal. It may be the scientific instrument of longest continuous use in essentially the same design, changing only for precession and choice of plotted stars. A studio may sell a few dozen or a hundred per year, an immense quantity for such a specialized device in the Middle Ages. Methods were developed to make quickly and accurately the parts for astrolabes, an early form of mass production. A studio may farm out the fabrication of parts and have its own lower-rank workers assemble the complete unit. In spite of the potential for a general industry for astrolabes, studios were mainly the operation of a single master. It closed when the master retired or died.
Planisphere --------- An astrolabe differs from the ordinary planisphere, star-wheel, star-finder by having more lines and points and fewer individual stars. Most planisphere plot way too many stars for easy correlation with the real sky. An other difference is that astrolabes of vintage were in small diameters, about 10-15cm, for portability and weight. Planispheres can be found up to 40cm diameter, clumsy but not overly heavy. Yet an other distinction is that an astrolabe is laid out in mirror image. When placed face up, its compass directions match those on your horizon. A planisphere is drawn such that you must hold it over your head to make the compass directions line up correctly. It usually is not practical to kludge a planisphere into an astrolabe. You would hae to doctor up the stars and horizon so much you should just as well build a new instrument from scratch.
Styles ---- There are two grand families of astrolabes, eastern and western. The eastern astrolabe was built in the Islamic world and was lettered in an eastern language, typicly Arabic. An eastern astrolabe may also have a qibla-finder and marks for praying hours, but these are not part of the basic astrolabe function. The western astrolabe was made in Europe and was lettered in a western language, notably Latin. Because our heritage springs from Europe, many modern works on astrolabes employ Latin for the parts and features of the instrument. Because the actual diameter of the astrolabe is a function of its latitude and the scale of the mapping in it, the usual way to specify the 'size' of an astrolabe is to give the diameter of its celestial equator. A 14cm astrolabe is one whose celestial equator is 14cm diameter. Its physical size can be many times larger if it's drawn for a low latitude. Both styles have the same function and same main components. Once you learn how one example works, it doesn't matter which style you use. About the only distinction is that a Western astrolabe tends to center on mid to high northern latitudes while the eastern ones are set at low northern latitudes. This reflects the geographic domains of the two cultures. There seems to be no native astrolabe from the southern latitudes. What examples we have come from northern fabricators to be taken to the south. There are actually several designs of astrolabe, but here and in the Museum talk only the planispheric model is treated. This is the one that looks like a souped up star-finder. It is also the design most commonly offered in modern form, like in kits or custom units.
Stereographic projection ---------------------- The astrolabe works because it is mapped with the stereographic projection. This is one of dozens of ways to transform the 3D celestial sphere to a 3D flat plane. Each mapping scheme has benefits and malefits. It turns out that the one known as the stereogrpahic projection has the most and strongest benefits with the mildest malefits for astrolabes. The stereographic projection is formed by a point source of rays placed on the surface of a transparent sphere. A realization of this method is a transparent patterned beach ball and a rice-grain lamp. Place the ball on the floor and shine the lamp thru it from the top. The shadow of the beach ball's pattern on the floor is the stereographic projection of the sphere onto the plane. Each point on the sphere is 'projected' like the image from a slide or movie projector, onto the flat map. The plane doesn't have to actually touch the ball. As long as it is parallel to the tangent plane it may be removed from the ball, either inward or outward. The distance away merely changes the size of the projection. The farther is is, the bigger is the shadow pattern. There are other ways to make maps that are not so simple. Some are projection with a different arrangement of lamp, sphere, and plane. Others are not projections in the strict sense. Because projection maps are so common and are the ones often explained in cartography, it's usual to call any mapping process a map projection. The source of rays is at the latent pole. The diametricly opposite point, where the tangent plane sits, is the patent pole. This is the pole in the center of the astrolabe. Sometimes these are called the north and south poles because the greater number of maps have the north pole as the patent pole in their center. It is impossible to map the entire sphere onto the plane because for points near the latent pole the rays must project thru enormous distances before reaching the plane. They reach it at infinite distance away from the very latent pole itself. A stereographic projection, to fit on the finite plate of the astrolabe, must cut off some way out from the latent pole. This is not a severe limitation in as much as from latitudes removed from the equator, a cap of the celestial sphere around the latent pole is always below the horizon and can be omitted from the astrolabe's star plate. This is the region of semperlatent stars. The stereographic projection is an easy mapping to do with only geometry tools. No calculations are needed. Every circle, arc, line in the sphere maps as a circle, arc, or line on the plane. There ae no weird curlicues to plot out or distorted lines to interpolate along. This property makes all angles and shapes (like asterisms) true against those in the sky. You can find the angle between two lines or arcs in the sky by measuring that angle on the astrolabe. One principal malefit of the stereographic projection is that the distances out from the patent pole enlarge drasticly. This can make the astrolabe physicly many times larger than the equator plotted on it. That is, the distance from the pole to the equator may be 10cm but from the equator farther south to, say, 60 deg south declination may be 20 cm. Your astrolabe could be, uh, 60cm diameter! You will do well to study a book on stereographic geometry. I do warn that they are rarely published today. You may find an older one from the early 20th century, but geometry didn't change since then. You can also acquire tuition on the stereogrpahic projection from other sciences. It is extensively used in mineralogy, crystallogrpahy, geology, atmospheric optics, aurora recording, physical chemistry. You'll learn interesting tricks from these fields to apply on the astrolabe.
Horizon ----- To better understand the discussion of the components of the astrolabe, you should get a work dedicated to astrolabes. They give not only a more detailed explanation but offer pictures of historical and modern astrolabes. You ideally should also have to hand a real specimen, even if assembled from paper cut-outs. Astrolabes have three main components. First is a ground or base plane with the altitude-azimuth grid on it. This covers the celestial sphere above your horizon, but some models include the crepuscular altitudes for twilight: civil, nautical, astronomical. There is no generally agreed Latin word for this plate. 'Tympanum' is one, meaning a flexible sheet. 'Lamina' is for a rigid sheet. 'Tabula' is for a slab of wood from the principle sense of a plank. All can describe the base plane on which the horizon is drawn. On the limb is a scale of hours. Zero is at the north or midnight point and the hours run clockwise thru 24 hours. By this means the astrolabe is set for the time of day by placing the Sun against the approprate hour mark. This plate is delineated for a specific latitude, typicly that of your home location. Extreme accuracy is not needed here. The latitude may be taken to one degree for perfectly valid operation. A fancier astrolabe has a thick base plane with a well or raised rim. Into this base, the mater (MAH-terr), is placed one of several horizon plates. Insert the one nearest your latitude. In this model, there are no scales around the edge of the horizon plate. They are inscribed on the rim of the mater. To orient the horizon the mater has a tooth near the east or north point. The horizon has a mating notch. When the two are engaged, the horizon is properly lined up with the scales of the mater. In this model the horizon plate is called a clima (KLIH-ma), after the east-west belts of the world having certain weather regimes. These evolved to our zones: torrid, frigid, and so on. The set of horizon plates is the astrolabe's 'climata' (KLIH-ma-ta), which gives us our word 'climate'. The alt-azimuth graduation depends on the size of the astrolabe. For most purposes lines 10 deg apart is plenty enough. The ultimate accuracy at best can only be about one degree in reading the lines, unless the astrolabe is really huge. Even if the azimuths are labeled, it's good also to mark the compass points. Remember, an astrolabe lines up with the horizon when looking down at it. In this position, the stars are standing in the proper azimuths around the horizon. The clockwise sequence is north, east, south, west, like on a regular map of the ground.
Rete -- Say 'REH-teh', not 'REET' or 'REE-tee', meaning a net or mesh. Lacking strong sculptile transparent material, the star plate had to be fretted to let the horizon show thru. The rete is a filigree or grillage on which stars are placed on arrow points. A much rarer method is to attach star markers onto a wire mesh, similar to window screen or farm fence. There was the antagonism for the instrument-maker between a rigid star map and enough useful stars. Doe to the limitations of metal working in the Middle Ages, only a dozen stars or so could be attached to the typical size of rete. These were the first magnitude stars with a second magnitude one in an empty part of sky. The outer edge is scaled for the right ascension. Some historians try to date the astrolabe by noting the right ascension of its stars. By applying precession they claim to know when the astrolabe was built. All they actually found was the epoch of the star lists that the maker worked from. These may be a few centuries old because they were not routinely updated and copies of any vintage were hard to get. In modern astrolabes a transparent solid plate, like Lucite, is used. The number of stars plotted can be large enough to recognize the major constellations and asterisms. Each star is a dot, not an arrow head with a bar to sit on. So, even with far more stars, the horizon is plainly visible thru the clear parts of the Lucite plate. Most astrolabes made for astronomers don't have lavish labeling. Just a few key stars are named because the astronomer knows the others from his general sky wiseliness. The solid rete allows you to mark temporary objects like novae and comets. When they pass on, erase their marks. Even with a solid star plate, the RA-dec grid is not laid down. There would be too much criss-cross of lines from both sky and horizon. The RA and dec of a point on the rete is found by laying the regula, explained bloew, over the point and reading the location from its scale and that around the limb of the rete.
Solstice cutoff ------------- In the mid to high northern latitudes the winter solstice is low in the south. South of it are only two major stars of value for the astrolabe: Antares and Fomalhaut. These stars are even lower in the sky, veiled by the air pollution in Middle Ages towns, or by skyline. To keep the overall diameter of the astrolabe within sensible bounds, it was common to cut off the rete at or a little south of the winter solstice, declination -23.4 degree. The result is that the horizon plate was clipped off in the far south. Since there was nothing there to work with, accepting the lack of Fomalhaut and Antares, there was no loss of function. For low north latitudes, there was significant activity south of the winter solstice and the entire horizon was constructed. Such astrolabes are huge compared with their more northern brothers.
Stars on the rete --------------- From about 50 brighter stars north of the winter solstice a selection of a dozen or so was inserted on a rete. Some stars were almost always included, making comparison easier among astrolabes from different eras and cultures, while others were often skipped. The names were inscribed on the star's arrow point or a nearby strut. Abbreves were common in the cramped space on a typical rete. The names were Latin or Arabic according as the style of instrument. Because Arabic star names came into the Western world in the Middle Ages a western astrolabe could bear them as well as Latin names. In right ascension order the set of possible stars was, with modern names:
bet Cas Caph alp And Alpheratz gam Peg Algenib bet Cet Diphda gam And Almach alp Ari Alhamal the Eri Acamar alp Cet Menkar alp Per Mirfak bet Per Algol eta Tau Alcyone gam Eri Zaurak alp Tau Aldebaran bet Ori Rigel alp Aur Capella bet Tau Elnath gam Gem Alhena alp CMA Sirius alp Gem Castor alp CMi Procyon bet Gem Pollux alp Hya Alphard alp Leo Regulus alp UMa Dubhe bet Leo Denebola gam Crv Gienah del Crv Algorab gam Vir Porrima eta UMa Alioth zet UMa Mizar alp Vir Spica alp Boo Arcturus alp Lib Zubenelgenubi alp CrB Alphecca alp Ser Unukalhai eps Boo Izar bet UMI Kochab alp Sco Antares eta Oph Sabik alp Oph Rasalhague gam Dra Eltanin alp Lyr Vega alp Aql Altair alp Cyg Deneb bet Cap Dabih alp Cep Alderamin eps Peg Enif del Aqr Skat bet Peg Scheat alp Peg Markab
Polaris was never marked because it was the axle of the astrolabe. Kochab was often skipped because it was under the bolt holding the astrolabe together. Antares was marked if the rete was extended a few degrees south of the winter solstice, probably on purpose to capture Antares. There were just about never any other far south stars from Puppis, Vela, Centaurus, Scorpius, Sagittarius. Even Fomalhaut was a rare entry. Alcyone was rarely marked. I suppose it was a bit tough to separate by bare eye from the rest of the Pleiades. A modern rete, on a transparent sheet, can have many dozens of stars. These could simply the the 100 or so brightest stars, enough to make recognizable patterns and lessen the need for labels.
Ecliptic band ----------- The ecliptic was a broad band, not a thin line, on the rete. It was scaled for ecliptic longitude, signs, and solar dates. These were important for setting the astrolabe to the date and marking the places of planets and Moon. In smaller examples, the date scale was omitted. The operator looked up the solar longitude from a separate table. The astrologer needed these scales to get the ascendent, descendent, and medium coelum. These are the ecliptic points rising, setting, and culminating at the instant date and hour. For most work, only the ecliptic longitude of a planet was used. The planet was assumed to sit on the ecliptic. Planets do wander north and south from the ecliptic by up to eight degrees. This approximation is not overly loose because a planet is bright enough to recognize in the sky when you look at its place along the ecliptic even if it's a few degrees north or south of that point. Even today, many tables of planet locations give only the longitude with no latitude. The broad ecliptic band also gave strength to the grillage of the rete. Bars sprang from it to support the star points.
Ecliptic coordinates ------------------ In the Middle Ages and thru the 1700s the all-important coordinate of a celestial body ws the ecliptic latitude and longitude. Right ascension and declination were used but they didn't surpass the ecliptic system until the late 1700s. The cause was likely the use of mechnicly good equatorial mounts for telescopes and the ease of taking equatorial coordinates over ecliptic ones. Astrologers clang to the ecliptic, up to the present era. yet I never saw or heard of an astrolabe whose rete was drawn with ecliptic coordinates. There was nothing to prevent one, given the simplicity of the stereogrpahic geometry. I suppose for a modern astrolabe there could be a swoppable rete for ecliptic -- and maybe galactic! -- coordinates.
Regula ---- 'REH-goo-la', not 'reh-GYOO-la', a ruler. This is a thin bar that pivots around the pole of the astrolabe for fixing the position of the Sun, approximating the location of the Moon and planets, marking off time intervals, taking RA-dec of stars, and other sundry functions. On some astrolabes the regula is fitted with sighting vanes for taking altitudes of stars. The idea was to have in the one instrument the ability to both observe the altitude and compute it. The regula has a scale of declination along it. When placed against a star on the rete, the declination is read off of this scale and the right ascension is taken from where the regula points along the RA scale on the rim of the rete. The regula was sometimes paired with a second one on the back of the astrolabe. This second regula was an index to read assorted parameters from graphs placed on the back.
Assembly ------ The horizon plate is on the bottom. It has a peg at the center for the north celestial pole. If the astrolabe has a mater and set of climata, place on the peg the clima for the desired latitude. There is a tooth-&-notch means of homing the clima onto the mater. When clicked into place the horizon is lined up with the hour scale of the mater. Over the horizon goes the rete, there being a hole at the north celestial pole to fit on the polar peg. Be sure to face the rete with its labels visible. The regula fits over the rete by its own central hole. Make sure the regula is faced right way round by its markings. The whole stack is locked together by a clasp or cap or nut. This should adjust to take up wear and to loosen for moving the regula snf rete. In antique astrolabes, lacking machined screw threads, a key in the shape of a horse-head was wedged thru a slot in the central peg. Even on large units this wedge obscured the far northern declinations, including the Big Dipper and Cassiopeia. A modern astrolabe avails of much smaller and more secure fasteners. As ornament, a fancy crown, is mounted at the top, north, edge of the tabula. It is either a separate piece fitted to the tabula or a one-piece casting that is later tooled. On the crown is a ring or rope loop. By this you hung the unit verticly for taking star altitudes. In a mdoern edition the ring or loop also hangs the instrument from a wall or on a stand. And that is the basic construction of an astrolabe!
Astrology ------- When the historical astrolabes flourished, astrology and astronomy weren't yet fully segregated. Many astronomers did astrology and vice versa. Astrolabes, therefore, sometimes catered to astrology by putting on the horizon plate lines and arcs for astrological houses. This feature didn't catch on because then, as now, there was no standard way to define the houses. There are about 20 methods, all different and all claiming to be the correct one. Modern computer astrology programs offer a choice of house systems. You go and pick the one you like. The concept of the house, also a mansion, is to divide the local sky into twelve parts, following the division of the celestial sphere into the twelve zodiac signs. The thinking was that a planet's strength was a mix of its position in the zodiac signs and that in the horizon houses. However, there is no obvious natural way to chop up the sky above the horizon. There are several poles and circles associated with the horizon to choose from, each leading to a different partition of the sky. Hence, you could not stock astrolabes with houses to satisfy a substantial market of astrologers. Any one house system on your astrolabes would be invalid for too many potential customers. Other than the house lines, there is really nothing unacceptable in an astrolabe built for an ancient astrologer rather than for an astronomer. In most cases the one instrument served for both fields.
Astronomical triangle ------------------- Problems worked by the astrolabe bank off of the astronomical triangle. This is the three lines, great circles, joining the north pole, zenith, and star. The sides and angles of this triangle are: -------------------------------------------- pole-zenith - colatitude, (90d) - (latitude) zenith-star - coaltitude, (90d) - (altitude) pole-star - codeclination, (90d) - (declination) at the pole - hour angle, distance from south meridian at the zenith - azimuth, distance from north point of horizon at the star - parallactic angle, litte practical use ---------------------------------------------------- By setting up certain of these angles and sides on the astrolabe, you can read out the other parts. By choosing a clima you set the colatitude. By placing a star on the horizon you set the coaltitude. By displacing a star from the meridian you set the hour angle. Solving the astronomical triangle can be done by formulae and equations or by geometric construction. The astrolabe does the work by manipulation of a mechanical model of the real sky.
Fake astrolabes ------------- You can find in various markets in your travels vendors of 'astrolabes'. It is not at all obvious from the construction or appearance if it is a genuine astronomy device or a toy. Bear in mind that astrolabes are like any other 'antiquity' that attracts fakes and counterfeits. If you're hunting for an astrolabe, bring along pictures of real ones to compare with the offered device. Ask the vendor to demonstrate some simple operation while you watch. Finding sunrise for the first day of your travel or the altitude of a given star at nightfall of that day will trip the fakers. Even if the astrolabe is a validly made device, it doesn't mean it is antique. It could be a modern construction with phony antiquing done on it. There are ways to make a new artifact look many centuries old. The rule to follow is that for the purchase of any other supposed antique. Pay only as much as you would if you knew for sure it was a fake. There's nothing wrong with buying a modern astrolabe with stains and rust from being artificially antiqued. Just know that's what you're buying and then bargain accordingly. Please understand that a antiquity item may be encumbered when you leave its home country. Countries have awfully strict laws about taking antiquities away, even if honestly purchased on open market. If you are detained for trying to leave with an artifact of national concern, please cooperate. Answer questions honestly and completely. The authorities want to learn where and how the vendor got the instrument. Do not try to sneak the instrument out. It will likely be found in the departure inspection and you will have a longer and harder go at explaining about it. Musea sometimes sell replicas of their astrolabes. These are fully functional and will serve for all of your astronomy satisfaction. You know it came from a specific real example and has all the features of the original. This is the safest way to keep out of trouble and have an authentic specimen for your self.
Current utility ------------- A historical astrolabe has little current utility for several reasons. One is that the workmanship, specially in the smaller sizes, can be crude. Metal-working was still immature in the Middle Ages and instruments like astrolabes were fashioned entirely by hand. The pieces may fit loosely, markings may be scratchy, the device may be flecked with tool bruises. In small sizes the detail is crammed into a tight area, mostly around the north pole. This makes the astrolabe harder to operate. There may be too few stars on the rete or too coarse a grid on the tabula to suit your needs. The device was built for an epoch possibly centuries earlier than its construction date. You have many centuries of precession drift since then. For demonstration or show-&-tell this may not matter. For any current skywatching application, you'll go pretty wrong. Unless by chance you happen to observe from a latitude close to that of the astrolabe, you're handling a device for some other wrong location. Even if the instrument came with climata, these were commonly made for only a selection of latitudes, based on ancient geography. As careful as the instrument-maker was, he had to rely on astronomy litterature around him. That could be in error from copying mistakes or real compilation errors. Recall that accurate star and planet positions didn't come until the end of the 16th century. Before then there could be discrepancies of a degree or so among star tables. Thus, on the rete the stars may be misplotted. It is likely impossible to seek an astrolabe owned by a specific astronomer like Grimaldi or Clavius. It could be tough to secure a credible provenance for a given astrolabe and there were so many made in the Middle Ages for all kinds of customers. As long as you can be assured that the device offered has a verifiable vintage, that's great. The motivation to own an antique astrolabe today is the attachment to your heritage as an astronomer. To hold in your hand the very tool some long-ago astronomer carried in his kit bag makes your profession all that more precious and valued.
Back face ------- There were many options for filling the back, dorsum (DORR-summ), of an astrolabe. Perhaps the most common features were a scale for seasonal hours and an altimeter. The altimeter is a rectangle or box graph to calculate the height of walls, towers, trees, &c by noting the altitude of the top from a known distance away. It was assumed you and the target were on level ground, which is often not the case in rough terrain. By sighting on the top of the target, the regula sits over a certain mark of the altimeter scale. This is the ratio of the tower height to the standoff distance. Say this is 0.4. This means the tower height is 0.4 time your distance from it. Because of the tangemt effect, for angles greater than 45 degrees, the inverse ratio was given, standoff over height. The scale of seasonal hours is of little use today. In former years, before good clocks, the question was more like 'how much of the day is gone?' or 'how much more of the night is left?'. Seasonal hours are the 12th part of the daytime and of the nighttime. While together they total 24 hours, they are separately of different length. This is due to the shifting ratio of day to night during the year. Other possible scales are for trig functions. These are not needed directly for using the astrolabe but are handy for computations in navigation and astronomy. By laying the regula over the angle the sine, cosine, and tangent are read off of the graph. The accuracy is only two decimals, adequate for the kind of work a Middle Ages person did. Conversely the angle for a given trig value is found by moving the regula to sit on the value and taking the angle from the rim of the astrolabe. By separate considerations, you have to figure out the proper quadrant for the angle, a task that still bedevils us today. In a modern astrolabe the dorsum could hold a circular slide ruler! A 'rete' replaces the slide and the standard scales of the normal slide ruler are allocated betwen it and the tabula. While totally supplanted by an electronic calculette, such a slide ruler could be quite handy, like when the calculette batteries run down.
My astrolabe ---------- I built a planispheric astrolabe in the summer of 1957 from instructions in an old astronomy book. The book was borrowed from the New York Public Library by my father, who then worked on Manhattan near the main outlet on 42nd St and 5th Av. As a Brooklynite, my own local library card was invalid for being an 'out of town' card. All I needed were the tools of high school geometry: a ruler and compass. Handicraft skills, like cutting a disc of plywood and working with nib-pens and India ink, were pretty much a necessity. as well. I first made several paper-&-pencil models to prototype the instrument and catch construction problems. There was one major problem for large radius of arc. Ordinary circle-makers weren't big enough. I taped a pin at one end of a wood slat. At the proper radius away I taped the pen. This was a crude beam compass, but it worked with careful handling. The tabula was a disc of plywood about 30cm diameter. The horizon was first laid down on paper, then cut, trimmed, and glued to the plywood. The outer margin of 1cm was for the hour and degree scales, leaving 28cm clear diameter for the horizon grid. Azimuths were spaced 15 degrees apart; altitudes, 10. I added the crepuscular circles for the twilight limits at -6, -12, -18 degree. The grid was hand labeled in degrees and compass direction. The rete was an acetate sheet cut to match the tabula. On it I scored with a stylus stars down to about 3-1/2 magnitude, enough to form major asterisms. I rubbed ink into the scratches, which were depressed into the sheet to avoid touching against the horizon. The star chart was plotted frontwards, like the view of the sky. When finished it was flipped over to set it on the horizon for the mirror view. This also put the ink marks on the inner surface of the acetate sheet, better protecting them against wearing off thru handling. I did not label any stars to avoid clutter. There were enough identity clues from the asterism and constellation patterns. The rim of the rete was scaled in right ascension. The ecliptic was plotted as an excentric circle by the methods of stereographic geometry. I put ticks along it at 10 degree intervals. I can eyeball the location of the Sun by looking up its ecliptic longitude from an almanac. A year or so later I added date labels to the right ascension scale. I can't remember why I used the mean Sun, traveling at a steady rate around the equator. Because the real Sun travels along the inclined ecliptic at a varying speed the dates should be a bit irregularly spaced. The error is only a day or two or a few minutes, well within the precision for routine skywatching. I also laid down the galactic equator as the centerline of the Milky Way. I skipped the galactic poles and galactic longitudes. The regula was a strip of acetate ruled off in declination. It has no sighting vanes because the instrument is too clumsy to hold up to the sky. Wind buffets it, which is why a marine version of astrolabe has large holes. These let the wind thru, like the slits in some hanging advertising banners. The acetate rete takes grease or dry-mark pen to plot planets and comets. I now use a bit of sticky note with the target's symbol and name on it. The location is indicated by the declination scale on the regula and the right ascension scale around the rete. My astrolabe has an empty dorsum because I never could decide which of many features to add there. Maybe I'll make overlays to swop as I need them. The instrument was built to the 1950 epoch, the prevailing one in the mid 20th century. Precession by the 20 thous pushed the ecliptic longitude of the stars about 2/3 degree farther east. This has no adverse effect for ordinary skywatching since the precision of reading the astrolabe is quite one degree anyway. For storing the astrolabe, I expropriated a thin gift box from A&S. It so far is holding up perfectly well over the decades. A&S department store folded in about 1995. Many of its outlets are now part of Macy's.
Commercial astrolabe ------------------ I bought a commercial contemporary astrolabe in the mid 1970s from a chandler store in South Street Seaport, Manhattan. It has a heavy plastic plate and a set of acetate overlays. In this model the stars are on the base and the horizons are on the overlays. This arrangement is the inverse of that in the usual astrolabe but it performs exacta mente the same. This model has the north pole centered on one face and the south pole on the other for use worldwide. Only about 60 stars are plotted, those used for navigation. There is ample clear space around them for their names. Leo is the region surrounding Regulus and Denebola; Pegasus around Enif, Markab, and Alpheratz; Scorpius around Antares and Shaula; Ophiuchus around Rasalhague and Sabik; and so on. The horizon plates are made for latitudes 5 thru 85 degree, north and south, at 10 degree intervals. They are lettered frontsy-backsy. Each can be used for either the north or south hemisphere by setting it on the star plate with the proper lettering frontwards. The backwards lettering is ignored. There is no regula but a whole extra acetate plate with the celestial grid on it. Laying this over the star plate allows reading positions and plotting new targets. The mapping is not a projection, but a simple equidistant azimuthal grid, like polar graph paper. A circle not centered on the pole is a roughed up circle on the map. That's why the horizon grids are so odd shaped. There is wild distortion of shape and angle away from the patent pole. On the other hand the entire sky can be covered on the plate, a boon for using the low latitude horizon plates. The latent pole, which is now in the open, becomes the extreme outer rim. It maps from a point on the sky to an all-enclosing circle on the map. There is no ecliptic on the original instrument. You are expected to mark the Sun manually for each instance. I plotted point by point the Sun at 10 day intervals, then joined the points with a smooth ink curve. These points were for a mid year between leap years to smear out calendar chatter. The dates are for the real Sun with his irregular motion built in. The original plate had only degrees around its rim. I added labels for right ascension. The omission of right ascension comes from the mariner's practice of using degrees. The conversion to time units is trivial but it was easier to put the hours right on the plate. I did not lay down the ecliptic on the southern side because probably 95% of uses would be in the north hemisphere.Moreover, the two sides are lined up in right ascension. Noting the Sun on the north side also fixes its location on the south. In use, the horizon plate closest to my instant latitude is pegged onto the star plate, north or south as the case may be. For New York I use the 35N latitude plate. The 45N plate feels too far north, even tho New York at latitude 41N is a mite closer to that one. The date is set by the Sun's location along the ecliptic. I place the celestial grid plate over the Sun's location and fix it with a paper clip. There after, problems are worked out like for any other astrolabe. The operation is smooth except that it is easy to flip the horizon plate wrong side up and all your azimuths and times are mirrored. Read the horizon plate to see which lettering is right way round. The set of horizons allows this astrolabe to be used for crude navigation in an emergency. From the observed altitude of a given star, the latitude can be guesstimated by seeing which horizon plates best match the observation and interpolating between them.
An extra treat ------------ Expecting to see some associates at this talk, I brang these two astrolabes with me. They suggested I display and explain the instruments to the audience rather than show the devices only to them individually! I offered during the Q&A to leave my instruments on a side table, away from the Museum's own instruments for safety and disturbance, after the presentation. Dr Chandler agreed! When the audience was socializing I set out my two astrolabes and was immediately thronged by curious visitors. These devices, I explained, you may handle and play with, while the Museum specimina were for eyes only. The curator minding them wore gloves to prevent contamination of the Museum artifacts frum hand oils. I illustrated a couple problems (I forget which!) on my own astrolabe. They were eager to learn how I built it. I long ago forget the actual book the instructions were in but I pointed out that I did not concoct the instrument all by myself. On this astrolabe it was easy to show the visitors the stereographic projection. I demonstrated the use of the horizon plates on the store-bought astrolabe. The visitors were fascinated by the double-sided horizons for use on either the north or south star plate. They were specially curious about the ecliptic on only the north side.
Conclusion -------- The astrolabe as a topic in home astronomy bubbles up every few years. The instrument, to be fair, is a cunning application of analog modeling, perhaps the first such technique ever applied by humans. Illustrations of astrolabes can look very mysterious and exotic. There is really nothing intimidating about an astrolabe. It just has the Earth on a base plate, the heavens on a grilled overlay, and an index ruler. That's it!