THE PLANISPHERIC ASTROLABE
------------------------
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.org
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!