Description and use of the
equinoctial astrolabe
displayed with my Java applet.
There is a set of Equinoctial Astrolabe displays
contained within this Astrolabe program.
These displays can be revealed in turn
by using the menu,
by clicking on the Equin+ button repeatedly or
by pressing 'e' or 'E' until the sequence repeats.
(At any time,
you can press f4 to return to
the original astrolabe display or
you can use the menu for this.)
The version provided here uses
a table of horizons rather than
the more conventional arrangement of
horizon and related almucantars and azimuth arcs.
It is thus not possible to determine
the precise position in the sky of the stars
unless they are on the horizon,
the East/Zenith/West arc or the meridian.
However, in medieval times,
this is all most people required, and
it has the advantage that
it can be used at any latitude throughout the world
without extra plates.
In that respect,
it forms an intermediate stage between
a conventional astrolabe and a Universal astrolabe.
It can be used as an astrolabe for northern latitudes
if the 'view' setting is heavens view,
or as a planisphere for northern latitudes
if the 'view' setting is earth view.
Conversely,
it can be used as an astrolabe for southern latitudes
if the 'view' setting is earth view,
and as a planisphere for southern latitudes
if the 'view' setting is heavens view.
When used in the northern hemisphere,
the horizon arc below the centre line is
the northern half of it, and
the southern horizon with southern latitudes.
For simplicity,
the description which is provided here
assumes it is used only in northern latitudes.
Without the rete,
the plate could also be used
with a thread and bead as a universal astrolabe.
This use is not described here.
It is common to describe
the superimposition of items to the South of the Equator
over the northern items as 'folded'
but I have used the term 'reflected' here
because I believe
'folded' better describes
the action when converting an astrolabe into a quadrant,
for instance.
The items to the south are plotted from
the northern axis rather than from the southern axis,
so are not really folded,
although it is convenient to consider that
they have been mirrored from the outside edge.
A beautiful example of this type of astrolabe
is displayed in
the Museum for the History of Science, Oxford.
Summary
An equinoctial astrolabe has
the equator around its outer edge and not
the Tropic of Capricorn as on an ordinary astrolabe.
Otherwise, they are similar in operation.
Because of this,
any items to the South of the equator are
reflected inwards and superimposed on
those items to the North.
Thus,
the circle representing the Tropic of Capricorn
is drawn precisely over
the circle representing the Tropic of Cancer, and
the South Celestial Pole
is placed at the same point as
the North Celestial Pole,
which is at the centre of the astrolabe.
To distinguish between
stars which are North and South of the equator,
those to the North are indicated
by small black-filled circles,
while those to the South are indicated
by small open circles.
The ecliptic circle is shown as two arcs,
one arc showing the Zodiac from Aries to Virgo,
the other showing it from Libra to Pisces.
Size for size,
this results in a significant increase in the scale,
which should result in greater accuracy.
It also means that
all of the bright stars above the horizon can be shown,
whereas
on an ordinary astrolabe
the area immediately above the southern horizon can't be shown
for latitudes below 66.6 degrees.
In this version of the equinoctial astrolabe,
the plate shows a table of horizons.
The area below the central line contains
the northern half of horizons for 0 to 90 degree latitude.
These horizons have been duplicated in the upper half,
these arcs representing
the southern halves of these horizons.
Such an arrangement makes this astrolabe universal,
in that a separate plate isn't necessary
for every latitude for which the astrolabe needs to be used.
However,
a table of horizons doesn't provide
the almucantars and azimuth arcs
which are usually shown on
a plate drawn for a single latitude.
Therefore it doesn't allow the user to determine
the azimuth and elevation of the Sun or stars
except when they are on the horizon,
the East/Zenith/West arc or the meridian.
Four displays are provided for this equinoctial astrolabe.
The first display is interactive.
It shows the plate,
over which is the rete.
With this view,
the stars can be seen which are visible in the sky
for the latitude, time and date
which have been selected using
the buttons in the panels on the left.
These settings can also be selected from the menu, or
the time/date can be that of
the constantly changing computer clock.
Precession is accommodated,
but only using the Gregorian calendar.
The second display shows the plate,
the third shows the rete and
the fourth shows a pointer.
These are suitable for printing,
allowing you to construct your own paper astrolabe.
(The rete and pointer should be
printed on transparent material.)
However,
when you are reading
a description of each of these items
in the next section,
you may find these displays useful,
either on screen or in printed form.
The 'heavens view/earth view' button
allows you to choose a viewing mode of
either looking down on the stars and earth
from above
(that is, from the heavens,
which was the way an astrolabe was used in earlier times)
or looking up at the stars from the earth,
as with a modern planisphere.
As you change between these viewing modes,
the East/West compass directions,
the stars and
the ecliptic circle with the zodiac signs
reverse from left to right.
The component parts of a Equinoctial Astrolabe
The plate
You will see that
the outside edge of the plate is
marked with the numbers 1 to 24,
these being used for the time as on a 24-hour clock.
The plate has a set of arcs which
converge at two points known as the poles, and
these arcs are known as the polar arcs.
There is a second set of arcs on the plate
that do not converge,
which are known as the parallel arcs.
As shown here, these are not parallel ,
but represent circles which are parallel.
A feature of these two sets of arcs is that
the crossing points are at right angles.
In the version shown here, there are
45 polar arcs in the top half of the astrolabe, and
45 in the bottom half.
Similarly,
there are 45 parallel arcs to the left and
45 to the right.
Every fifth arc (10 degree arc) is coloured green, and
those representing 30 and 60 degrees are coloured blue.
The polar arcs are used in pairs as
horizons for different latitudes,
and are for latitudes 2, 4, 6... to 90 degrees
from the centre to the outside edge.
The straight line in the centre is for
the horizon of an observer at the equator,
0 degrees latitude.
As with the parallel arcs,
the polar arcs which indicate every tenth degree are green, and
those for 30 and 60 degrees latitude are blue.
The two arcs for
the horizon with the currently selected latitude are
highlighted in red for your convenience.
The red arc in the lower part of the astrolabe shows
the northern half of the horizon,
with the North at its centre, and
the upper red arc shows
the southern half of this horizon,
with South at its centre.
(Set your latitude with
the buttons in the panel on the left.)
Another polar arc is coloured black.
This represents the arc from
the East point of your horizon to
the West point, passing overhead.
The centre point of this arc shows
the position of your zenith
(the point directly above your head).
If you click repeatedly on the latitude buttons
you can watch the red arcs and the black arc
move in accordance with your latitude setting.
On brass astrolabes the desired latitude arcs
were not highlighted in red, of course, but
you can see that it would be possible to
select a pair of arcs to represent
any required horizon from the range presented,
and counting 45 arcs above this would take you to
the East/West/Zenith arc.
Your meridian is represented by a line from
the North point on the horizon to the top of the astrolabe
and then down to the South point on the horizon.
Again, this line is bisected at your Zenith by the black line.
The points which are known as the 'poles' represent
the east and west points on the astrolabe.
Which is which will depend upon
the setting of the 'View' button.
If you have selected 'Heavens View',
east is on the left and
west is on the right,
otherwise they are reversed.
Knowing which is east and west,
you can now decide
which halves of the two red horizon arcs represent
the NE, NW, SE and SW arcs of the horizon.
The 'parallel' arcs can be seen to cross
the selected horizon arc at right angles.
They are used to indicate
the azimuth angle of any point on it and
are spaced at two degree intervals.
(The azimuth angle is the angle around the horizon.)
The arcs at every ten degree interval are green,
and the arcs for 30 and 60 degrees are blue.
Whether you count the azimuth angle from
the North, South or East is up to you.
Different people have different ideas about this.
Travellers generally work from the North, clockwise.
Astronomers usually work from the South.
In Medieval Times,
it was common to work from the East,
particularly when considering
the rising of the Sun or a star.
The Rete
The rete is rotated above the plate
and is normally printed on transparent material
so that you can see through the rete to examine
the plate beneath.
The outside edge of the rete has a date scale.
As you rotate the rete to align a date on its edge with
a particular time on the edge of the plate,
you are moving the rete into a position
which is related to that date and time.
On the rete is shown a representation of the sky.
Stars to the North of the equator
are indicated by filled circles, and
those to the South of it by open circles.
Whereas on a conventional astrolabe
only the stars to the North of the Capricorn Circle are shown,
on an Equinoctial Astrolabe
you can show stars as far South as the South Pole.
The stars closest to the celestial equator
are shown close to the outside edge,
and those close to the North and South Poles
are shown close to the centre.
The North Star, Polaris, is
virtually at the very centre of the rete (circa 2000 AD).
There are two symetrical arcs which
meet at the outside edge of the astrolabe area.
These two arcs show the position of the ecliptic circle,
which is marked to show the signs of the Zodiac.
One arc is marked Aries to Virgo and
the other shows Libre to Pisces.
The points where they touch the outside circle,
the equator, are the points where
the ecliptic crosses the equator.
The pointer
The pointer has a scale showing declination. If you move the pointer over one of the
stars or the selected position of the Sun on the ecliptic circle, you can read its
declination on the pointer. If the star is shown as a filled circle or the Sun is on the
ecliptic arc from Libre to Pisces, its declination is negative.
Using the Folded Astrolabe when it is displayed on a computer
Ensure that the settings of the latitude, time and date are the ones you require. (The
current settings are displayed in the panels to the left of the astrolabe display.) You
can adjust the settings by clicking on the buttons.
The stars which appear as filled circles in the area above the lower red horizon arc and the
stars which appear as open circles in the area above the upper horizon arc are those which are
above the horizon at the selected time and date.
When you view the Equinoctial Astrolabe on a computer you have the advantage that the
settings are made with the buttons or menu, and the position of the Sun along the
ecliptic arcs is shown by a yellow circle.
More details of its use common to both the displayed and printed version are given below.
Making a 'paper' version of the Folded Astrolabe
To make a 'paper' version, you must print out the three components - the plate, the rete
and the pointer. (The latter two must be printed on transparent material. Suitable
material is usually intended for overhead projector printouts.)
By repeatedly pressing the 'e' or 'E' key, you can cycle through the four displays of the
Folded Astrolabe. The first display shows the active display, the second shows just the
plate, the third shows just the rete and the fourth shows a suitable pointer. To make a
paper astrolabe, the latter three are printed out, the plate on paper or card and the
rete and pointer on transparent material. These are cut out and coupled together so that
the rete can rotate over the plate and the pointer can rotate over the rete. A pin
pushed through the centre of each, and then into a cork is adequate initially. A cork-
board pin (with a large, coloured head) which has been cut to size is preferable, pushed
into an ear-ring clip. Better still is a press-stud, but you need a larger diameter hole
through the centre of each of the three components.
Before printing
Ensure that the displayed size of the astrolabe is suitable. There are menu selections
allowing you to choose various sizes for the astrolabe window on the screen, and it is
suggested that you might want to select the 745x545 setting, which will result in a
printed astrolabe having a diameter of about 6.25inches (16.0cm).
Remember to select your latitude before printing the plate, and to print the rete and
pointer on transparent sheets. On the rete, you may want to select the option to display
the star names either from the menu or by clicking on the 'Star Names' button. The
plate and rete must also have the same viewing mode, of course (heavens view or earth
view).
Printing
Whichever method of printing you use, you must first select the astrolabe component you
want to print, using 'e' or 'E' to cycle through the components.
Printing directly from the program is not supported by browsers, because these are only
able to display this Java Applet. Printing directly is only possible if you can run this
astrolabe program as an application, and at the standard of Java 1.1 or above. When this
program is run as an application, select 'Printing' and then 'Print Astrolabe' from the
menu.
If you are unable to print out the astrolabe components directly, you will probably be
able to copy the contents of the astrolabe window into another application and print it
from there. With Windows 95/98, for instance, you can save the display of the
(highlighted) window to the clipboard by pressing Alt/PrntSc. Then load WordPad. In
WordPad you can press Ctrl/V to insert the contents of the clipboard into the WordPad
window. Finally, you can use the Printing facilities of WordPad, using the File/Print
menu selection.
No matter which method of printing you use, you will find that the position and angle of
short lines is obviously not quite right, particularly on the scale markings.
This is a limitation of Java 1.0.2 and 1.1.
Using the Equinoctial Astrolabe
Setting the date and time
On the outside edge of the rete is a scale of dates. Start by aligning the pointer over
the current date. On the outside edge of the plate is the time scale of a 24-hour clock.
For all of the operations below, you will now move the pointer and rete together so that
the pointer shows the required time on the outer edge of the plate. The current date
will thus be aligned with the required time.
Sometimes, you will move the rete to align some feature on it with some position on the
plate and will then read the time which is next to the required date.
General
Finding the position of the Sun
After you have set the pointer, rete and plate to show the required time and date, you
can find the position of the Sun. You can assume that the Sun lies under the pointer,
and on the ecliptic arc. (This is slightly inaccurate, and a better method is to use the
date/zodiac scales on the reverse of the astrolabe to find the zodiac position of the Sun
on the ecliptic circle.) When you have found the position of your horizon on the plate,
you can determine whether the Sun is above or below the horizon by following the
directions given below.
Finding the horizon arcs for your latitude
The two red arcs on the plate show the horizon for the latitude which has been set with
the buttons on the left (or with the menu). (You can still use it for different
latitudes if you wish, ignoring the red-coloured arcs and selecting an alternative pair.)
The upper red arc shows the southern horizon, and the lower one shows the northern
horizon, the points where they join indicating the East/West positions on the horizon.
To be above the horizon, the Sun must be over the lower horizon arc if it is on the Aries
to Virgo section of the ecliptic circle, and above the upper horizon arc if on the Libre
to Pisces section.
Holding the rete and pointer together so that the pointer is over the date, you can now
rotate them until the pointer is pointing to, say, 23.00 hours - an hour before midnight.
Stars indicated by filled circles which are close to the vertical line between the zenith
position (the point where the black arc crosses the vertical line) and the lower horizon
arc are to the North at an hour before midnight on the date selected.
Similarly, filled circles
which are close to the vertical line between the zenith and the top of the astrolabe, and
open circles which are between the top of the astrolabe and the upper red arc, are to the
South.
First, the Sun
After having aligned the pointer over the date, the position of the pointer over the
ecliptic circle roughly shows the position of the Sun. (A more accurate position of the
Sun can be found by using the date and zodiac scales on the back of an astrolabe,
revealed by pressing f8.) You
can see whether this point is above or below the horizon, using the lower red horizon arc
during the spring and summer months (March 21st to September 22nd, approx), otherwise the
upper red horizon arc.
By rotating the rete and pointer, you can move the zodiac scale around until the position
of the Sun on the zodiac is directly over the appropriate horizon arc. The pointer will
then point to the time of sunrise or sunset. If you align the pointer to a different
date, you can use the above technique to find the times of sunrise and sunset on that
date.
When the Sun is on the horizon, the parallel arcs (which descend from the top to the
bottom of the astrolabe) allow you to find the compass bearing (azimuth) of the Sun. (On
the upper horizon arc, South is in the centre, East is on the left and West is on the
right (assuming a 'heavens view'). On the lower horizon arc, North is in the centre.)
Details of finding the Sun's altitude when it is due South are given later.
Second, the stars
The outside edge of the astrolabe represents the equator. The positions of stars are
shown either by filled circles or open circles.
The filled circles represent stars which are North of
the equator and the open circles those to the South of it. Because the outside edge of
the device represents the equator, stars to the South of it have been 'reflected inwards'
and indicated as open circles. (If their positions were not reflected inwards, they would
have to be drawn outside the circumference of the astrolabe.)
Thus, close to the scale for June you can see three open circles, and close by are two
filled circles and two more open circles. These indicate the Orion constellation. The two
filled circles represent the two northern stars. The three open circles in a line represent the
three stars across the centre of Orion (his belt) and if not 'reflected' would otherwise
have to be drawn just inside the June scale, between the 10 and 20. The other two open
circles indicate the two most southerly stars of Orion which, without the reflecting,
would have to be drawn in the position of the 'hours' scale.
With suitable viewing conditions, you should be able to see the stars displayed above the
horizon lines. When indicated by a filled circle, stars should be visible if positioned above
the lower horizon arc, and when indicated by an open circle they should be visible if
above the upper horizon arc. The times when stars are on the horizon can be found in the
same way that you find the times of sunrise and sunset, and you can use the azimuth arcs
to find the compass bearing of the point on the horizon where a star rises or sets.
Altitude of the Sun or a star on the meridian
The meridian is the arc which goes from the northern point of your horizon up to your
zenith (the point directly over your head) and then down to the southern point of your
horizon. (The circle continues under the earth, but we are not concerned with that here.)
On the Equinoctial Astrolabe, the northern arc of the meridian is the straight line from
the centre of the northern horizon arc to the zenith point (which is the point where the
black arc crosses this line) and the southern arc of it continues from the zenith point
to the top of the astrolabe and then down to the centre of the southern horizon arc.
The altitude of a star can be found if it is above the horizon and is positioned on the
meridian. When the star has been drawn as a filled circle, count the horizon arcs from the
zenith (which is at 90.0 degrees) downwards to the star. When the star has been drawn as
an open circle, count the horizon arcs downwards to it from the outer diameter of the astrolabe
(90.0degs) and add your co-latitude (which is 90.0degrees minus your latitude).
(However, the meridian altitude of a star can be calculated more easily by adding 90
degrees to its declination and subracting your latitude.)
Finding the altitude of the midday Sun is similar. On the reverse side of the astrolabe,
(f8), find the position of the Sun in the Zodiac for the day in question, then rotate that
position on the ecliptic arc to be on the zenith. When the Sun is in Aries to Virgo,
count the horizon arcs downwards from the outer edge of the astrolabe (90 degrees) and
add the co-latitude (that it, 90.0degrees minus the latitude). Otherwise, count horizon
arcs downwards from the zenith (90 degrees) to the position of the Sun.
RA and declination
The point where Pisces on one ecliptic arc touches Aries on the other marks the position
on the equator of the First Point of Aries (FPoA) which is 0.0 hrs RA. If you rotate
this position on the rete to the 24.00 hrs (midnight) point of the scale, the RA of any
star can be found by subtracting the time indicated on the scale from 24 hours.
The concentric circles on the plate allow you to find the declinations of the marked
stars, zero degrees on the outside edge (equator) to +/- 90 degrees at the centre.
You can also use these techniques to find the position on the rete of stars which are not
marked.
The remaining arcs
It will be apparent from the above that only three of the horizon
arcs drawn on the plate are generally used at any one time. These
are the two which show the user's horizon and the one which shows
the arc from the east point on the horizon, through the zenith,
to the west point on the horizon. Similarly, the 'parallel arcs'
are only used to determine the azimuth of a celestial body as it
crosses the horizon, or the elevation as it crosses the arc
through the zenith. The only exception is that as a celestial
body crosses the vertical line down the centre, which represents
the arc from the south, through the zenith, to the north, the
remaining horizon arcs are used to determine the elevation. Other
than this, the other portions of the remaining arcs appear to
serve little purpose.
However, one can consider a rather strange coordinate system
whereby there are arcs radiating from the east, travelling to a
point which is so many degrees above either the north or south
point on the horizon, and continuing to the west. It is rather
like standing in the centre of an enormous transparent orange
whose segment outlines cross the sky from the east to the west.
Meanwhile, one can consider there to be other arcs which extend
from points on the southern half of the horizon to the northern
half of the horizon, marking the equal angles along these
segments. Using this rather weird 'orange segment' coordinate
system it would be practical to define the position of a
celestial body in the sky.
This orange segment coordinate system is indicated by the grid of
horizon arcs on the table of horizons, crossed by the parallel
arcs. (Well, only those arcs which are above the selected
horizon arcs need be considered, of course, unless you are
interested in the angle of the Sun beneath the horizon.)
When a star is over the crossing point of a horizon arc and a
parallel arc, it is possible to read the orange segment
coordinates.
These coordinates can now be converted to azimuth and elevation
by using a pointer over the plate.
Using the horizon arcs, count the number of degrees from your
actual horizon arc up to the appropriate orange segment arc.
Also, count the parallel arcs from the East or West point to the
appropriate orange segment coordinate arc. You will now have
two angles.
If you have a paper equinoctial astrolabe, position the plate so
that the converging points of the horizon arcs are to the left
and right. Raise the pointer from a horizontal position until it
is at an angle determined by the first of these coordinate
angles. Using the marks on the pointer (but not the declination
numbers printed on it) find the point along it which indicates
the second of these angles. Now, examine the arcs on the plate
underneath that point. Counting from the centre, the polar arc
shows the azimuth. Counting from the centre, the parallel arc
shows the declination.
Thus, using this technique with a table of horizons, you can
determine the azimuth and elevation of a celestial body at any
time of the day or night on any day of the year.
(Yes, you have used the universal grid to solve a right angle
spherical triangle. The angle of the pointer from the central
parallel arc shows the hypotenuse, and the distance along the
pointer from the centre represents an adjacent angle. The
crossing point shows the lengths of the two remaining sides, the
polar arc showing the side adjacent to the angle. Easy, wasn't
it! John Blagrave describes this technique for solving right
angled spherical triangles in The Mathematical Jewel (1585) bk 5
ch 4.)
I do not know whether this technique was used in earlier times to
determine the azimuth and elevation of a celestial body when it
was over the crossing point of a horizon arc and parallel arc on
a table of horizons. However, I would be surprised if it had been
overlooked, particularly by the tenth century instrument makers
of Moslem Spain.
|
