Java applet page:
displayed with my Java applet.
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.
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.
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 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 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.
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.
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 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.
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.
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.
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.
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.
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.
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.
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.