Keith's Spherical Astrolabe

Unfortunately, there is no active display for the spherical astrolabe. To study it you must construct one, printing out the four displays provided here. Fortunately, this is not difficult.

The astrolabe you will make will consist of two spheres - a transparent sphere which rotates over a paper sphere. The paper sphere has a scale around it showing the time as on a 24-hour clock, whereas the transparent sphere has a scale around it showing the months and days through the year. To use it, you rotate the transparent sphere over the paper sphere to align the current time with the current date. You then position the astrolabe so that the horizon circle around the paper sphere is level, and the northern point on the horizon circle is to the North.

Now, if you imagine a line from the centre of the astrolabe through any of the stars shown on the transparent sphere, and continue that line to the sky, it points directly to that star! Similarly, a line from the centre through the current position of the Sun on the ecliptic circle points to the Sun in the sky. The effect is truly magical!

Of course, all of the other tricks of using an astrolabe are applicable. Finding the North, the time (equal or unequal hours), or identifying a star are intuitive. When the astrolabe is correctly aligned, it is easy to imagine that a pin will cast a shadow directly over itself if pushed into the transparent sphere at the current position of the Sun on the ecliptic circle. Another way of putting it is: breath-taking!

To help you to construct a spherical astrolabe, this program provides a set of four displays. These displays can be seen by using the menu system, by clicking on the Spher+ button four times or by pressing 's' or 'S' four times after which this series of displays repeats.

To make a spherical astrolabe, first set your latitude and select a suitable window size. Then, print and cut out each of the four displays, using paper (thick paper if possible) for the first two displays (the body) and transparent film for the other two (the rete).

These components are then assembled over a thin rod to form two spheres, one over the other, using suitable spacers. (Assembly details are given below.) After assembly, the paper sphere can be seen through the encircling transparent sphere. Because the transparent sphere is slightly larger than the paper sphere, it can be rotated into a suitable position with respect to it.

Requirements

The two 'body' displays (front and back) should be printed on paper. If you have it, it is better to use thicker paper rather than 'photocopy' quality paper.

The two 'rete' displays (front and back) should be printed on transparent film. In Britain, transparent film is sold at office stationers and at shops stocking computer supplies. The packaging indicates that it is intended for overhead projectors. Ensure you purchase the correct type for your printer (ink jet or laser). If your printer driver supports it, you may want to select the option whereby printing on the transparent material is a mirror image of that seen on the screen. This allows the printed side to be on the inside of the transparent sphere.

You will also need a thin rod on which to assemble the astrolabe. A large paper-clip which has been straightened out is suitable, provided that its length when straight is at least 25mm (one inch) longer than the overall length of the 'diams' diagram which you will see printed at the side of the four displays. I commonly make prototype spherical astrolabes which are about 10cm (four inches) in diameter, and for these I use a paper-clip which is initially about 4.5cm (one and three quarter inches) long, which becomes about 16.0cm long (six and a quarter inches long) when straightened.

Finally, apart from a piece of paper which you will roll to make spacers, you will need transparent adhesive tape and a broad elastic band - say, 0.5cm (quarter of an inch) wide, and a stand.

A 'stand' on which to place your astrolabe isn't essential - you can probably rest your finished astrolabe on a coffee cup. However, it is worth while cutting two long strips, perhaps an inch wide, from the unused portion of the transparent material. These two strips can be taped together, overlapping, to construct a circular band, perhaps about three-quarters of the diameter of your spherical astrolabe. This band makes a suitable stand on which to rest your spherical astrolabe.

Construction

Make holes at the points you will see within the circles at the top and bottom of each of the segments. Ideally, the holes in the transparent rete should be slightly larger than the rod. I make a hole with a pin, and then make the hole slightly larger by pushing a short, thin nail through the hole.

You now need two tiny 'outer' spacers plus a longer spacer which is almost equal in length to the diameter of the body sphere. These are cut from a tube made by loosely rolling a wide and long piece of paper, say 15cm by 15cm (6 inches by 6 inches) as tightly as is practical round and round the rod. Cover this tube in adhesive tape to keep it in the shape of a thin cylinder. From this tube, cut off two short pieces each about one millimetre (a sixteenth of an inch) in length which will be used as outer spacers. Then trim the remainder of the tube to be a couple of millimetres (an eighth of an inch) smaller than the size indicated by the inner marks of the 'diams' diagram.

Cut the elastic band to make four rectangles of elastic, perhaps a centimetre long and half a centimetre wide (half and inch long, quarter of an inch wide). Fold each length in two and make a tiny cut in the centre of the fold (I use scissors to make the tiny cut). These elastic spacers will be used over the rod on either side of the ends of the paper sphere so that the paper sphere doesn't rotate around the rod.

To assemble the astrolabe, push the long spacer over the rod, and push an elastic spacer over each end of the rod. Using the holes you have made, push the segment ends of the paper sphere over the rod in the order indicated within the circles. You should finish with a close approximation to a sphere. Now push the other two elastic spacers over the ends of the rod followed by the small paper spacers. Finally, thread the segments of the transparent sphere over the rod in the order indicated by the numbers so that the transparent sphere encloses the paper one. You shouldn't need anything else on the rod to keep the transparent sphere in shape.

Bend over one end of the rod so that you have something to hold when you are rotating the transparent sphere into position.

Your spherical astrolabe is now ready for testing.

Using the Spherical Astrolabe

1. Holding one end of the rod, rotate the rete until the position of the current date on it is aligned with the current time on the body, the scales for these being shown along the 'equators' of the two spheres.

2. On the body, find the point at which the blue lines cross. This point represents your Zenith, the point in the sky which is directly over your head. These lines start at a circle around the body, this circle representing your horizon.

3. Place the astrolabe on its stand (a mug, perhaps) so that the Zenith is uppermost and the horizon is horizontal.

4. Rotate (orientate) the astrolabe and its stand until the N, S, E and W printed along the horizon circle are precisely in the directions of North, South, East and West.

The rod will now be pointing directly towards the North Star, Polaris.

5. You will see that the transparent sphere around the body shows the positions of several stars. You will recognise Ursa Major (the Great Bear /Plough /Big Dipper) and Cassiopeia (a 'W' shape) close to the rod, which emerges at the position of the North Star, Polaris. The celestial equator is shown in black. The ecliptic circle is shown in red.

6. A line from the centre of your spherical astrolabe through any one of the stars shown on the transparent rete will point directly to that star in the sky. Magic!

7. The point on the ecliptic circle which is closest to the alignment point of the time and date shows the position of the Sun. A line from the centre of your spherical astrolabe through this point on the ecliptic circle will point directly towards the Sun. Magic! (Any slight misalignment will be due to the Equation of Time.)

8. Blue lines on the body indicate your elevation and azimuth. Currently, these are only shown at intervals of 30 degrees because more lines proved to be rather confusing. One day, perhaps I will try 15 degree lines between these in green...

Coordinates

Similarly, if the latitude is set to 66.6 degrees, (90 degrees minus 23.4 degrees) the resulting spherical astrolabe will have the ecliptic circle and ecliptic pole of the rete directly over the horizon circle and Zenith on the body. In this case, the azimuths and almucantars on the body can be interpreted as circles of ecliptic longitude and ecliptic latitude, allowing the ecliptic longitude and latitude of the stars on the rete to be read directly.

Unequal Hours

Beneath the horizon circle of the spherical astrolabe are green lines. These can be used to determine the time by the 'unequal hours' system.

Set the astrolabe by aligning the rete over the body according to the time (ideally, this should be local time) and date. Find the position of the Sun. If it is daytime, look underneath the astrolabe and find the point on the ecliptic circle which is directly opposite the position of the Sun. This position can now be used to read the unequal hours time from the green unequal hour lines. At night time, use the same procedure except that you will use the position of the Sun to determine the unequal hours time directly.

The surviving spherical astrolabe

Unlike the one you can make from the displays provided here, the spherical astrolabe in the museum is universal. A line of holes at 2 degree intervals was provided from the Zenith to the horizon on the body. A short rod was pushed through the celestial pole of the rete, and this rod was then inserted into a hole in the body. By selecting the hole for this pivoting rod, it was possible to set the astrolabe for any even latitude.

Normally, a vertical rod through the body would hold it in position with the Zenith uppermost. When it was to be used, it would be accurately aligned with the North, so that the short rod through the celestial pole on the rete was precisely in the direction of the celestial pole in the sky.

As with the 'paper' version, when the body was correctly orientated and the rete correctly aligned, a line from the centre of the astrolabe though one of the star pointers would point directly at the star in the sky.

An alignment 'ring' for the Sun's rays can be slid along a scale on the rete between the tropics of Capricorn and Cancer. This ring has a hole at the top like a ring dial. With an appropriate alignment, the rays of the Sun passing through this hole can be seen to fall centrally on the opposite side of the ring. After the ring had been slid to an angle corresponding to the current declination of the Sun, the rete would be rotated until the Sun's rays fell precisely through the hole. The position of the ring over the body would then indicate the azimuth and elevation of the Sun. The point on the body which was directly opposite this position was then found. (This was an operation which would require the repositioning of the rete.) This point would indicated the time among the unequal hours curves.

Above, it was indicated that by printing and constructing a 'paper' spherical astrolabe having a latitude setting of 90 degrees, it would be possible to use the azimuth and almucantar markings on the body to read the RA and declination of the stars. This was also the case with the medieval spherical astrolabe, of course, although presumably the short metal pin wouldn't be necessary because the rete could be positioned over the rod through the centre of the body.

Similarly, it was a simple matter to set the 'latitude' to 66.6 degrees because a silver indicator on the medieval astrolabe showed this position. Such a setting would have allowed the ecliptic latitude and longitude of the 19 star pointers to be read directly.

Comments

Currently, the design is not particularly well executed. For instance, in many places I have drawn straight lines where I should have drawn arcs. The drawing of the unequal hour lines is not particularly well executed, especially when the astrolabe is set for latitudes above 58 degrees. Similarly, the drawing of the elevations is rather messy. Finally, I have plotted everything assuming that the segments are curved rather than being flat. I hope these short-comings do not distract you from the magic of the device.

The idea of a paper spherical astrolabe was the result of a chance remark by Vit Planocka who mentioned the mathematical principle used here to construct a sphere from sections.

Have fun!