HOW TO BUILD A
Giorgio Carboni, June 1996
Translated by Enrico Bovalini and revised by Don Stauffer
||In this article, we talk about the construction of a sidereal pointer. It is an instrument that allows you to localize each celestial object in the night sky, just knowing its coordinates. Television, newspaper and also astronomy magazines, often tell about heavenly objects given their position in an imprecise or in a few comprehensible manner. Since the position of the celestial bodies is precisely defined on the basis of the celestial coordinates system and since there exist astronomy books which bring this values, why do not build an instrument which help us to locate every body in the sky? Therefore, let us build a simple tool which help us walking among stars without getting lost. It will drive us in the astronomic observations at naked eye, with binoculars and with all optical instruments without equatorial mounting, as most of the selfconstructed telescopes. This instruments will be very useful also for learning to recognize the constellations, to locate the celestial bodies not visible to the naked eye, to track comets of which astronomers give you the coordinates, etc. It will be useful also to know in which direction is the center of our galaxy, and to find out other major celestial points. This know-how, will help you to locate yourself in the space and to tighten a new and more awake relationship with the Cosmos.
THE CELESTIAL COORDINATES SYSTEM
For some aspects, the system of celestial coordinates (fig. 2) is similar to the Earth one. Like this, it is formed by meridians and parallels. The two systems have in common the polar axis. In fact, the apparent rotation of the celestial vault is due to the rotation of the Earth on itself. The Earth's axis points toward the Polar Star, hence the celestial vault spins around the same star. In virtue of the coincidence of the terrestrial axis with the celestial one, also the equatorial plane of the Earth and the celestial one coincide. Like the terrestrial ones, also the celestial parallels go from 0° (at the equator) to +90° (North celestial Pole) and - 90° (South celestial Pole).
And so, which are the differences? Mainly, they are the followings: the earthly meridians are affixed to the terrestrial surface, while those celestial are "to" the starlight vault. In this way, as in the earthly system a city has always the same coordinates , in the heavenly system a star has always the same coordinates . These coordinates are called longitude and latitude in the terrestrial system, right ascension (R.A.) and declination (D) respectively in the celestial one. This is widely true for us, also if the coordinates of these objects may change a bit during the time. In fact a city, "floating" with the Earth crust, because of the convective motions of the mantle which stand below, may vary its own position. In a similar way the stars, for their own motion, and for the change of the inclination of Earth's axis, which tracks a circle in the sky in 26,000 years, change their location too. For us, who are not professional astronomers, these changes are so little to be negligible. Another difference among these two systems of coordinates is that we count the terrestrial meridians in degrees, while the celestial ones in hours. And so we have 24 main meridians, each of which divided in minutes and seconds. The declination, instead, is measured in degrees, like the latitude.
STRUCTURE AND WORKING WAY OF THE POINTER
The sidereal pointer (fig. 3 and 4) is made by 2 axis, the first one carrying the hourly disk (for the right ascension), and the second the angular disk (for the declination). The 2 axis are orthogonal, and so also the 2 disks that they carry on are at 90° apart. On the declination disk is fixed a little plate, with two sharpened screws. We point the stars using them, just like a rifle. On each disk is glued a graded quadrant, that allows you to orient and direct the pointer. Then there are 2 indexes, one for each quadrant, and there are also some clamps to block one disk or the another.
The whole instrument is hold by a fork, that can be mounted on a photographic tripod. You can fabricate the fork by cutting a piece of draw steel "C" shaped, or folding a steel bar (# 6 x 25 x 250 mm). Both the trees are made of rectified steel (diameter 10 mm) and each one revolves on two elastic bushes. You can easily find in warehouse of semi-manufactured steel, bars of rectified carbon steel. A whole bar, 4 meter long and with a diameter of 10 mm, costs about 3 $.
You can buy the 4 needed bushes in an industrial equipment shop. If they are not open, you have to engrave it along a generatrix. The supports where are fitted two of the bushes, are elastic too, and regulated by screws. You can obtain them from an aluminum bar with a section of 12 x 25 mm.
At the top of each tree, there is a plastic flange for the connection with the respective disks.
The disk of the declination is made of a plastic plate 4 mm thick. Its external diameter is 120 mm. The disk of the ascension is made of a plastic plate 4 mm thick. Its external diameter is 140 mm. Notice that this disk is free to move, and it can be blocked only by the lateral brake. The color of the disks should be black, to reduce the reflex on the pointer of the light of the flashlight illuminating the "pointing" screws. The index disk, instead, is in a transparent plastic plate (Plexiglas), 4 mm thick and with an external diameter of 136 mm.
||The pointing system is made of a strip of black plastic, 4 mm thick, bearing two sharpened screws. You can obtain the index of the declination quadrant from a stripe of aluminum 2 mm thick, suitably folded. The index of the declination quadrant is under the "index disk". This is a transparent disk which is mounted on the ascension disk in a coaxial way. Under the index disk, you have to trace a thin radial groove, using a metallic point. This groove, filled with Indian ink, will be the index of the hourly circle. This disk must be orthogonal by rapport to the declination tree.
To glue the quadrants, you may use an aerosol bomb of transparent varnish for cars, and you may use it also to cover the quadrants with a thin, protective transparent layer. Before gluing, take a roll of rubber or plastic, to expel the air bubbles and the varnish in excess.
Most of the mechanical working can be hand - made using common bricolage tools. Some of them, instead, must be made using a lathe. To do these you can ask a turner. You will need the lathe to prepare the angular disk, the hourly disk, the index disk, the 2 flanges and the counterweight. This parts are to be worked just on the external and internal diameters. This is a little work, and so it will not be expensive.
SETTING THE POINTER
When the contruction of the pointer is ended, before using it, you must set it. For making this, look at the figure 5 and follow its instructions.
ORIENTATION OF THE POINTER
It is night. You are in a dark place, without lights. You can easily see the stars in the sky. You have taken with you the pointer, the tripod, the flashlight with a red filter, the maps of the constellations, the coordinates of the celestial objects that you want to find out. The flashlight is necessary to read the coordinates on the maps, and to bring some light on the quadrants and on the screws of the pointing system. The reflex of the flashlight on the screws tips will help you to point the instrument towards the sky.
ORIENTATION OF THE MAIN TREE
In order that your pointer be able to work, it is before necessary to refer it to the celestial coordinates system. The first thing you have to do is to orientate the main axis (the R.A. disk tree) towards the Polar Star. After the setting of the pointer, if you adjust the declination at 90°, the line passing through the pointing screws is parallel to the main tree. Hence to orientate it towards the Polar Star you have to:
- put the declination scale at 90°
- point to the Polar Star, moving the tripod head
- fix the head of the tripod
- verify that the declination is still 90°
Since then, never move the tripod or the main axis of the instrument. Now, the main tree is pointing the Polar Star and the plane of the R.A. disk is parallel to the terrestrial and celestial equatorial plane. The declination quadrant is oriented. You just have to refer the R.A. quadrant to the celestial meridians. At this moment you are already able to observe where the heavenly equator passes (***lies) in the celestial vault. For making that, bring again the declination scale at 0°, and rotate the pointing system around the main axis.
ORIENTATION OF THE RIGHT ASCENSION SCALE
Now you must refer the right ascension scale to the celestial vault. Choose a star that you can recognize, and of which you know the coordinates. For instance the "Eta" star of the Ursa Major, or the "alpha" of Cassiopeia (in figure 6 you can see the coordinates of these stars and the maps of their constellations). Why these constellations? Because we can always see them at northern latitudes and never set. People living in the austral hemisphere have other constellation which do no set. Instead, people living near the equator, between the two tropical parallels, can refer to equatorial constellations, as we will see later. Ursa Major and Cassiopeia are one opposite to the other, in respect to the Polar Star, and so if one of these is low on the horizon an can be hidden from haze, the other one will be high, and so at least one of the two will be always visible at night.
Why these stars? Because they have the lowest declination among the brighter stars of these constellations.
To orientate the R.A. scale, you have to:
- point the instrument to the star you have chosen, moving the ascension and declination disks
- tighten the clamp of the main tree (so you fix the index disk)
- rotate the ascension scale to the value of the ascension of the star
- fix the ascension scale with its clamp
- finally, unlock the index disk.
Now the instrument is oriented: both scales are referred to the celestial coordinates system. A problem with these constellations is that they have a high declination, and so, referring to them of the ascension disk, may be your pointer is affected by a quite large error. To improve the precision of the orientation of this scale, you can use constellations closer to the celestial equator.
IMPROVING THE REGULATION OF
THE RIGHT ASCENSION SCALE
The first orientation you made is sufficient to find the star that you will use for a better regulation. Some constellations easy to recognize and useful for this purpose are the following:
- set on the scales the coordinates of the star of the constellation you have chosen (figure 7)
- the instrument will point quite close to that star, so you can identify it. With the map of the constellation, verify that it is the right star. Usually, you will find out an error in the pointing
- point the instrument exactly towards the star you have chosen
- lock the index disk
- unlock the ascension scale
- adjust the ascension disk on the value of R.A. of that star
- lock the ascension scale
- write the time (later I will explain why)
- unlock the index
For better clarity, let us summarize what you made:
You pointed the ascension tree of the instrument towards the Polar Star; you oriented the R.A. scale with a star of the Ursa Major or of the Cassiopeia. With this imprecise regulation, you have found a star near to the celestial equator and you rectify the orientation of the ascension scale to the celestial meridians.
USING THE POINTER
Now the instrument is ready to indicate you any celestial body, whose coordinates you know. Its use is extremely easy: just regulate the scales at the coordinates of the celestial body, and the pointer will show where it is placed in the sky. To see the screws in the dark, you may use an flashlight with a red filter, holding it 1 meter far. The reflex of this light on the tips of the screws will appear like a star, and so you will have two shining points that will drive you in the sky.
This instrument has an error of some tenth of degree. It can be interesting to know that Ipparco from Nicea, astronomist of the Hellenistic age, about 2.100 years ago was the first man to determine the position of the stars in the sky, and made a catalogue with the location of 850 stars. This job let him discover important things, such as the precession of the equinoxes. Once found your target, you can look at the celestial body with the naked eyes, or a binoculars or a mirror-telescope.
While you are doing all these maneuvers, the celestial vault keeps rotating at the speed of about one degree every 4 minutes. So the pointer fastly loses its reference to the celestial meridians. Never mind! If you set the instrument at 10 p.m. and at 10.15 you would like point out a star, you just have to subtract from the right ascension (R.A.) of the star the 15 minutes elapsed since the orientating of the pointer:
R.A.' = R.A. - et (where et = elapsed time since the orientation of the pointer)
and don't tell me that it is difficult!
There is another little error to consider: the sidereal day is 3' 56" shorter than the solar one, and so if you use the pointer all night long, at dawn you will have an error in the right ascension of one minute and a half. If you multiply this 3' and 56" for the 365 days of the year, you obtain another day which is the one that the Earth "loses" with an entire rotation around the Sun. In other words: by rapport to the Sun, the Earth make about 365,25 rotations in a year, whereas by rapport to the stars the Earth make a rotation more.
This little instrument will be very useful for many astronomic observations, even with the naked eye. Figure 8 gives you the coordinates of some important celestial points and of some interesting objects to observe. Among them there is the famous Galaxy of Andromeda, a nebula of such magnitude that you can observe it with the naked eye or a binoculars, while you can observe the other ones only with instruments with large aperture. However you can scarcely perceive Andromeda because of its low brightness. In any case, its light voyaged for 2 million of years before attaining the Earth! Other objects that can be observed with low aperture instruments are clusters of stars, such as the Pleiads. We give you the coordinates of central star of the elegant constellation of Cygnus as an example of how you can use this instrument for recognizing constellations.
An interesting point to find is the center of our Galaxy: R.A. = 17h 42' 30" D = -28° 59' 18"
Another interesting point is the famous "gamma point" with coordinates R.A. = 0 D = 0. This point is placed at the intersection of the equatorial plane with the ecliptic one (the plane on which lies the orbit of the Earth around the sun). This point is considered as the reference of the celestial coordinates system.
Pointing the main tree of the instrument towards the point with coordinates R.A. = 18h 00' D = 66° 34', the ascension plane will be parallel to the ecliptic one. On this plane are placed most of the planets, and the constellations of the Zodiac run one after the other in a majestic ring-a-ring-a-roses. As they are placed at 30° one from the other, after localizing the first one, all the others are quite easy to find with the pointer. Furthermore, on the ecliptic plane takes place the apparent motion of the Sun on the celestial sphere. When the Moon is moving on the ecliptic, its shadow may run on the Earth, and so who comes under it sees the Sun darken: it is an eclipse.
The coordinates of the constellations of reference and the one you can find in figure 8, are enough to set the pointer and to do a deal of observations. You can find maps of constellations and the coordinates of many interesting celestial bodies in astronomy text books, such as the one in bibliography, which is cheap and very well done. With this book and the sidereal pointer, you will be able to localize all constellations you want, and at least learn to recognize them. In addition, this book gives you many other interesting information that will satisfy your curiosity and your desire to learn something more about astronomy.
As planets move by rapport to stars, they have not fixed coordinates. To find the planets, are useful the so-called "ephemeris almanacs", published yearly, and that you can find in any book-shop. Those almanacs also report the position of little planets and close comets. Remember that, if the instrument is pointing under-Earth this does not means that it is wrong: it is right, and the object is in that direction!
In his simplicity, the pointer is really useful: it is a valuable guide to astronomy, and constructing it you have done an interesting exercise of mechanics and physics in building an equatorial mount. Furthermore, you have learnt how it is organized the celestial coordinates system and you have found in which direction is the center of our Galaxy. One of the major qualities of astronomy it is not so much to show far objects, as is to drive us to reflect about ourselves, our condition, the sense of life and the whole.
Patrick Moore, The Guinness Book of Astronomy, Guinness Publishing,1988