HOW TO BUILD A
Giorgio Carboni, June 1996, updated in February 2004
Translation edited by Robert May
Figure 1 - The Sidereal Pointer is an instrument that allows you
In this article, we deal about the construction of a Sidereal Pointer (Indicator?). An instrument that allows you to localize celestial objects in the nightly sky, just knowing their coordinates. What can be the use of this instrument? Firstly, it can help you to learn to know the constellations. It can help you also to locate in the sky the position where point your telescope to observe an object invisible at naked eye, like a nebula or one of the heavenly bodies called "Messier Objects".
Since television, newspapers and often astronomy magazines give the positions of heavenly objects only imprecisely and the position of the celestial objects are precisely defined on the basis of the astronomical coordinate system and since there exists astronomy books which contain these values, why not build an instrument which can help us locate every body in the sky? Thus, let us build a simple tool which help your walking amongst the stars without getting lost. It will guide you in the heavenly observations with the naked eye, with binoculars and with any optical instrument that don't have an equatorial mount, such as most of the homemade telescopes fail to have. This instrument will also be very useful for learning to recognize the constellations and locate the celestial objects not visible to the naked eye, to track comets of which astronomers give you the coordinates, etc. With this instrument, you will also be able to track on a star map the path of planets and comets. It will also be useful to know in which direction the center of our Galaxy is, and to find out the other major celestial points. This knowledge will help you to locate where you are and to obtain a new and more aware relationship with the sky.
This instrument, which was once known as a Torquetum, was first described by the ancient Greek scientist Ptolemy. Subsequently it seems this first model was perfected or reinvented by an Arab astronomer in the XI or XII century. Then, it has been used by several European astronomers since the XIII century. We will describe two models adapted to modern and quite simple enough construction.
THE ASTRONOMICAL COORDINATE SYSTEM
In certain respects, the astronomical coordinate system (figure 2) is similar to the Earth's coordinate system. Like it, 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 itself. The Earth's axis points approximately toward the Pole Star, hence the celestial vault spins around that same star. By the defined virtue of the coincidence of the terrestrial axis with the celestial one, the equatorial plane of the Earth and sky also approximately coincide. Like the terrestrial ones, the celestial latitude goes from 0° (at the equator) to +90° (North celestial Pole) and -90° (South celestial Pole).
What then are the differences? Mainly, they are as follows: the earthly meridians are "integral" to the terrestrial surface, while celestial ones are "integral" to the starry vault. In this way, as in the terrestrial system a city has always the same coordinates, while 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 astronomical ones that are used by astronomers.
It is widely known that the coordinates of these celestial objects may change a bit over time. In fact a city, by "floating" with the Earth's crust, due to the convective motions of the mantle that are below, may vary its own position. In a similar way the stars, due to their own motion, and due to the change of the inclination of Earth's axis, which tracks a circle in the sky in 26,000 years of time, change their location too. For us, who are not professional astronomers, these changes are so little in size as to be negligible. Another difference among these two systems of coordinates is that we count the terrestrial meridians in degrees, while the celestial ones are counted in hours. So we have 24 main astronomical meridians, each of which divided in minutes and seconds. The Declination is, instead, measured in degrees, like the latitudes of the earth.
By convention, the origin of the astronomical coordinate system has been placed at the intersection between the ecliptic plane (the plane of the terrestrial orbit around the Sun) and the plane of the heavenly equator that occurs in the spring equinox. This "0" meridian of the astronomical system passes by this intersection at that time.
THE FIRST POINTER DESIGN
We will see how to build two Sidereal Pointers in the following sections. The first is a simple instrument, made of cardboard, wood and plastic (figure 4), while the second is built of more substantial metal, thus more precise and lasting , but also more difficult to fabricate. Before we start, this article was originally written in Italian so all of the measurements are done in the Metric system. As such, equivalent inch dimensional stock can be used without any problems.
Figure 4 - The first Sidereal Pointer.
A Sidereal Pointer (figure 4) is made by 2 disks that are held 90° relative to each other. The first one carries the Right Ascension scale, and the second the Declination scale. In order for the instrument to work correctly, the R.A. disk has to be parallel to the equatorial plane. In this way, its axis is parallel to the Earth's axis of rotation and, as such, it's axis points toward the Pole Star (figure 5). The Declination disk has to be orthogonal to that of the R.A.. In this way, its divisions will correspond to the celestial parallels. The R.A. disk is also called the hour disk and the Declination one the angular disk.
You can build Pointers with techniques and materials different from those if you so desire. In any case, the scales of the Pointer must be oriented according the astronomical meridians and parallels. If you understand this concept, the construction of this instrument will be much easier for you.
The fact that the Pointer is not placed in the center of the Earth, but on its surface, could generate parallax errors with near objects however, due to the enormous distances of the asters from the Earth, this problem really does not exist.
Now let's see how to build the first Pointer. Figure 4, shows the basic design of the first Pointer. Its scales are in heavy paper (cardboard or cardstock), the plane of the scale of the Right Ascension is in plastic, the base of the instrument and the support of the scale of the Declination are in wood. It could be simpler to make the whole Pointer out of cardboard, but in a short time its structure would inevitably be deformed by its own weight. In order to allow the instrument to last longer and to be more precise, I make some parts with stiffer materials, like wood and plastic. Let's start the construction of the Pointer with it's base.
As the figures 6 and 7-A show, the base is formed by the pedestal, the plane for the R.A. scale and it's supporting leg. For the pedestal, use a board in wood or in chipboard. This board should have a certain weight in order to give a good stability to the instrument. Apply 4 felt feet under the board corners.
A suitable material to make the supporting plane for the R.A. scale is a 5 mm thick plastic plate. Fasten it at its base by means of two hinges, so its slope can be adjusted. On the lower side, again using a hinge, fasten the leg. The length of this leg changes as a function of the latitude where you will tend to use the Pointer. Give this leg a suitable length, then, by means of a little plastic plate, stop it in such a position that the corner between the R.A. plane and the pedestal is equal to 90° minus the latitude of the observation point (figure 7-A). With a square check this value. On this scope, you can also use another copy of the Declination scale to indicate the angle of the R.A. plate with the scale suitably supported so that you can read the angle. At this point, the R.A. plane will be close to parallel with the equatorial plane, and its axis will be close to parallel to the Earth's axis.
On the piece on which the R.A. scale will be put, trace a orthogonal (time) line to the base of the plane and which passes on the center of rotation of the scale as shown in figure 7-B, (red line). I made this line with red color for clarity in the drawing. As the background is black, make this line with white color (figure8).
Figure 6 - Base of the Pointer. Notice the hinges, the leg, the stop for the leg and the screw on which the R.A. scale rotates.
I designed this base for the temperate latitudes of the northern (boreal) hemisphere, where most of inhabitants of our planet live. For our friends in the south, the absolute angle will be the same and you will be pointing to the southern pole. In any case, the length of the leg has to be fitted to the latitude of the observer. If you desire, you can make the leg adjustable if you normally change latitude a lot. For the artic and equatorial regions, more radical adaptations to the base of the Pointer will be necessary to point the Pointer in the right direction. In order to orient the instrument in the southern hemisphere with circumpolar constellations, you will have to refer to different constellations than those I indicated to you. The equatorial constellations will work well for those of you in the equatorial regions.
CONSTRUCTION OF THE POINTING DEVICE
Let's define the pointing device as all the parts that are placed upon the plane of the R.A.. By using little wood boards, build the support of the scale of the Declination as shown by the figure 7-A.
The main components of this instrument are the scales. Due to the difficulties of drawing them, I supply them already made for you; I made these drawings with a program for mechanical design and I saved them as a ".gif" image. To give precision and clarity to the marks, I gave these drawings a high definition. For this reason, you will see them rather big on the monitor, but do not worry because they can be printed in the needed size. The same is valid for the indexes drawings.
Downloading the drawings.
Click on: "scales of the 1st Pointer design" to open the drawing. Then save it on your hard disk or on a diskette. Make the same for the drawing of the
Then save it on your hard disk or on a diskette by pressing on the right button of the mouse (a suitable little window will be opened). Make the same for the drawing of the "sight".
Resizing the scales.
It is necessary to adjust the print parameters in order to obtain the scales in the right sizes. With a suitable software for image editing, open the drawing of the scales and resize it as follows:
- height = 2204 pixels;
- height = 19 cm or = 7,471 inches;
- width: = it is automatically resized (keep the ratio);
- resolution = 116 px/cm or = 295 px/inch.
Do not save the drawing when you have resized it or give it another name if you wish to save the image! You do not want to overwrite the original file.
Printing the scales
Before you print the scales, deactivate the function that fits the image to the sheet. Insert in the printer a sheet of heavy paper or cardstock. Chose the horizontal direction of printing and print. Check that the size of the scales you obtained are right. If there are some little changes in the size, there will be no problem. The important is you process also the drawing with the sight with the same procedure, so to obtain prints with the same scale. If you do not succeed to obtain prints with the right sizes, change the program you have for image editing.
Figure 8 - R.A. index. You can do it also in metal or in plastic.
Resizing and printing the sights
The resolution of this drawing is a half of that of the scales, so it is necessary to again resize it as follows:
- height = 1102 pixels;
- height = 19 cm or = 7,471 inch;
- width = it is automatically resized;
- resolution = 58 px/cm or = 148 px/inch.
Put two A4 sheets of heavy paper or cardstock, as you did with the scales, in the printer. Chose the horizontal direction of printing. Print two copies of the sights. Check that the size you have obtained is the right one.
Cutting and mounting the scales
- Cut the figures, following the external borders;
- with a 4 mm hand punch, make the holes;
- glue the small R.A. index to its support (figure 8);
- mount the R.A. scale on its plane;
- mount the Declination scale and clamp it moderately by its screw;
- adjust the orientation of the Declination scale so that the line which goes from -90 to +90 is parallel to the R.A. plane;
- glue the Declination scale to its wooden support;
- do not glue the R.A. scale to its plane, but let it free to rotate;
- glue together two copies of the sight, by keeping its upper part open, as shown in figure 4. The little "V" channel that emerges will help you to locate heavenly objects and will make the sight more rigid as a pointing device. I called this little channel the "Pointer.
ORIENTING THE FIRST POINTER
The Pointer is now basically finished, but before you use it, it is necessary to orient it according to the astronomical coordinate system. The operations I will describe in the following have to be made by night and with a good visibility of the starry sky. You have to bring with you the Pointer, a clock, a calculator, a flashlight with a red filter, the maps of the constellations of this article, the coordinates of the celestial objects that you want to look for. The flashlight is necessary to read the coordinates on the maps, and to bring some light on the scales. When I will say to observe in the inverse direction, it merely means that you have to see in the opposite direction of the arrow of the sight.
To orient the instrument and the Declination scale:
- put the instrument on a table;
- with a level, check the level of the table and if necessary, level it;
- align the instrument in the north-south direction, so that R.A. axis points to the Pole Star and the sight looks toward south;
- set the R.A. Index on the reference line on the R.A. plane (figure 7, red line);
- set the Declination index in the -90° position;
- looking in the inverse direction, rotate the base of the instrument so that the sight points to the Pole Star;
- if it is necessary, adjust also the slope of the R.A. plane.
At this point, the scale of the Declination should be oriented. From now on, do not move the base any more, but limit yourself to rotating the pointing device on the scales. From now on you use the instrument looking in the normal direction (in the arrow direction).
Orienting the R.A. scale to the heavenly meridians:
- chose a suitable star among the constellations near the equator as I indicated in table 1 and in figure 16;
- by rotating the pointing device on the scales (do not move the base of the instrument!), point the sight to the star you have taken as a reference;
- now, by keeping the R.A. Index still, rotate the scale of the R.A. until the value of the Right Ascension of this star is in correspondence with the index. With a hairpin or a piece of double sided adhesive tape, stop the R.A. scale. Do not move this scale during the night of observations;
- verify that the instrument points again to that star.
At this point, also the R.A. scale is oriented to the astronomical coordinate system.
HOW TO USE THE FIRST POINTER
The instrument is now ready to be used. It is simple to use: just bring the two indexes to the values of the coordinates of the of celestial body, and the Pointer will show where it is placed in the sky. While you pass from one star to another, the celestial vault will continue to rotate and your Pointer will quickly lose the reference to the heavenly meridians. Don't worry! Imagine you oriented the instrument at 22 o'clock, if at 22 hours and 15 minutes, you want to locate an object, subtract from the R.A. of the object the 15 minutes that elapsed from the orientation of the R.A. scale or:
R.A.'= R.A. - td
where td is the time difference between when you set the R.A. dial and the present time.
Let's do an example. If after 22 minutes of time since you oriented the Pointer, you want locate Cygnus g (gamma), a star of the constellation of the Swan, you have to subtract 22' to its R.A and bring the index of this scale to this new value. The Declination isn't modified with time so it's value isn't changed.
At this point, I wish you to have a good time with your Sidereal Pointer! In the paragraph: "Observations", you will find some information to try with the instrument and to do some first observations. In the bibliography, I indicate an astronomy text that gives the coordinates of thousands of stars and other heavenly objects, as well as a lot of interesting information about them. This book can act as your guide during your observations, just as if you would to have an astronomer at your side.
Due to the design of the pointer, you will not be able to point to the stars located between the zenith and some degrees northward. The second Pointer has been designed so to avoid this problem and it is for this reason it has to be mounted on a tripod. To also avoid interference between the pointing device and the R.A. plane, the scale of the Declination and the sight have been brought on the side. However, you can still see a wide portion of sky to be observed with this first design of the Pointer.
According to the following article, with only a little change it would be possible to use this instrument with the three sets of astronomical coordinates: horizon (alt-azimuthal), equatorial, and ecliptic. The equatorial one is the one I have chosen for this project.
The second Sidereal Pointer (figures 9, 10 and 11) is made up of two shafts which carry the Right Ascension and the Declination disks. As we saw in the first design, these two disks must be at 90° apart. On the Declination disk, there is fixed a small plate with two sharpened screws that serve as the pointer. On each disk is glued a graduated scale that allows you to orient the Pointer. Then there are 2 index pointers, one for each scale, and there are also some clamps to clamp the disks still while operating the instrument. The whole instrument is held by a fork, that is designed to be mounted on a photographic tripod.
Notice that in this second model, atop the R.A. disk, and coaxial with it, is a transparent disk which has the reference line for the R.A.. We call it Index disk and on it are attached the supports for the Declination shaft.
Figure 9 - The second Sidereal Pointer Design.
BUILDING THE SECOND POINTER
Now let's see how to build this instrument. As before with the previous design, you are allowed to do all the changes you wish to the design. During this description, we will take into account a part of the design at a time.
Figure 12 - Second Sidereal Pointer. This
image shows some changes
Figure 13 - The Right Ascension disk and fork. Notice the la-
Here are the main parts of the Second Pointer Design.
1 - FORK (figure 13)
Its main function is to hold the R.A. shaft. The holes through which this shaft passes are made elastic by means of sawcut slot. The two lateral holes and their cuts have been made so as to make clamp more flexible. The clamp serves to hold the shaft when necessary. The screw in the upper part of the fork serves only to reduce the movement of the shaft in the bushing. You can fabricate the fork by cutting a piece of "C" shaped rolled steel, or bending a steel bar (6 x 25 x 250 mm) to the shape. In the back of the fork, you have to tap a 1/4 W (1/4"x20) threaded hole in order to mount the instrument on a tripod.
2 - R.A. SHAFT. (figure 13)
This is made with a round ground steel rod 10 mm in diameter. You can usually find this in good hardware stores. At the bottom of the shaft, you have to attach a little disk or collar to prevent the shaft from slipping off. On the upper part of the shaft, you will have to make a little flat (this is wise anytime that you have to clamp anything onto a shaft so that the item can be later removed without worrying about the setscrew scoring holding the part on the shaft) on which the set screw of the flange will grip the shaft without burring up the shaft. This shaft revolves on two flexible bushings in the fork.
3 - BUSHINGS (figure 13)
The two main holes made on the fork have been done with a drill. In order to make the hole smoother for the rotation of the shaft, a bushing is inserted in them. To be flexible, these bushings have to be slotted. You need 4 bushings, two of them serve for the Declination shaft and two for the R.A. shaft. You can buy the bushings in a bearing shop. You want Oillite bushings and you have to cut them along the length of the bushing. You may also get a longer bushing and cut it in two for two bushings if desired.
4 - HOUR STOP PLATE (figure 13)
This little plate is screwed onto the fork and the R.A. disk sets on it. This plate has to be parallel to the R.A. disk, so, if it is necessary, file the part until you obtain the necessary parallelism between the R.A. disk and the fork. On this little plate, you will mount the R.A. disk brake.
5 - THE RIGHT ASCENSION DISK (figure 13)
This disk is made of plastic stock 4 mm thick. Its external diameter is 140 mm and it has a hole of 10 mm on its center in order to let the shaft pass through it. Notice that this disk has to be free to move on the shaft, and it can only be stopped from rotating by the R.A. brake. On this disk is glued the R.A. scale which can be made with paper. To glue the scale, you may use a clear furniture varnish which you can apply with a brush, or a spray can. You may use it also to cover the scale with a thin, protective transparent layer. When gluing the scale to the disk, take a rubber or plastic roller and push the bubbles out from under the scale. The color of the R.A. and Declination disks should be flat black, so as to reduce the reflection of light from them.
6 - THE R.A. DISK BRAKE (figure 13)
This brake is mounted on the plate 4. It is shown in figure 11, in the partial view B, this brake is a clamp which pinches on the edge of the R.A. disk.
The threaded rod has to be attached to the clamping knob. The handle is threaded and the threaded rod has to be tightened into it. You may also want to upset the threads with a pair of sidecutters so that the threaded rod won't come out of the knob while in use. You can also use Locktite to hold the threaded rod in place in the knob as an alternative.
Figure 14 - The R.A. index as seen from below.
A flange and the two
7 - R.A. INDEX DISK (figure 14)
The Index disk has to be made with a 4 mm thick transparent plastic plate (Plexiglas), and with an external diameter of 136 mm (or 4 mm less than the R.A. disk so that the R.A. clamp can hold onto the R.A. disk). This disk also has a center hole and bushing through which passes the R.A. shaft. The Index disk has to be attached to the R.A. shaft (figure 11). A black plastic flange links the disk to the shaft. On the bottom side of the disk, it is necessary to scribe a thin radial groove. This scribed line needs to be orthogonal to the Declination shaft and filled with black Indian Ink or paint. In addition, the distance around the disk in either direction needs to be exactly the same or the pointer that this line is will not repeat when the R.A. shaft is turned 180° around. In this way, you will have a reference line that will work as an index for the R.A. scale. The Index disk also has the important function of supporting the Declination shaft. To do this, you have to use two elastic supports to support the shaft and provide the necessary resistance to easy movement, one of which should have an adjustment knob on it.
8 - THE R.A. FLANGE (figure 14)
The flange is in black plastic and its external diameter is 30 mm. It has the function of linking the R.A. shaft to the index disk. Three flat headed screws hold the flange on the Index disk and a set screw attaches it onto the R.A. shaft. To insure that this set screw holds without scoring the shaft there needs to be a flat upon which the setscrew sets filed onto the shaft.
9 - DECLINATION SHAFT SUPPORTS (figure 14)
The main function of these supports is to hold the Declination shaft. You can make them from an aluminum bar with a section of 12 x 25 mm. The hole through which the shaft passes is made elastic with a saw cut. To make the rotation of the shaft smoother a bushing is inserted in each hole as you did with the R.A. shaft support. The supports are fastened to the disk of the Index by means of two flathead screws (figure 11, partial section A). They have to be located in such a position that the shaft is at 90° to the index line of the R.A. (it may be best to carve this line after having fastened the supports onto the disk). One of these supports also holds the Declination index pointer, the other has a clamp which can restrain the shaft.
10 - DECLINATION SHAFT (figure 14)
The Declination shaft is made with a ground steel bar 10 mm in diameter. At the left end, it connects with the Declination disk by means of a flange. At the right end, there is a handle which also has the function of a counterweight.
11 - DECLINATION FLANGE (figure 14)
It is like that of the R.A. flange and has similar functions. It is connected to the Declination disk and to its shaft by means of screws.
12 - DECLINATION SHAFT HANDLE
This is made up of a steel tube with a thin bar through it. Its function is to help in moving the Declination disk. Its weight also used to balance the instrument, keeping the Declination side from falling downward.
13 - DECLINATION BRAKE (figure 12)
A knob has been mounted on the right support. With it you can tighten the elastic Declination shaft support to slow down or stop the rotation of the Declination disk.
14 - SPACER RINGS (figures 10 and 11)
These rings are used in several places to stop the axial movement of the two shafts. They have the shape of bushings. You also should put flats on the shaft where the setscrews are to keep from galling the shaft itself.
15 - DECLINATION DISK (figures 11 and 12)
16 - DECLINATION INDEX (figures 12 and 14)
17 - SIGHTING PLATE (figures 10, 11 and 14)
18 - SCALES
19 - A TABLE SUPPORT
Most of the mechanical parts can be made with ordinary tools. However, some of them will be best made with a lathe. To get them made, ask a machinist friend to make them. The pieces which have to be made with the lathe are the Declination, R.A. and Index disks, the rings and the counterweight. The internal and the external diameters of these pieces have to be machined so the amount of work is minimal so the cost of them should be low. Even then, accurate work with hand tools, a clever approach to the work and appropriate stock, you can do the work by hand.
When you are finished with building the Pointer and before you use it, you have to align it. Figure 15 explains how to do this operation.
ORIENTING THE SECOND POINTER
It is night and the starry sky is well visible. You are in a dark place, without lights around you. You have brought with you the Pointer, the tripod, the flashlight with a red filter, the constellation maps and the coordinates of the celestial objects that you want to find. The flashlight is necessary to read the coordinates on the maps and to bring some light onto the scales and screwtips of the pointing system. The reflection of the flashlight onto the screwtips will help you to point the instrument toward the sky.
ORIENTING THE R.A. SHAFT
In order that your Pointer is able to point properly, it is necessary to reference it to the astronomical coordinate system. The first thing you have to do is to align the R.A. shaft towards the Pole Star. After setting the Pointer, if you adjust the Declination at 90°, the line passing through the pointing screws is parallel to the main shaft. Then you point it towards the Pole Star, you have to:
- put the Declination disk at 90° and to stop it from moving;
- by moving the tripod head, point to the Pole Star;
- lock the head of the tripod;
- verify that the Declination is still 90°;
- release the Declination disk.
After you have done this, don't move the tripod or the main axis of the Pointer. Now, at this time, the pointer is pointing to Polaris and the plane of the R.A. disk is parallel to the terrestrial and celestial equatorial planes and the Declination is oriented properly. You just have to refer the R.A. scale to the celestial meridians. At this moment you are already able to observe where the heavenly equator lies in the sky. To do this, bring the Declination scale to 0°, and rotate the pointing system around the main shaft.
ORIENTING THE RIGHT ASCENSION SCALE
Now you must align the Right Ascension scale to the celestial vault. To do this, choose a star you can recognize and you know the coordinates, then point the instrument toward it and rotate the disk of the R.A. until you bring the value of the Right Ascension of that star under the Index of the instrument. In the following table and in the figure 16, I indicated some constellations you may recognize with ease. They are placed close the celestial equator, so that the error you will make while orienting the R.A. scale will be minimal.
|Table 1 - A set of Reference Constellations
to orient the R.A scale.
To orient the R.A., scale you have to:
- according to the season, choose the suitable constellation in table 1;
- look for it in the sky;
- chose a known star of that constellation;
- move the pointer of the instrument to point the instrument to the star you have chosen;
- tighten the clamp of the Declination disk;
- with the clamp on the bottom of the fork, stop the Index disk;
- rotate the scale of the Right Ascension scale until the value of R.A. of the star is under the Index;
- with the R.A. clamp, stop the R.A. disk (during your observations, this scale must always be keep this position);
- read the hour on your watch, or better start a stopwatch;
- unlock the Index disk;
- unlock the Declination disk and use the instrument.
At this point, both scales are oriented according to the astronomical coordinate system. If you don't succeed in finding the constellations I indicated to you, you can also align to Ursa Major and the Cassiopeia which are very easy to recognize (figure 17) although you must point to those stars more accurately than stars near the equatorial region. Adjust the R.A. scale on the basis of one star of these constellations. As these stars have a Declination high enough that this adjustment will be afflicted by a certain amount of error. The orientation you obtain will be precise enough to use the Pointer to locate one of the star of the equatorial constellations I indicated in the figure 16 and then you will be able to perfect the orientation of the R.A.. scale.
When they are low on the horizon, the circumpolar constellations can be hidden by haze. As Ursa Major and the Cassiopeia are on the opposite of each other to the Pole Star, if one is low, the other is high, so at least one of these constellations should always be visible in a decent evening for astronomical observations in the boreal hemisphere.
USING THE SECOND POINTER
Now the instrument is ready to indicate to you any celestial body of which you know the coordinates. Its use is extremely easy: just rotate the scales to the coordinates of the celestial body, and the Pointer will show where it is located in the sky. To see the screws in the dark, you may use an flashlight with a red filter, holding it about 1 meter away. The reflection of this light on the tips of the screws will appear like stars, so you will have two shining points that will guide you in the sky.
This instrument has an error of some tenths of degree. It is interesting to note that Hipparchus of Nicea, astronomer 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 coordinates of 850 stars. This job let him discover important things, such as the precession of the equinoxes. Once you have found your target, you can look at the celestial body with the naked eyes, or a binoculars or 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 quickly loses its reference to the celestial meridians. Never mind! Here how you can compensate foe this difference. If you set the instrument at 10 p.m. and at 10.15 you would like point a star, you just have to subtract from the Right Ascension of the star the 15 minutes elapsed since the orientation 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 of one minute and a half in the Right Ascension. 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: relative to the Sun, the Earth make about 365,25 rotations in a year, whereas to the stars the Earth make one rotation more. So, after 6 hours, we have made an error of one minute in the R.A. (this also is to be subtracted in the formula above).
HOW TO MAKE THE SCALES
The scales are the most important part of this instrument, but they are also the most demanding part to be made. In the following paragraphs, we will see some techniques which can be used.
Printing on cardboard
This technique is suited for the first Pointer. You have simply to print the scales on a cardboard 0.2 or 0.3 mm thick. This operation will be done with a computer and a printer. I already described this technique in the chapter on the construction of the first Pointer. To protect the scale of the R.A., you can put it on a disk cut from a transparent plastic sheet. This disk, made integral with the support of the Declination and provided with a black line, can also do the function of the Index disk.
Printing on paper
This technique is suited for the second Pointer. You have to follow the same procedure of printing on cardboard, with the difference that, lacking of stiffness, the scale on paper has to be glued on a rigid support. For the support, it is better to avoid using wood because it has a tendency to warp. Plastic or metal are more suitable. To glue the scales, you can use glues, transparent varnish or such. There are also double faced adhesive sheets which can be cold-applied and also ones which can be hot-applied. These latter have the advantage you can position them without problems, then pass a hot iron on them to cause the scale adhere to the support. The scales on paper should be covered with a protective varnish such as a transparent furniture varnish or transparent varnish for cars. It is also possible for these materials to tend to dissolve the marks of the scale. To avoid it, look for another varnish or, before you apply it, fix the drawing with a suitable spray for pencil drawings. These varnishes can be used also as a glue.
Printing on white adhesive plastic sheet
In a stationery store, you can find special plastic sheets used to decorate T-shirts. With a ink-jet printer, you can print the scale on one of these plastic sheets. Cut the drawing and apply it on a metal or plastic disk by means of a hot iron.
Printing on a transparent plastic sheet
With a computer and a laser printer, you can print on plastic sheets used for transparencies (those which are used in executive meetings). Use the transparent sheets for laser printers as they are special sheets which are able to resist to the high temperature of the oven which fuses the toner to the paper, without becoming deformed. Once you have cut it, the scale can be glued on a rigid support, for example in plastic or in metal. The color of the support has to be white to allow you to see the divisions of the scale. To allow the division to last longer, you can print the sheet in a reverse direction and glue the printing in contact with the support. This technique is simple and effective. If you use this method to obtain the R.A. scale of the first Pointer, do not glue it to the supporting plane.
The laboratories which produce plates use special machines to make scales. Some are basically mechanical dividers, other are pantographs, or use lasers and are controlled through computers. As support, special plastics for scribing (formica, phenolic resins, brass, aluminum, stainless steel and other metals) are used. Some metals can also be anodized. The cost of these tools are out of reach of an amateur so, to use them, ask a laboratory which works on plates and bring with you a diskette with the drawings of the scales.
Transfer of the toner of laser printers.
There is a method to make printed circuit boards which avoids using ultraviolet light and acids and which could be also used to obtain scales. This system is based on the transfer the toner obtained with a laser printer and for this reason it is called: "laser printer toner transfer". It consists of doing a print by means of a laser printer and, with a hot iron (without using steam), transfer the toner (and so the drawing) on another part, for example a plate of aluminum or stainless steel. To make the transfer easier, the receiving surface has to be well cleaned. The different parameters of this procedure, such as the temperature of the iron, the pressure of the iron on the paper, the time of the pressing, etc. have to be experimented with to obtain the best process. There are also transfer papers that are suitable to this process and which easily release the toner, once you put them in water. I tried this method without obtaining satisfactory results, anyway, with the right paper and experimenting with the parameters, it is possible to make good scales. The method is cheap, so you can try it if you desire.
Internet Keywords: laser printer toner transfer pcb iron
POINTING THE TELESCOPE
The pointing devices of the Pointers I described are quite somewhat uncomfortable and inaccurate. This is not only due to the systems I suggested, but also to the Light Pollution which, raising the luminosity of the background of the night sky, which reduces the visibility of the stars. A little telescope with a magnification of 1 - 2 X would be a good solution. This telescope should have a wide field of view and an illuminated reticle with adjustable brightness to assist in viewing the sky.
If you have enough knowledge in electronics, you might provide your instrument with a remote control with which, by typing in the coordinates of a heavenly body, the Pointer would indicate it by itself.
By providing the R.A. shaft with a suitable constant rotation, the Pointer would keep itself oriented to the celestial meridians all during the night.
This little instrument can be very useful for many astronomic observations, even with the naked eye. Figures 16, 17 and 18 give you the coordinates of some important celestial points and interesting objects to observe. Among them, there is the famous Andromeda Galaxy, a nebula of such a bright magnitude that you can observe it with the naked eye or binoculars, while you can observe the other ones only with instruments that have a larger aperture. However you can scarcely perceive Andromeda because of its low surface brightness. In any case, its light travelled for 2 million years before getting to your eyes! Other objects that can be observed with low aperture instruments are clusters of stars, such as the Pleiades. 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.
You may also want to obtain an astrolabe. It is a map of the constellations with a rotating elliptical window on it. With an astrolabe, you can tell which part of the sky is visible at the time you are doing your observations. With the Pointer, you can locate single heavenly objects and also constellations, but with the astrolabe you will be able to better see the position of each constellation to the others. Together, these two instruments will be a great help in your discoveries of the night sky.
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 Aries Point, also called Gamma Point. It is the zero point of the astronomical coordinate system and so it has these coordinates: R.A. = 0 and D = 0. This point is placed at the vernal intersection of the equatorial plane with the ecliptic one (the plane on which lies the orbit of the Earth around the Sun). It also marks the moment of the spring equinox.
By pointing the main shaft of the instrument towards the point with coordinates R.A. = 18h 00' D = 66° 34', for some minutes 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 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 also lies the apparent motion of the Sun on the celestial sphere. When the Moon is moving on the ecliptic, its shadow may hit the Earth, and so who ends up under it sees the Sun darken in an eclipse. You could try to use the Pointer to forecast eclipses.
The coordinates of the constellations of the figures 16 and 17 and the coordinates you can find in figure 18, are enough to set the pointer and do some first observations. In astronomy text books, like the one indicated in bibliography which is cheap and very well done, you can find maps of constellations and the coordinates of a lot of interesting celestial objects. With this book, the astrolabe and the Sidereal Pointer, you will be able to find all the constellations you want, and at least learn to recognize them. In addition, this book gives you a lot of interesting information that will satisfy your curiosity and your desire to learn something more about astronomy.
As the planets move relative to the stars, they do not have fixed coordinates that can be referred to but rather paths that are marked with special tables. To find the planets, the so-called ephemeris almanacs, published yearly, are useful and you can find them in any book-shop. Those almanacs also report the position of little planets and some close comets. Remember that, if the instrument is pointing towards the Earth this does not mean that there is something wrong but rather it is right, and the object is in that direction and not in the night sky!
In its simplicity, the Pointer is really useful: it is a valuable guide to astronomy, and by constructing it you have done an interesting exercise of mechanics and physics in building an equatorial mount. Furthermore, you have learned how the celestial coordinates system is organized and you have found in which direction the center of our Galaxy is. One of the best 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.
On the Internet there are a lot of websites which can supply you the coordinates of heavenly objects and many other useful information on astronomy.
Maps of the constellations and, for each of them, the coordinates of the
stars and other celestial objects
http://www.absoluteastronomy.com/ Coordinates and other information on heavenly objects.
http://www.fourmilab.to/yoursky/ Your Sky, an interactive planetarium.
http://www.geocities.com/m_s_pettersen/index.html Build an astrolabe.
http://my.execpc.com/~tgrunewa/astro/astro_links.html Links on astronomy.
http://www.seds.org/billa/psc/hist1.html Important Astronomers, their Instruments and Discoveries
http://www.humboldt.edu/~rap1/EarlySciInstSite/Instruments/Torquetum/Turq.html The Torquetum
http://www.21stcenturysciencetech.com/articles/fall01/Tanawa/tanawa.html Building a Torquetum
Internet Keywords: torquetum, celestial objects, heavenly objects, astronomical coordinate system, star atlas, astronomy links.
Patrick Moore, The Guinness Book of Astronomy, Guinness Publishing,1988
This book supplies the maps of the constellations, the coordinates of a lot of stars, variable stars, double stars, star clusters, nebulae, galaxies, etc. You will find also a lot of other information on heavenly objects and on the constellations, which will be able to satisfy your curiosity of knowledge in astronomy.
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