What conditions should a theodolite meet?

A theodolite is the mechanical part of a telescope that allows the telescope to point in different directions. The theodolite has two mutually perpendicular axes to adjust the azimuth and horizontal height of the telescope. This type of stand has a simple structure and low cost. It is mainly used with ground telescopes (for geodesy, bird watching, etc.). If it is used to observe celestial bodies, since the diurnal movement direction of celestial bodies is usually not perpendicular or parallel to the horizon, it needs to be rotated at the same time. Only by changing the rotation speed of two axes over time can you track celestial objects. However, other celestial objects in the field of view will rotate relative to the target celestial object. Unless a mechanism is added to offset the rotation of the field of view, it is not suitable for long-exposure astrophotography.

However, due to the development of electronic technology, the above problems have been solved, and theodolite can minimize the change in the spatial attitude of the telescope when pointing in different directions. Therefore, many large-aperture telescopes in professional observatories use theodolite to reduce the problem caused by Decrease in accuracy caused by mechanical deformation. Some astronomical enthusiasts even made their own astronomical telescopes specifically for low-magnification visual observation.

According to accuracy: DJ07, DJ1, DJ2, DJ6, DJ30, etc., D and J are the geodesic and theodolite respectively. initials.

On some construction project sites, we will often see some technicians carrying an instrument for measurement work. The instrument they use is theodolite. The initial invention of the theodolite was closely related to navigation. In the fifteenth and sixteenth centuries, some developed countries such as Britain and France needed to draw various maps and charts due to navigation and war. The earliest method of drawing maps was triangulation, which is to find the position of a third distant point based on the observation results at two known points. However, due to the lack of suitable instruments, the angle measurement methods were limited and the accuracy was not high. The topographic map produced is also not very accurate. The invention of the theodolite improved the accuracy of angle observation, simplified the process of measurement and calculation, and provided more accurate data for drawing maps. Later, theodolite was widely used in the measurement of various engineering constructions. Theodolite consists of three parts: base, dial (horizontal dial and vertical dial) and sighting part. The base is used to support the entire instrument. A level dial is used to measure horizontal angles. There are telescopes, level tubes, reading devices, etc. on the sighting part.

Theodolite is the main angle measuring instrument in surveying work. It consists of telescope, horizontal dial, vertical dial, level, base, etc. When measuring, place the theodolite on a tripod, use a vertical ball or optical plummet to align the center of the instrument with the ground station, use a level to level the instrument, use a telescope to aim at the measurement target, and use a horizontal and vertical dials. Determine horizontal and vertical angles. According to the accuracy, it can be divided into precision theodolite and ordinary theodolite; according to the reading equipment, it can be divided into optical theodolite and vernier theodolite; according to the axis system structure, it can be divided into re-measurement theodolite and directional theodolite. In addition, there are coded dial theodolite that can automatically record dial readings according to coded holes; automatic tracking theodolite that can continuously and automatically aim at air targets; gyrotheodolite and laser theodolite that use the principle of gyro orientation to quickly and independently determine the orientation of ground points; with theodolite, meridian An all-purpose theodolite for astronomical observation with three functions of a celestial instrument and a zenith instrument; a photographic theodolite that combines a camera and theodolite for ground photogrammetry, etc.

How to make your own theodolite

1. Right ascension and declination

In the vast sea, when a sailing ship encounters danger and seeks first aid, the first thing to do is to The rescuers should be informed of the location of the ship, which means the rescuers should be informed of the latitude and longitude of the ship. Latitude and longitude do more than just point out a ship's location on the ocean. Its biggest advantage is that it can make the exact position of an object simple and clear to everyone. Similarly, once a new star is discovered in the endless sea of ??stars in the night sky, how do you make its correct position known to the world? Have you ever thought that there should be a measurement system similar to latitude and longitude to calibrate the position of the planet and make star maps? The measurement systems used by astronomers are Right ascension and Declination. The units of Declination are Degrees, and the units of Right Ascension are Hours and Minutes. We may not understand these very well. Not familiar, but not difficult to understand.

Because the stars are so far away from us that we cannot tell the difference between them with our eyes alone, these planets all appear to be equally far away from us. We imagine that there is a suspended spherical shell covering the entire earth. This imaginary sphere is called the celestial sphere, and these stars are fixed on the inside of the spherical shell. We can only see half of the sphere at a time. Because of the rotation of the earth, the celestial sphere seems to be constantly rotating around us from east to west. The north (south) pole of the celestial sphere is directly above the geographical north (south) pole of the earth, and the celestial equator is also directly above the earth's equator. , ascended the throne in the center of the two celestial poles. Like the earth, we mark the celestial sphere with latitude and longitude. In astronomy, this is equivalent to the latitude (longitude) of the earth, which is called declination (right ascension). From the celestial pole to the celestial equator, the declination is 90°; the right ascension is 24 hours, and 1 hour is 60 minutes, that is, 1h=60m=15°. This is because the earth or celestial sphere rotates every hour. It is named after 15°.

This method of determining the position of celestial bodies seems quite complicated, but it has many advantages.

For example, the celestial sphere is constantly rotating, so the apparent positions of stars are constantly changing, such as crossing the night sky from east to west. At the same time, due to the revolution of the earth, even at the same moment, a few days later, the positions of stars are slightly westward; or As you walk from north to south, the relative positions of the stars to the horizon also change. Since the apparent positions of stars are so fickle, it is quite difficult to explain their positions based on what we see. We can only explain them through right ascension and declination, because each planet corresponds to a set of right ascension and latitude. . But since the stars change rapidly, how should we measure their right ascension and declination?

2. Production of theodolite

Theodolite is used to measure right ascension and declination. It is an observation device with many characteristics of an astronomical telescope.

Now we will introduce a simple theodolite method. The required materials are listed in Table 1. The size of each material is for reference only and can be modified at your own discretion, but the relative position of each part must be clarified.

Before making, take a look at Figure 1, Figure 2, Figure 3, and how to do it:

1. Use a (3/8)" thick plywood to cut out two circles. The diameter of the plate should be about (1/2)" slightly smaller than the protractor (protractor). Use strong glue to glue two protractors on each disc. The midpoint of the bottom edge of the protractor must be firmly glued to the center of the disc. (See Figure 2).

2. Fix a disk on D with two screws. The line connecting the center of the disk and 90° must overlap the center line of D. Screw a screw on each end of D. The screw circle, (note that it is not nailed to the side with the disc, see Figure 2) can be observed through the two small circles.

3. Drill a (1/4)" hole at the center of the other disk. This hole should pass through A and C at the same time (see Figure 3), and use a screw to pass through the bolt. OK, adjust the tightness so that C can rotate easily.

4. Drill a hole from the center of the protractor attached to D, and tighten D and C with wooden pegs or screws. It can be rotated, but not fixed.

5. Cut out three triangles with iron sheets and attach them to C with screws or small nails. The tips of the triangles must be flat against the protractor.

< p> 6. Connect A and B with hinges (see Figure 1)

7. Drill a small hole (3/4)" from one end of G and H, 1 inch from this hole. Starting from ", along the center line of each wooden tape, cut a thin slit wide (3/16)" until it is 1" away from the other end. Use screws to fasten G and H to the two sides of A in the small hole, and then Use a seat drill to bolt G and H to the edge of B through the slit. This is used to adjust the angle B can be overlapped.

The theodolite can now be used

3. Use of the theodolite

Put the theodolite on a stand, like a chair or a camera. A tripod can be used, the purpose is only to make it easy to observe through the screw circle of D. Place the theodolite facing south, first do not raise the sight arm D (that is, the latitude meter E points to zero), adjust the tilt of the B plate so that The line of sight reaches the horizon along the viewing arm. Fix the B panel at this position. At this time, the B panel remains horizontal. Now rotate C and D to observe the celestial body, and E will indicate the altitude of the celestial body.

< p> Now raise plate A of the theodolite to angle x, x = 90° - (the latitude of the measurement place). For example, if you measure in Taipei, the latitude is about 25°3', the angle x is equal to 64°57'; another The method is to point the sight arm to Polaris, keep D in this direction, and move plate A so that the reading of latitude table E is 90°. At this time, plate A is at an x ??angle with B. Of course, you will know after a little thought. This method is used to measure the latitude of your location. Why do A and B form an angle of x? (Note 1)

When you look up at the celestial pole (i.e., the North Star), the elevation angle is your latitude, so When the E reading is zero, after lifting plate A at the x angle, the viewing arm points to the celestial equator. Why? (Note 2) The purpose of adjusting the x angle is to find the elevation angle (i.e. declination) of the star to the celestial equator. , without taking into account the changes in the apparent position of the stars caused by the different latitudes of the observing site, the position of the celestial equator is drawn by rotating the apparent arm from west to east.

In order to measure the equator. Longitude, you must mark the longitude table F into the right ascension unit - hour, every 15° is 1 hour, starting from zero degrees in the counterclockwise direction.

Now move the sight arm to look at the southern sky. To know the stars, determine the right ascension and declination of the star from star charts, astronomical calendars or other reference star sources, and rotate the longitude table F so that the pointer of C points to the appropriate right ascension value. At this time, the latitude meter should automatically point to the correct declination value, otherwise the instrument will be biased. Fix F, now rotate C and D, and point the sight arm to another planet. At this time, you can read the declination and right ascension of this planet from E and F. The declination of a star north of the celestial equator is positive, and the declination of a star south of the celestial equator is negative. That is, the protractor degree toward the opening on the E disk is positive, and the other is negative.

For example: Spica is visible in the night sky in April, May and June. Its right ascension (R.A.)=13h23m37s and declination (D.)=-11°00' 19'', point the visual arm to the star Spica. At this time, the latitude meter E should read about -11°. Adjust the longitude meter F to 13h23m37s. Now rotate the visual arm D and look at Regulus. At this time, you can read about 12°06' on E and about 10h07m on F. So we know that R.A.=10h07m and D.=12°06' of Regulus. .

For another example, Sirius is visible in the winter night sky

R.A. is about 6h44m, D. is about -16°40', after adjusting F to 6h44m, Raise the sight arm to about 25° declination, then rotate it westward until the right ascension is about 3h45m. At this time, through the screw circle on D, you can see the Pleiades.

In the early evenings of autumn and winter, a hazy bright band can be seen near the Great Square of Pegasus. It is the Andromeda Nebula. It is the only spiral nebula that can be clearly seen by the naked eye. I saw it, are you interested in asking for its approximate location? It is approximately R.A.=0h40m, D.=41°.

The advantage of using this method to calculate right ascension and declination is that you don’t have to worry about the factors that cause changes in the apparent position of the planet due to different observation times. Why? Because plate A coincides with the celestial equatorial plane after being corrected by the x angle, what E obtains is the elevation angle of the star to plate A (that is, the celestial equatorial plane), which is naturally the declination. In addition, although the celestial sphere is constantly rotating, almost all the stars are extremely distant stars, and their relative positions do not change. We know the right ascension of one star, and based on this, we can naturally determine the distance between this star and other stars. angle, and find the right ascension of another star, so no matter what latitude, season, or time you observe, there will be no difference in the right ascension and declination of the star you find.

Some reference star sources are listed in Table 2.

The devices required for many great experiments are often quite simple, so don’t underestimate the theodolite. It is very likely that one day you will use it to calibrate the surface of a planet that has never been discovered by anyone. Location and world-famous?

The original text is excerpted from "Projects and Experiments" on page 117 of "Challenge of the Uriverse" published by the "National Science Teachers Association" in 1962.

The original text only explains the production method and does not discuss the principles. The translator has added some simple explanations of the principles.

Note 1: See Figure 4. Panel B points to the southern horizon, D points to the celestial north pole, and panel A is perpendicular to D. ∠Y is the latitude of the observation place. Because the North Star is far away from the earth, it points to the celestial north pole. D is parallel to the line connecting the North Pole to the center of the earth. We can easily prove that ∠Z=∠Y, and ∠x+∠Z=90°, so ∠x=90°-∠Z=90°-∠ Y=90°-(latitude of the observation place).

Note 2: When the E reading is zero, D is parallel to A. As shown in Figure 4, A is at right angles to the celestial north pole, which means it points to the celestial equator, so D also points to the celestial equator.