# I.1 Rotation of the Earth

The Earth moves in several ways. First, it turns around its polar axis; one turn takes 24 hours. Then it moves along its orbit around the Sun; one full revolution takes 1 year. And third, its polar axis changes direction very slowly, just like a spinning top. This effect is called precession and one full turn lasts almost 26,000 years.

When you live on the Earth, these motions are not obvious. This is why most ancient Greek astronomers and many others after them thought that it is the sky that moves around a motionless Earth, not the Earth that turns under the sky.

In this exercise, we will observe the rotation of the Earth around its polar axis and we will find the location in the sky of the celestial poles and equator. The word celestial comes from Latin and means `of the sky'.

### Observe the rotation of the Earth

Every 24 hours, the Earth makes one turn around its polar axis. The polar axis is the imaginary line that connects the North Pole in the Artic and the South Pole in the middle of the Antarctic continent.

The rotation of the Earth around its polar axis.

#### Exercise 1: How to locate the celestial poles among the stars

Here is the material you need: a notepad, a skymap, a photographic camera that is able to make long exposures, a shutter release, a sturdy tripod and a photographic film (for instance 200 ISO).

First, we try a simple way with the naked eye.

At the beginning of the night, note where the brightest stars are seen above the trees and houses around you. Repeat this two hours later, and look for changes. You will have no difficulty in seing that the whole sky has moved in the meantime!

Some stars have risen in the Eastern part of the sky, others are setting towards the West. But there is also a direction where the stars seem to be nearly motionless. If you live North of the Earth's equator, that is in the northern hemisphere, you will find this area between the constellations of the Big Dipper and Cassiopeia. They are easy to find by means of your skymap.

If you live in the southern hemisphere, this area will be between the Southern Cross and the Small Magellanic Cloud.

They are the areas where the celestial poles are located in the sky. You may think of these poles as the points where the prolongation of the Earth's polar axis intersects the celestial sphere!

Here is now a more accurate way by means of a long-exposure photo.

Fix an ordinary photographic camera (with focal length somewhere between 30 and 50 mm) on a stable tripod. Point it towards the area of the celestial pole, open the shutter and make an exposure that lasts at least half an hour. You may wish to do some test exposures before you make a long one. Be careful not to touch the tripod during the exposure!

When the film has been developed, you will find on it several incomplete, circular arcs, especially if you live far away from any town, at a completely dark site. Each arc is the photographic track of a star. There is a star with a very short arc in the north. This is the famous Pole Star and it is quite near the celestial North Pole. Unfortunately, there is no bright star near the South Pole.

The exact location of the celestial pole is the common centre of all these arcs.

The lengths of the arcs, compared to full circles, together with the duration of the exposure, will enable you to calculate how long one full turn will take. If your calculation is correct, you should of course find that this period is about 24 hours.

You may also find the direction of the motion. Towards the end of the exposure, put a hat over the camera during a few minutes, and remove it again just before the last minute of the exposure. That will break the arcs on the photo. At the end of each arc, the light from the star will produce a spot. In this way, you can easily see the direction of its motion in the sky.

Think of this: If you would determine the position of the celestial pole in the sky on different days during the whole year, as explained above, you would find that the pole stays at the same place, even though the Earth moves in its orbit around the Sun. Why is this so?

#### Exercise 2: How to locate the celestial equator

Once you have found the position of the pole, you can also find where the celestial equator is, again by means of simple observations.

For this exercise, you need the same equipment as before, plus a small tube (or a piece of a water pipe) and a set square (a triangle in which one angle is 90 degrees).

The celestial poles are located in the sky where the extension of the Earth's polar axis `intersects' the celestial sphere. You may find the celestial equator in the same way; it is where the plane of the Earth's equator `intersects' the celestial sphere. It does so along a circle all around the Earth. As the Earth is a very small sphere compared to the distances to the stars, we see this circle, the celestial equator, from its own centre. So, on different kinds of skymaps, the equator plane is always a line.

Here is first a simple way to find the celestial equator by sighting at a direction that is 90 degrees removed from (`perpendicular to') the pole direction.

With the photos taken for the previous exercises, you can find the celestial pole. You now replace the camera on the tripod with the tube (or pipe), and you point it towards the pole. If you are in the northern hemisphere and you do not want the highest accuracy, you just aim it towards the Pole Star. Then place one side of the set square along the pipe. The other side will then point towards the celestial equator.

You only have to turn the set square around the tube to find the whole equator plane. You will notice that half of this plane is above the horizon, symmetrical between East and West. Just as the pole axis and the celestial pole is fixed for one observer, so is the equatoreal plane in the sky, because it is always perpendicular to that axis.

If you do not travel on the surface of the Earth, you will always see the equator plane at the same place in the sky, compared to the horizon. During the night, you will see the equatoreal constellations moving from East to West in the sky, one behind the other. All stars which are situated exactly on the celestial equator, stay above the horizon during twelve hours.

In Winter, the most interesting and impressive equatoreal constellation is Orion, and in Summer you can look at Altair in the Eagle.

There is also a more complicated, but quite accurate way to find the celestial equator by means of a long-exposure photo in this direction.

When you point your camera towards the celestial equator, the laws of perspective produce surprising photos that look quite different from the polar photos. Each track of star is still a circular arc, but now we do not see the center of the circle anymore; it is far outside the border of the photo. However, we see that some arcs are curved towards the North, others in the opposite sense, and some are very nearly straight. In fact, all arcs are differently curved and only the arcs from stars which are located right on the celestial equator are straight. The longer the duration of the exposure, the more obvious is this phenomenon.

In this way, you can find the exact position of the celestial equator. Try to check your result with a skymap on which the equator is shown.

The author of this exercise is Daniel Toussaint (Comite de Liaison Enseignants Astronomes - CLEA), 20, rue Renaudot, F-10 160 Aix-en-Othe, France. Please direct any related questions or remarks to: Josee Sert (France) who will pass them on to CLEA.