In astronomy for convenience of measurements and the solution of practical problems on determining the location of stars, motion of planets, etc. the concept of celestial sphere is used.

The celestial sphere is the imagined sphere of an arbitrary radius on which all stars are projected as they are seen by an observer at a certain time from a definite place (a space point) (fig. 123). The center of the celestial sphere usually coincides with the center of the Earth or with the place of the observer (with his eye).

On the celestial sphere only angular distances are used. The angular distance is the distance measured by an arch or by a corresponding to the arch central angle between two points on the sphere, i.e. it is an angle between the lines connecting the eyes of the observer with these two points. It is known that this principle is used also in geography: latitude and longitude are the geographical coordinates of the points on the globe expressed in angular units.

In the history of mankind the concept of the celestial sphere appeared long ago because people imagined the sky in the form of a huge dome covering the surface of the Earth. According to an ancient world outlook the Universe consists

Fig. 123 Fig.124

of spheres. On the surface of these spheres the so called motionless celestial bodies (Moon, Sun, planets and stars) are located. The echo of this outlook is the word «aspan» in the Kazakh language meaning the sky and originating from an old Indian language in which it designates a stone dome. By the notion of the Turkic people, the sky consists of seven or nine layers. These layers are occupied by deities according to their rank. Astronomy in the course of its development showed an erroneousness of such notions, however for the solution of a number of practical problems the idea about location of bodies on the celestial sphere is very useful.

If in a remote past people believed that the celestial sphere really rotates then nowadays we know that this rotation is the result of Earth¢s spin on its axis. As the Earth spins on its axis from the West to the East all sky seems to us moving from the East to the West, so making understandable the rise and set of celestial bodies.

II. Basic elements of the celestial sphere are shown in fig. 124. Zenith (Z) is the point on the celestial sphere that lies directly above an observer, nadir (Z_{1}) lies on an opposite to zenith point of the sphere. The line connecting these two points is called vertical or plumb line. The plane perpendicular to the plumb line is called the plane of a celestial or a rational horizon. The plane of the horizon divides the celestial sphere into two hemispheres: visible and invisible. This plane draws a great circle on the celestial sphere (i.e. a circle which has the center of the celestial sphere as its center) that is called the rational horizon (or simply the horizon). The arch of the great circle passing from a zenith through a celestial body M to a nadir is called the vertical of the celestial body or the circle of the altitude.

Daily rotation of the celestial sphere occurs round the celestial axis. As the Earth sizes are negligibly small compared with distances to stars then for the observer at any point of the Earth the world axis is parallel to the spin axis of the Earth. The points of intersection of the world axis with the celestial sphere don't participate in rotation of the celestial sphere. Therefore these points are called the celestial poles. The pole relative to which the celestial sphere circles counterclockwise (for the observer who is at the center of the sphere) is called the North celestial pole and the opposite is the South celestial pole. Near the North celestial pole (at the distance about 1°) there is the bright star Polaris (pole star).

The plane passing through a zenith and a celestial axis is called the plane of a celestial meridian and the great circle cut by the intersection of this plane and the celestial sphere is called the celestial meridian. The celestial meridian doesn't participate in daily rotation of the sky and intersects the horizon at two points: the North (N) and the South (S). The line of intersection of the plane of a celestial meridian and the plane of the celestial horizon is known as the meridian line, called so because a shadow of a vertically located body at noon falls to this line. The direction north – south at any point of the Earth¢s surface is determined by this line. Therefore this line plays an important role for the correct orientation on the Earth¢s surface. On the sky the same function is carried out by a celestial meridian.

The plane passing through the center of the celestial sphere and making a right angle with the celestial axis is called the plane of the celestial equator. It is parallel to the terrestrial equator and the line of its intersection with the celestial sphere is called the celestial equator. The celestial equator divides the celestial sphere into northern and southern hemispheres and intersects the horizon at two points: the East (Ĺ) and the West (W).

The great circle passing through celestial poles and a star is called a celestial meridian of the star.

Any star due to rotation of the celestial sphere during a day moves along a small circle which is called a diurnal circle. These concentric circular paths can be seen at the photo of the star sky taken by means of a fixed camera with a long exposition.

Ecliptic is a great circle of the celestial sphere along which the Sun moves once a year against the zodiac constellations. The Sun movement along the ecliptic is due to annual movement of Earth round the Sun. The circle of the ecliptic is tilted relative to the plane of the celestial equator by an angle of e = 23 °27¢. The center of the solar disk crosses the celestial equator twice a year: about March 21 and on September 23. These points of intersection are called Vernal Equinox and Autumnal Equinox. From the Vernal Equinox (it is designated by a sign of Aries constellation - ) the Sun moves the northern hemisphere and from the Autumnal equinox (it is designated by a sign of Scales constellation - ) the Sun moves southern hemisphere.

The points of an ecliptic remote on 90° from the equinoxes are called solstice points. The summer solstice is on the border of constellations Taurus and Gemini. It is designated by a zodiac sign of the Cancer - . The winter solstice is in Sagittarius and is designated by a sign of the Capricorn - (fig. 125).

The main planes and great circles of the celestial sphere are used in the system of celestial coordinates.

Fig.125

Self-testing questions

1. What is called the celestial sphere?

2. What points, lines and great circles of the celestial sphere are known to you?

3. What observations verify the daily rotation of the celestial sphere?

4. At what points do the celestial meridian and the celestial equator cross the horizon?

5. What is the location of the celestial axis relative the spin axis of the Earth?

6. What are the main planes on the celestial sphere?

7. What is the location of the celestial axis relative the plane of the celestial meridian?

8. What is the line of intersection of the celestial meridian and the celestial horizon?

9. What is the location of the ecliptic relative the celestial equator?

10. What are the points of intersection of the ecliptic and the celestial equator? When and in what direction do these points cross the Sun?

11. What is the location of solstice points relative equinox points?

Experimental assignment

1. Make the elementary goniometric tool — an astronomical staff (fig. 126). It consists of two mutually perpendicular strips of wood supplied with attachment for sighting. At one end of the strip-ruler about 1 m long there is the washer of diameter 3-4 mm with an opening, serving as a sight.

Fig.126

On the ends of the strip-slider there are two nails. The strip-ruler is graduated by means of the protractor located so that the center of its semi-circle coincides with the position of the sight.

2. Using the astronomical staff measure the angular distances between several stars: a and b of the Great Bear (or Big Dipper), a and d of the Great Bear, a of the Great Bear and a of the Little Bear. For this purpose bring the sight closer to an eye and move the slider along a strip-ruler until the nails coincide with the stars to measure the angle between them. Fixing the position of the slider write down the value of the angle.

3. Using the received measurements check whether the angular distance between a of the Little Bear and a of the Great Bear is five times greater than that between b of the Great Bear and a of the Great Bear.