..... Click the link for more information. , the coordinate axes are great circles on the celestial sphere. In most systems of this type, the reference points are fixed on the sphere, so the two coordinates needed to locate a body are relatively constant.
celestial sphere
Apparent surface of the heavens, on which the stars seem to be fixed. For the purpose of establishing celestial coordinate systems to mark the positions of heavenly bodies, it can be thought of as a real sphere at an infinite distance from Earth. Earth's rotational axis, extended to infinity, touches this sphere at the northern and southern celestial poles, around which the heavens seem to turn. The intersection of the plane of Earth's Equator with the sphere marks the celestial equator.
celestial sphere
celestial sphere [sə′les·chəl ′sfir]
Celestial Sphere
an imaginary sphere of arbitrary radius on which celestial objects are projected; it is used for the solution of various astrometric problems. The concept of the celestial sphere originated in remote antiquity; it was based on the visual impression of a dome-shaped celestial surface. This impression results from the enormity of the distances to celestial objects; the human eye is unable to estimate differences in such distances, so that all the objects seem uniformly distant. Ancient peoples associated this with the presence of a real sphere that bounds the whole world and has numerous stars set in its surface. Thus, according to their concept, the celestial sphere was a most important element of the universe. With the growth of scientific knowledge, this concept of the celestial sphere lost importance. However, the geometry established in antiquity for the celestial sphere had already been developed and perfected into a modern form, in which it continues to be used in astrometry.
The radius of the celestial sphere may be taken to be whatever is convenient; in order to simplify geometrical relations, it is taken equal to unity. The type of problem dictates where the center of the celestial sphere is to be located; at the position of the observer (topocentric celestial sphere), at the center of the earth (geocentric celestial sphere), at the center of a planet (planetocentric celestial sphere), at the center of the sun (heliocentric celestial sphere), or at any other point in space. To each celestial object there corresponds a point on the celestial sphere that is the point at which the straight line connecting the center of the celestial sphere and the center of the object intersects the celestial sphere. In the study of the relative positions and apparent motions of objects on the celestial sphere, some particular coordinate system is chosen. (See.) The coordinate system is defined by primary points and lines. The latter are usually great circles of the celestial sphere. Each great circle has two poles that are defined as the endpoints of the diameter perpendicular to the plane of the given circle.
Figure 1 depicts the celestial sphere as seen by an observer situated at a point on the earth’s surface with latitude Ф. A plumb line (vertical) drawn through the center of this sphere intersects the celestial sphere at points Z and Z’, called the zenith and nadir, respectively. The plane that passes through the center of the celestial sphere perpendicular to the vertical intersects the sphere along the great circle NESW, called the mathematical (or true) horizon. The mathematical horizon divides the celestial sphere into a visible hemisphere and an invisible hemisphere; the zenith is located in the former, and the nadir in the latter. The line that passes through the center of the celestial sphere parallel to the earth’s axis of rotation is called the polar axis, and it intersects the celestial sphere at the north and south celestial poles P and F, respectively. The plane that passes through the center of the celestial sphere perpendicular to the polar axis intersects the sphere along the great circle AWA’E, called the celestial equator. From the construction it follows that both the angle between the polar axis and the plane of the mathematical horizon and the angle between the vertical and the plane of the celestial equator are equal to the latitude Ф of the point of observation. The great circle that passes through the celestial poles, the zenith, and the nadir is called the celestial meridian.
The celestial meridian intersects the horizon at two points—the one nearest the north celestial pole being called the north point N, and the one diametrically opposite being called the south point S. The line NS that passes through these points is the meridian line. The points on the horizon situated at 90” from the points N and S are the east point E and the west point W. The points N, E, S, and W are called the principal points of the horizon. The planes of the mathematical horizon and of the celestial equator intersect along the diameter EW.
Note to Figure 2. Celestial sphere: 
celestial equator, 
ecliptic, (r) and 
vernal and autumnal equinoxes, (E) and (E’) summer and winter solstices, (P) and (P’) north and south celestial poles, (IT) and (Π’) north and south ecliptic poles
The great circle on the celestial sphere that the sun traces out during its apparent annual motion is called the ecliptic (Figure 2). The plane of the ecliptic forms an angle € = 23°27’ with the plane of the celestial equator. The ecliptic intersects the equator at two points, one of which is the vernal equinox (at which the sun in its apparent annual motion crosses from the southern celestial hemisphere into the northern celestial hemisphere), and the other, the autumnal equinox, which is diametrically opposite to the vernal equinox. The points on the ecliptic situated at 90° from the vernal and autumnal equinoxes are called the summer solstice and the winter solstice; the former is in the northern celestial hemisphere and the latter is in the southern celestial hemisphere. The great circle that passes through the celestial poles and the equinoctial points is called the equinoctial colure, and the great circle that passes through the celestial poles and the solstitial points is called the solstitial colure. When drawn on a star map, these circles cut off the tails of the ancient representations of the constellations Ursa Major (equinoctial colure) and Ursa Minor (solstitial colure).
The apparent diurnal displacement of the stars, which is a reflection of the real rotation of the earth about its axis, corresponds to a rotation of the celestial sphere about its polar axis with a period equal to one sidereal day. Because of the rotation
of the celestial sphere, all representations of objects on it describe circles in space that are parallel to the equator, called diurnal circles. Depending on the position of the diurnal circles with respect to the horizon, three types of celestial objects are distinguished: (1) objects that do not set (diurnal circles located entirely above the horizon), (2) objects that do not rise (diurnal circles entirely below the horizon), and (3) objects that rise and set (diurnal circles intersecting the horizon). The diurnal circles KN and SM, which are tangent to the horizon at points N and S, respectively (Figure 1), are the boundaries for these groups of celestial objects. Since the visibility of a celestial object is determined by the position of the horizon, whose plane is perpendicular to the vertical, the conditions for visibility of celestial objects are different for points on the earth’s surface having different latitudes Ф. This phenomenon, already known in antiquity, has served as one proof of the spherical shape of the earth. On the equator (Ф =0°), the polar axis PP is located in the plane of the horizon and coincides with the meridian line NS. The diurnal circles (KK, MM) of all celestial objects intersect the plane of the horizon at right angles. In this case, all celestial objects rise and set (Figure 3). The angle between the polar axis and the horizon increases as the observer moves along the earth’s surface from the equator to the pole. More and more objects cease to set or to rise. At the pole (Ф = 90°), the polar axis coincides with the vertical, and the equatorial plane coincides with the plane of the horizon. In this case, each celestial object either never sets or never rises, since the diurnal circles (KK, MM) are situated in planes parallel to the horizon (Figure 4).
REFERENCES
Blazhko, S. N.Kurs sfericheskoi astronomii. Moscow-Leningrad, 1948.Kazakov, S. A.Kurs sfericheskoi astronomii, 2nd ed. Moscow-Leningrad, 1940.
V. P. SHCHEGLOV
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