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to be mentioned first. Initially, it helps to have some idea of the location of north from your observing position. (We shall see shortly how this may be determined accurately from the stars themselves.)

      Everything in the sky appears to lie on a gigantic sphere (the celestial sphere), centred on the observer. From our position on Earth, we can, of course, see only half of this at any one time, because half is below our horizon. Although in practice the actual horizon is irregular, and quite large parts of the sky may be hidden by mountains, hills, trees, buildings or other objects, the astronomical horizon is assumed to be a perfectly even boundary, like a sea horizon. It forms the basis of one method of describing positions in the sky, using co-ordinates known as altitude and azimuth.

      Altitude is the elevation of an object, in degrees, above the horizon, ranging from 0° (object on the horizon), to 90° (object directly overhead). Note that objects may have negative altitude, i.e., be below the horizon. The second co-ordinate, azimuth, is measured from 0–360 degrees, clockwise, from the north point of the horizon. Due north is thus 0° (and 360°), east 90°, south 180°, and west 270°. (Note that some older books use a different definition of azimuth, but the one just described is the form generally used today.)

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      Important terms for positions in the sky, relative to the observer at the centre.

      The point directly above the observer’s head is known as the zenith (altitude 90°) and is frequently used in astronomy. The corresponding point directly below the observer’s feet is known as the nadir.

      An important line in the sky is the meridian, which runs around the sky from the north point, through the zenith, the south point, the nadir, and back to the north point. From the surface of the Earth, only half of the meridian is visible at any one time, of course. Astronomers use the term ‘transit’ for when an object crosses the meridian in the south, when it is also said to ‘culminate’ (reach its highest altitude).

      Because of the Earth’s rotation from west to east, the celestial sphere seems to rotate round the Earth once a day from east to west. Everyone is used to seeing the Sun (and Moon) rise in the east and set in the west, but it still comes as a surprise to some people that the stars and planets do the exactly same.

      The celestial sphere appears to rotate around an invisible axis, running from the north celestial pole, through the centre of the Earth, to the south celestial pole. The location of the celestial poles relative to an observer depends upon the latter’s position on Earth, more specifically, on their latitude. At the North Pole, the North Celestial Pole is directly overhead (at the zenith); at the Equator, both celestial poles lie (theoretically) on the horizon; and at the South Pole, it is the South Celestial Pole that is at the zenith, with the North Celestial Pole at the nadir. The altitude of the celestial pole is exactly the same as the observer’s latitude. At 40°N, for example, the North Celestial Pole has a altitude of 40°, and an azimuth of 0°. Similar considerations apply in the southern hemisphere.

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      The altitude of Polaris above the northern horizon is equal to the observer’s latitude.

      This has an important effect. An area of sky around the celestial pole, with a radius equal to the observer’s latitude, is always above the horizon. Stars in this region are circumpolar: they are visible whenever it is dark. Identifying the constellations in this area is therefore easy, and an ideal way of starting to learn your way around the sky.

      Although it would be possible to locate anything in the sky by referring to its altitude and azimuth, this is not particularly practical for most observers. Both co-ordinates alter throughout the night as an object moves across the sky and, in any case, they are different for every observer. Computer-controlled telescopes (including the largest telescopes on Earth) do use altitude and azimuth, but the positions of objects on the celestial sphere, on charts and atlases, and in catalogues are always specified by a different pair of co-ordinates.

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      How the celestial co-ordinates Right Ascension and Declination are determined.

      From this point (0h), right ascension is measured eastwards along the celestial equator (anticlockwise looking down on the North Pole). As the Earth rotates, the right ascension on the meridian (or in any other fixed direction) continuously increases. As we shall see shortly, however, after 24 hours as shown by our terrestrial clocks, the right ascension on the meridian will not be precisely the same as the previous day, but will have increased by approximately 3m 56s. The line of right ascension passing through an object is known as the hour circle.

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      Because of precession, the vernal equinox has migrated from Aries into Pisces, and is moving southwest towards Aquarius.

      Describing the directions of celestial objects may cause confusion unless one is careful. We must be certain whether we are talking about the position of an object relative to the horizon and the standard compass points, or whether we are referring to its position on the celestial sphere. Generally if a celestial object as said to lie north-west (for example) of a particular star it is taken to mean that the directions are those that apply on the celestial sphere.

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