A well-defined co-ordinate system is an essential requirement if individual objects are to be identified in a unique manner. In astronomy, objects are observed on the celestial sphere with positions defined in spherical co-ordinate systems, measured in angular units (degrees, radians). These are directly analogous to the system of longitude and latitude used to determine positions on the surface of the Earth; indeed, the primary celestial system is a direct projection of the geographic system.
There are four main celestial systems, each defined with reference to a fundamental reference plane which passes through the centre of the sphere (the observer). The circle defined by where this plane intersects the celestial sphere (AFBC in Figure 1.2) is a great circle: defining the diameter of the sphere as r = 1 unit, the length of this circle is 2-k, the maximum possible. Any circle defined by a plane which does not pass through the centre of the sphere (such as DSE, parallel to ABC, in Figure 1.2) has a smaller circumference and is known as a small circle. Each great circle has two poles - the two diametrically-opposed points on the celestial sphere which lie 90° from every point on the great circle. In Figure 1.2, P and Q identify the two poles of the great circle ABC.1
Any circle drawn through both poles is a great circle, intersecting the reference circle ABC at an angle of 90°. Choosing one 180° segment of a polar circle (for example, PBQ in Figure 1.2) as a second reference then defines an orthogonal coordinate system. Consider the point S in Figure 1.2. This point is defined uniquely by two angles: the angle between the reference polar circle, PBQ, and the polar circle passing through S (the angle BPS, which is also the angular length of the arc BF); and by the angular distance PS. In most systems, the latter angle is defined with respect to the fundamental circle, so the angle becomes FS = 90° — PS. In the case of the terrestrial system of latitude and longitude, the fundamental circle is the equator, while the Greenwich meridian defines the reference polar circle. The angle BPS then defines the longitude of a given location on the Earth's surface, while FS gives the latitude.
1 Since P and Q are the poles of only one great circle, ABC, it is clear that a given co-ordinate system can be defined unambiguously either by the position of the reference great circle or by the positions of the poles of that great circle.
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