In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location.

The celestial sphere is a practical tool for spherical astronomy, allowing astronomers to specify the apparent positions of objects in the sky if their distances are unknown or irrelevant. In the equatorial coordinate system, the celestial equator divides the celestial sphere into two halves: the northern and southern celestial hemispheres.

The celestial sphere can be considered to be infinite in radius. This means any point within it, including that occupied by the observer, can be considered the center. It also means that all parallel lines, be they millimetres apart or across the Solar System from each other, will seem to intersect the sphere at a single point, analogous to the vanishing point of graphical perspective. All parallel planes will seem to intersect the sphere in a coincident great circle.

The ancients assumed the literal truth of stars attached to a celestial sphere, revolving about the Earth in one day, and a fixed Earth. The Eudoxan planetary model, on which the Aristotelian and Ptolemaic models were based, was the first geometric explanation for the “wandering” of the classical planets. The outermost of these “crystal spheres” was thought to carry the fixed stars. Eudoxus used 27 concentric spherical solids to answer Plato’s challenge: “By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?”

Observers on other worlds, such as the Moon or Mars, would see objects in that sky under much the same conditions, as if projected onto a dome. Therefore, coordinate systems based on the sky of that world could be constructed. These could be based on the equivalent “ecliptic”, poles and equator, although the reasons for building a system that way are as much historic as technical.

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