Celestial sphere

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 conceptual tool used in spherical astronomy to specify the position of an object in the sky without consideration of its linear distance from the observer. The celestial equator divides the celestial sphere into northern and southern hemispheres.

Introduction

Because astronomical objects are at such remote distances, casual observation of the sky offers no information on their actual distances. All celestial objects seem equally far away, as if fixed onto the inside of a sphere with a large but unknown radius,
which appears to rotate westward overhead; meanwhile, Earth underfoot seems to remain still. For purposes of spherical astronomy, which is concerned only with the directions to celestial objects, it makes no difference if this is actually the case or if it is Earth that is rotating while the celestial sphere is stationary.

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 (a "vanishing circle").

Conversely, observers looking toward the same point on an infinite-radius celestial sphere will be looking along parallel lines, and observers looking toward the same great circle, along parallel planes. On an infinite-radius celestial sphere, all observers see the same things in the same direction.

For some objects, this is over-simplified. Objects which are relatively near to the observer (for instance, the Moon) will seem to change position against the distant celestial sphere if the observer moves far enough, say, from one side of planet Earth to the other. This effect, known as parallax, can be represented as a small offset from a mean position. The celestial sphere can be considered to be centered at the Earth's center, the Sun's center, or any other convenient location, and offsets from positions referred to these centers can be calculated.

In this way, astronomers can predict geocentric or heliocentric positions of objects on the celestial sphere, without the need to calculate the individual geometry of any particular observer, and the utility of the celestial sphere is maintained. Individual observers can work out their own small offsets from the mean positions, if necessary. In many cases in astronomy, the offsets are insignificant.

The celestial sphere can thus be thought of as a kind of astronomical shorthand, and is applied very frequently by astronomers. For instance, the ''Astronomical Almanac'' for 2010 lists the apparent geocentric position of the Moon on January 1 at 00:00:00.00 Terrestrial Time, in equatorial coordinates, as right ascension 6^h 57^m 48.86^s, declination +23° 30' 05.5". Implied in this position is that it is as projected onto the celestial sphere; any observer at any location looking in that direction would see the "geocentric Moon" in the same place against the stars. For many rough uses (e.g. calculating an approximate phase of the Moon), this position, as seen from the Earth's center, is adequate.

For applications requiring precision (e.g. calculating the shadow path of an eclipse), the ''Almanac'' gives formulae and methods for calculating the ''topocentric'' coordinates, that is, as seen from a particula