## The Celestial Sphere

The celestial sphere is an imaginary sphere of infinite radius centered on the Earth, on which all celestial bodies are assumed to be projected. It is assumed to be fixed, so as the Earth rotates the celestial sphere appears to rotate in the opposite direction (once per day). This apparent rotation of the celestial sphere presents us with an obvious means of defining a coordinate system for the surface of the celestial sphere - the extensions of the north pole (NP) and south pole (SP) of the Earth intersect with the north celestial pole (NCP) and the south celestial pole (SCP), respectively, and the projection of the Earth's equator on the celestial sphere defines the celestial equator (CE). The celestial sphere can then be divided up into a grid, just as the Earth is divided up into a grid according to latitude and longitude.

 [NMSU, N. Vogt]

We can never observe the whole celestial sphere from the Earth, as the horizon limits our view of it. In fact, we can only ever observe half of the celestial sphere at any one time, and the half we observe depends on our position on the Earth's surface. As shown above, an observer has the impression of being on a flat plane and at the center of a vast hemisphere across which the celestial bodies move. On all sides, the plane stretches out to meet the base of this celestial hemisphere at the horizon. The point directly overhead the observer (as defined by a line passing through the center of the Earth and perpendicular to the horizon) is known as the zenith. The point opposite this, which the observer cannot see, is known as the nadir. Because the radius of the celestial hemisphere is infinite compared with the radius of the Earth, the directions of the north celestial pole and the celestial equator as viewed by the observer (NCPo and CEo) are indistinguishable from their real directions (NCPE and CEE), which are defined relative to the center of the Earth.

As the observer moves further north in latitude, the north celestial pole moves closer to the zenith until they become coincident when the observer is at the north pole. At the north pole, the celestial equator lies on the horizon. As the observer moves further south in latitude, the north celestial pole moves further away from the zenith until it lies at the horizon when the observer is at the Earth's equator. At the Earth's equator, the celestial equator passes through the zenith.

The Earth rotates from west to east and hence the stars appear to revolve from east to west about the celestial poles on circular paths parallel to the celestial equator once per day. Circumpolar stars never set, and remain visible at night all year. A circumpolar star at its maximum altitude above the horizon is said to be at its upper culmination and at its minimum altitude above the horizon is said to be at its lower culmination. Stars further from the pole rise, attain a maximum altitude above the horizon (when they are said to transit) and then set below the horizon. These stars are visible at night only during that part of the year when the Sun is in the opposite part of the sky. Which stars are circumpolar depends on the latitude of the observer; stars within an angle l of the north pole are circumpolar for an observer at northern-hemisphere latitude l, and stars within an angle l of the south pole are never seen by such an observer; the reverse is true for an observer in the southern hemisphere. This means that for observers at the Earth's poles, all of the stars are circumpolar and the observers never see any of stars in the opposite hemisphere. For observers at the Earth's equator, none of the stars are circumpolar and the observers see the whole celestial sphere during the course of a year.

 [NMSU, N. Vogt]

The Sun not only revolves with the stars on the celestial sphere each day, it also moves much more slowly along a path relative to the stars, making one revolution of this path in one year. This motion is due to the fact that the Earth makes one rotation of the Sun each year and because the Sun is much closer to the Earth than the stars. An observer who notes each month what group of stars is first visible above the western horizon after sunset will notice that there is a regular progression along a strip in the celestial sphere. The constellations along this strip are known as the signs of the zodiac.

The apparent path of the Sun in the sky is known as the ecliptic and is actually the intersection of the plane of the Earth's orbit with the celestial sphere. Because the rotation axis of the Earth (which defines the celestial sphere) is tilted at an angle with respect to the plane of the Earth's orbit, the ecliptic is inclined at an angle to the celestial equator. The angle is known as the obliquity of the ecliptic and is currently about 23°27´.

The ecliptic and the equator intercept at two points, associated with the zodiacal constellations of Aries and Libra. The first point of Aries, , is defined to be the point where the Sun, moving along the ecliptic, crosses the celestial equator from south to north. This occurs at the spring equinox (or vernal equinox), on March 21, when day and night are of equal length. Day and night are also of equal length at the autumnal equinox, on September 21, when the Sun crosses the celestial equator from north to south in the constellation of Libra.

The maximum altitude of the Sun in the sky, as viewed from the northern hemisphere, gradually increases from the spring equinox until it reaches a maximum on June 21 - the summer solstice (when the Sun appears to `stand still' in the sky before starting to move back towards the celestial equator). At the summer and winter solstices the Sun is directly overhead at noon at the Tropics of Cancer and Capricorn, respectively, these being the zodiacal constellations associated with those parts of the ecliptic where the Sun is at these times. Similarly, the Sun reaches its minimum altitude in the sky when viewed from the northern hemisphere on December 21 - the winter solstice.

 [NMSU, N. Vogt]