The celestial sphere is the imaginary sphere covering the sky surrounding the Earth with the Earth at the center of the sphere. It is a way to map the location of stars, galaxies, and extra-solar objects in the sky, as well as track the movements of the Sun, Moon, and planets among the background stars.
There are a few important locations on the sphere that should be defined to help get a sense of what to look for in the sky.
Zenith: the point on the celestial sphere directly above your location on Earth. This point is dependent on where you are on Earth. To someone in Pittsburgh, PA, USA, their zenith is not that same as to someone in Sydney, New South Wales, Australia.
Nadir: the point on the celestrial sphere directly below your location on Earth. Like the zenith, this is location dependent.
The North (South) Celestial Pole: the point on the celestial sphere directly above the North (South) Pole on Earth. The North (South) Celestial Pole is the zenith for the North (South) Pole and the The South (North) Celestial Pole is the nadir for the South (North) Pole.
The Celestial Equator: similar to the equator on Earth. In fact, it is the imaginary line on the celestial sphere is directly above the Earth's equator. It is used to help explain the equinoxes as well as the solstices.
Celestial Prime Meridian: the line on the celestial sphere equally 0h Right Ascension. It is the line directly corresponding to 0° longitude on Earth, i.e. the prime meridian running through Greenwich, England.
Right Ascension: equivalent to longitude on Earth, this is an angle measured in hours, minutes, and seconds from 0h to 24h. The angle increases from east to west, from the Celestial Prime Meridian
Declination: equivalent to latitude on Earth, also measured in degrees, arcminutes, and arcseconds from 0° to 90° from the Celestial Equator to the Celestial Poles. Travelling north from the Celestial Equator to the North Celestial Pole, the angles are positive, and travelling south from the Celestial Equator to the South Celestial Pole, the angles are negative.
Ecliptic: this is defined in another page, located here. It is the imaginary path the Sun traces over a course of the year on the Celestial Sphere. It is tilted at 23.5° with respect to the Celestial Equator and when it crosses the Celestial Equator, the equinoxes occur. At the Sun's northernmost point on the ecliptic, we have the summer solstice in the Earth's northern hemisphere and the winter solstice in the southern hemiphere. At the Sun's southermost point, the solstices are switched.
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