Equatorial coordinate system in the context of "Origin (mathematics)"

The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at Earth's North Pole and South Pole, respectively. As Earth spins on its axis, the two celestial poles remain fixed in the sky, and all other celestial points appear to rotate around them, completing one circuit per day (strictly, per sidereal day).

The celestial poles are also the poles of the celestial equatorial coordinate system, meaning they have declinations of +90 degrees and −90 degrees (for the north and south celestial poles, respectively). Despite their apparently fixed positions, the celestial poles in the long term do not actually remain permanently fixed against the background of the stars. Because of a phenomenon known as the precession of the equinoxes, the poles trace out circles on the celestial sphere, with a period of about 25,700 years. The Earth's axis is also subject to other complex motions which cause the celestial poles to shift slightly over cycles of varying lengths (see nutation, polar motion and axial tilt). Finally, over very long periods the positions of the stars themselves change, because of the stars' proper motions. To take into account such movement, celestial pole definitions come with an epoch to specify the date of the rotation axis; J2000.0 is the current standard.

Right ascension (abbreviated RA; symbol α) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.

An old term, right ascension (Latin: ascensio recta) refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle. It contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from most latitudes on Earth, where the celestial equator intersects the horizon at an oblique angle.

In astronomy, declination (abbreviated dec; symbol δ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. The declination angle is measured north (positive) or south (negative) of the celestial equator, along the hour circle passing through the point in question.

The root of the word declination (Latin, declinatio) means "a bending away" or "a bending down". It comes from the same root as the words incline ("bend forward") and recline ("bend backward").

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. Due to the Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic (the plane of Earth's orbit), but has varied from about 22.0° to 24.5° over the past 5 million years due to Milankovitch cycles and perturbation from other planets.

An observer standing on the Earth's equator visualizes the celestial equator as a semicircle passing through the zenith, the point directly overhead. As the observer moves north (or south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect the horizon due east and due west, regardless of the observer's position on the Earth. At the poles, the celestial equator coincides with the astronomical horizon. At all latitudes, the celestial equator is a uniform arc or circle because the observer is only finitely far from the plane of the celestial equator, but infinitely far from the celestial equator itself.

Proper motion is the angular speed of a celestial object, such as a star, as it moves across the sky. It is an astrometric measure, giving an object's change in angular position over time relative to the center of mass of the Solar System. This parameter is measured relative to the distant stars or a stable reference such as the International Celestial Reference Frame (ICRF). Patterns in proper motion reveal larger structures like stellar streams, the general rotation of the Milky Way disk, and the random motions of stars in the Galactic halo.

The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μ_α) and of declination (μ_δ). Their combined value is computed as the total proper motion (μ). It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year.

Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.

An example of precession and nutation is the variation over time of the orientation of the axis of rotation of the Earth. This is important because the most commonly used frame of reference for measurement of the positions of astronomical objects is the Earth's equator — the so-called equatorial coordinate system. The effect of precession and nutation causes this frame of reference itself to change over time, relative to an arbitrary fixed frame.

Star position is the apparent angular position of any given star in the sky, which seems fixed onto an arbitrary sphere centered on Earth. The location is defined by a pair of angular coordinates relative to the celestial equator: right ascension (α) and declination (δ). This pair based the equatorial coordinate system.

While δ is given in degrees (from +90° at the north celestial pole to −90° at the south), α is usually given in hour angles (0 to 24 h). This is due to the observation technique of star transits, which cross the field of view of telescope eyepieces due to Earth's rotation. The observation techniques are topics of positional astronomy and of astrogeodesy.

The galactic plane is the plane on which most of a disk-shaped galaxy's mass lies. The directions perpendicular to the galactic plane point to the galactic poles. In actual usage, the terms galactic plane and galactic poles usually refer specifically to the plane and poles of the Milky Way, in which Planet Earth is located.

Some galaxies are irregular and do not have any well-defined disk. Even in the case of a barred spiral galaxy like the Milky Way, defining the galactic plane is slightly imprecise and arbitrary since the stars are not perfectly coplanar. In 1959, the IAU defined the position of the Milky Way's north galactic pole as exactly RA = 12 49 , Dec = 27° 24′ in the then-used B1950 epoch; while in the currently-used J2000 epoch, after precession is taken into account, its position is RA 12 51 26.282, Dec 27° 07′ 42.01″. This position is in Coma Berenices, near the bright star Arcturus; likewise, the south galactic pole lies in the constellation Sculptor.