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  1. Plural of declination

Extensive Definition

In astronomy, declination (abbrev. dec or δ) is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Dec is comparable to latitude, projected onto the celestial sphere, and is measured in degrees north and south of the celestial equator. Therefore, points north of the celestial equator have positive declinations, while those to the south have negative declinations.
The sign is customarily included even if it is positive. Any unit of angle can be used for declination, but it is often expressed in degrees, minutes, and seconds of arc.
A celestial object that passes over zenith, has a declination equal to the observer's latitude, with northern latitudes yielding positive declinations. A pole star therefore has the declination +90° or -90°. Conversely, at northern latitudes φ > 0, celestial objects with a declination greater than 90° - φ, are always visible. Such stars are called circumpolar stars, while the phenomenon of a sun not setting is called midnight sun.
If instead of measuring from and along the equator the angles are measured from and along the horizon, the angles are called azimuth and altitude (elevation).


Because a star lies in a nearly constant direction as viewed from earth, its declination is approximately constant from year to year. However, both the right ascension and declination do change gradually due to the effects of precession of the equinoxes and proper motion.

Varying declination

The declinations of all solar system objects change much more quickly than those of stars.


The declination of the Sun (δ) is the angle between the rays of the sun and the plane of the earth's equator. Since the angle between the earth axis and the plane of the earth orbit is nearly constant, δ varies with the seasons and its period is one year, that is the time needed by the earth to complete its revolution around the sun.
When the projection of the earth axis on the plane of the earth orbit is on the same line linking the earth and the sun, the angle between the rays of the sun and the plane of the earth equator is maximum and its value is 23°27'. This happens at the solstices. Therefore δ = +23°27' at the northern hemisphere summer solstice and δ = -23°27' at the northern hemisphere winter solstice. Due to the changes in the tilt of the Earth's axis, the angle between the rays of the sun and the plane of the earth equator is slightly decreasing.
When the projection of the earth axis on the plane of the earth orbit is perpendicular to the line linking the earth and the sun, the angle between the rays of the sun and the plane of the earth equator is null. This happens at the equinoxes. Therefore δ is 0° at the equinoxes.
Since the eccentricity of the earth orbit is quite low, it can be approximated to a circle, and δ is approximately given by the following expression:
\delta = -23.45^\circ \cdot \cos \left [ \frac \cdot \left ( N + 10 \right ) \right ]
where cos operates on degrees; if cos operates on radians, 360° in the equation needs to be replaced with 2π and will still output δ in degree; N is Day of the Year, that is the number of days spent since January 1.
An alternative form is given as:
\delta = 23.45^\circ \cdot \sin \left [ \frac \cdot \left ( N + 284 \right ) \right ]
A more precise formula is given by:
\ \delta = \frac \cdot (0.006918 - 0.399912 \cos \gamma + 0.070257 \sin \gamma - 0.006758 \cos 2\gamma + 0.000907 \sin 2\gamma - 0.002697 \cos 3\gamma + 0.00148 \sin 3\gamma)
\gamma = \frac ( N - 1 )
is the fractional year in radians.
More accurate daily values from averaging the four years of a leap-year cycle are given in the Table of the Declination of the Sun.


The Moon also has an annual cycle, with maximum declination at northern hemisphere midwinter and minimum at midsummer. There is also an approximately 19 year long cycle, varying the maximum declination from +28°35' to +18°18' and the minimum from -18°18' to -28°35'.

See also

Declination is used in some contexts that rule out astronomical declination, to mean the same as magnetic declination.
Declination is occasionally and erroneously used to refer to the linguistic term declension.


declinations in Arabic: میل
declinations in Asturian: Declinación (astronomía)
declinations in Bulgarian: Деклинация
declinations in Czech: Deklinace
declinations in Danish: Deklination (astronomi)
declinations in German: Deklination (Astronomie)
declinations in Estonian: Kääne (astronoomia)
declinations in Modern Greek (1453-): Απόκλιση αστέρος
declinations in Spanish: Declinación (astronomía)
declinations in Esperanto: Deklinacio (astronomio)
declinations in Persian: میل
declinations in French: Déclinaison (astronomie)
declinations in Irish: Diallas
declinations in Korean: 적위
declinations in Croatian: Deklinacija (astronomija)
declinations in Indonesian: Deklinasi
declinations in Italian: Declinazione (astronomia)
declinations in Latin: Declinatio (astronomia)
declinations in Luxembourgish: Deklinatioun (Astronomie)
declinations in Lithuanian: Deklinacija
declinations in Latvian: Deklinācija (astronomijā)
declinations in Malayalam: ഡെക്ലിനേഷന്‍
declinations in Dutch: Declinatie (astronomie)
declinations in Japanese: 赤緯
declinations in Norwegian: Deklinasjon
declinations in Norwegian Nynorsk: Deklinasjon
declinations in Polish: Deklinacja (astronomia)
declinations in Portuguese: Declinação
declinations in Slovak: Deklinácia
declinations in Serbo-Croatian: Deklinacija (astronomija)
declinations in Finnish: Deklinaatio
declinations in Swedish: Deklination (astronomi)
declinations in Thai: เดคลิเนชัน
declinations in Vietnamese: Xích vĩ
declinations in Chinese: 赤纬
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