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. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and south of the celestial equator. 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. A pole star therefore has the declination near to +90° or −90°. 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 the Sun not setting is called midnight sun.
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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, proper motion, and annual parallax.
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. The Earth's axial tilt (called the obliquity of the ecliptic by astronomers) is the angle between the Earth's axis and a line perpendicular to the Earth's orbit. The Earth's axial tilt changes gradually over thousands of years, but its current value is about ε = 23°26'. Because this axial tilt is nearly constant, δ☉ varies with the seasons and its period is one year, which is the time needed by the Earth to complete one revolution around the Sun.
At the solstices, the angle between the rays of the Sun and the plane of the Earth's equator reaches its maximum value of 23°26'. Therefore δ☉ = +23°26' at the northern solstice and δ☉ = −23°26' at the southern solstice.
At the moment of each equinox, the center of the Sun appears to pass through the celestial equator, and δ☉ is 0°.
The Sun's declination is equal to the inverse sine of the product of sine of Sun's maximum declination and sine of Sun's tropical longitude at any given moment. Instead of computing the Sun's tropical longitude, if we need Sun's declination in terms of days, the following procedure may be used.
Since the Earth's orbital eccentricity is quite low, its orbit can be approximated as a perfect circle:
![\delta_\odot = -23.45^\circ \cdot \cos \left [ \frac{360^\circ}{365} \cdot \left ( N + 10 \right ) \right ]](http://images-mediawiki-sites.thefullwiki.org/10/3/1/4/77708301727581997.png)
where the cosine operates on degrees; if the cosine's argument is in radians, the 360° in the equation is replaced with 2π. In either case, the formula returns δ☉ in degrees. N is the number of days elapsed since January 1.
An alternative form is given as:[1]
![\delta_\odot = 23.45^\circ \cdot \sin \left [ \frac{360^\circ}{365} \cdot \left ( N + 284 \right ) \right ]](http://images-mediawiki-sites.thefullwiki.org/07/2/3/7/03498911356899801.png)
A more precise formula is given by:[2]
where
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.
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Declination is a measure of how far on the north-south axis an astronomical object is located. It is the celestial equivalent of latitude.
Declination should not be confused with declension, which is a term in grammar.
Declination (abbrev. dec or δ) is a word used in astronomy to describe 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.
   | '''Table of the Declination of the Sun:''' Mean Value for the Four Years of a Leap-Year Cycle - Table of the Declination of the Sun |
| | Declination function for Excel, CAD or your other programs. - The Sun API > Documentation > sdxDecl Function |
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