Declination From Wikipedia, the free encyclopedia Jump to: navigation <#mw-head>, search <#p-search> For other uses, see Declination (disambiguation) . Equatorial coordinates.png 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. * An object on the celestial equator has a declination of 0°. * An object at the celestial north pole has a declination of +90°. * An object at the celestial south pole has a declination of −90°. 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 directly overhead (at the zenith ) has a declination very nearly equal to the observer's latitude. A pole star therefore has the declination near to +90° or −90°. At northern latitudes φ (φ = observer's latitude) > 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 . When an object is directly overhead its declination is almost always within 0.01 degree of the observer's latitude; it would be exactly equal except for two complications. The first complication applies to all celestial objects: the object's declination equals the observer's astronomic latitude, but the term "latitude" ordinarily means geodetic latitude, which is the latitude on maps and GPS devices. The difference usually doesn't exceed a few thousandths of a degree, but in a few places (such as the big island of Hawaii) it can exceed 0.01 degree. For practical purposes the second complication only applies to solar system objects: "declination" is ordinarily measured at the center of the earth, which isn't quite spherical, so a line from the center of the earth to the object is not quite perpendicular to the Earth's surface. It turns out that when the moon is directly overhead its geocentric declination can differ from the observer's astronomic latitude by up to 0.005 degree. The importance of this complication is inversely proportional to the object's distance from the earth, so for most practical purposes it's only a concern with the moon. Contents [hide <#>] * 1 Stars <#Stars> * 2 Varying declination <#Varying_declination> o 2.1 Sun <#Sun> * 3 See also <#See_also> * 4 References <#References> * 5 External links <#External_links> [edit ] Stars A star lies in a nearly constant direction as viewed from Earth , with its declination roughly constant from year to year, but right ascension and declination do both change gradually due to precession of the equinoxes , proper motion , and annual parallax . [edit ] Varying declination The declinations of all solar system objects change much more quickly than those of stars. [edit ] Sun 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, solar declination (δ_☉ ) varies with the seasons and its period is one year . 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 summer solstice and δ_☉ = −23°26' at the southern summer 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. For years with 365 days, the following approximation may be used: \delta_\odot = -23.44^\circ \cdot \cos \left [ \frac{360^\circ}{365} \cdot \left ( N + 10 \right ) \right ] 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 ordinal date ; N=1 at the beginning of January 1; N=365 at the beginning of December 31. An alternative form is given as:^[1] <#cite_note-0> \delta_\odot = 23.44^\circ \cdot \sin \left [ \frac{360^\circ}{365} \cdot \left ( N + 284 \right ) \right ] A more precise formula is given by:^[2] <#cite_note-1> \ \delta_\odot = \frac{180^\circ}{\pi} \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) where \gamma = \frac{2\pi}{365} ( 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 Sun's path over the celestial sphere changes with its declination during the year. Azimuths where the Sun rises and sets at the summer and winter solstices , for an observer at 56°N latitude, are marked in °N on the horizontal axis. [edit ] See also * Celestial coordinate system * Ecliptic * Geographic coordinate system * Inclination * Lunar standstill * Setting circles * Euler angles [edit ] References 1. *^ <#cite_ref-0>* Desmond Fletcher (2007). "Solar Declination" . Archived from the original on 2008-05-24. http://web.archive.org/web/20080524032606/http://holodeck.st.usm.edu/vrcomputing/vrc_t/tutorials/solar/declination.shtml. Retrieved 2010-02-18. 2. *^ <#cite_ref-1>* J. W. Spencer (1971). /Fourier series representation of the position of the sun/ . http://www.mail-archive.com/sundial@uni-koeln.de/msg01050.html. [edit ] External links * *Table of the Declination of the Sun:* Mean Value for the Four Years of a Leap-Year Cycle * Declination function for Excel, CAD or your other programs. The Sun API is free and extremely accurate. For Windows computers. * How to compute planetary positions by Paul Schlyter. 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