# Declination: Wikis

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# Encyclopedia

Updated live from Wikipedia, last check: May 23, 2013 18:37 UTC (43 seconds ago)

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 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.

## Stars

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.

## Varying declination

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

### 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, 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:

$\delta_\odot = -23.45^\circ \cdot \cos \left [ \frac{360^\circ}{365} \cdot \left ( N + 10 \right ) \right ]$

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]

$\delta_\odot = 23.45^\circ \cdot \sin \left [ \frac{360^\circ}{365} \cdot \left ( N + 284 \right ) \right ]$

A more precise formula is given by:[2]

$\ \delta_\odot = \frac{180^\circ}{\pi} \cdot (0.006918 - 0.399912 \cos \gamma + 0.070257 \sin \gamma - 0.006758 \cos 2\gamma + 0.000907 \sin 2\gamma - 0.002697 \cos 3\gamma + 0.00148 \sin 3\gamma)$

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.

## References

1. ^ Desmond Fletcher (2007). "Solar Declination". Retrieved 2010-02-18.
2. ^

# 1911 encyclopedia

Up to date as of January 14, 2010
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# Wikibooks

Up to date as of January 23, 2010

### From Wikibooks, the open-content textbooks collection

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.

# Simple English

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.