In astronomy, declination 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. 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 dec of 0°.
An object at the celestial north pole has a dec of + 90°.
An object at the celestial south pole has a dec 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. 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.
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 and proper motion.
Sun
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.
Moon
Declination of the Moon is computed by adding Sun's declination (which is called Declination of Place while computing declination of other planets and Moon) to Moon's latitude. Sun's declination (± 23.44°) is much larger in magnitude than Moon's latitude (± 5.14°). The Moon's declination can be said to have an annual cycle synchronous with that of the Sun starting with the vernal equinox.
Moon's latitude is a function of the difference between True Moon and its ascending node. Since lunar nodes make one revolution in nearly 19 years, lunar latitude has an approximately 19 year long cycle. Lunar latitude is equal to inverse sine of the product of sine of maximum lunar latitude and sine of difference between Moon and its node.
For greater accuracy, reduced latitude is used instead of Moon's true latitude, which is obtained by multiplying lunar latitude with a multiplier having a maximum value of 1 for tropical Moon at 180° and 0.91745 for tropical Moon at 0°. This is caused by a third cycle in lunar declination which has a period of one lunar month and a maximum range of ± 0.425°. Summing all three components gives a range of maximum declination from +28°35' to +18°18' and the minimum from -18°18' to -28°35' for lunar declination.
