Solar declination

The position of the Sun in the sky is a function of both time and the geographic coordinates of the observer on the surface of the Earth. As the Earth orbits the Sun during the course of the year, the Sun appears to move with respect to the fixed stars on the celestial sphere, along a planar path called the ecliptic. The Earth's rotation about its axis causes the fixed stars to move across the sky in a way that depends on the observer's geographic latitude. The time when a given fixed star transits the observer's meridian depends on the geographic longitude. To find the Sun's position for a given observer at a given time, one may therefore proceed in three steps:

This calculation is useful in astronomy, navigation, surveying, meteorology, climatology, solar energy, and for designing sundials.

These equations, from the Astronomical Almanac, can be used to calculate the apparent coordinates of the Sun, mean equinox and ecliptic of date, to a precision of about 0°.01 (36″), for dates between 1950 and 2050.

Start by calculating n, the number of days (positive or negative) since Greenwich noon, Terrestrial Time, on 1 January 2000 (J2000.0). If you know the Julian date for your desired time then

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