Solar declination

Solar declination is the Sun’s angular distance north or south of Earth’s equator, measured on the celestial sphere. Its value changes through the year as Earth orbits the Sun with a tilted axis.

Earth's axial tilt: The angle between Earth’s rotational axis and the perpendicular to its orbital plane, about 23.4 degrees. This tilt causes the Sun’s declination to vary between the tropics over the year.
Solar zenith angle: The angle between the direction to the Sun and the local vertical. Declination helps determine how high the Sun stands above the horizon at a given place and time.
Celestial sphere: An imagined sphere centered on an observer, used to describe the apparent positions of celestial objects. Declination is defined as an angular coordinate on this model of the sky.
June solstice: The annual moment when the Sun reaches its greatest northern declination, marking summer in the Northern Hemisphere. Solar declination reaches its northern limit at this point in the year.
Ecliptic: The apparent annual path of the Sun across the celestial sphere, lying in the plane of Earth’s orbit. The Sun’s position on the ecliptic determines its declination when projected onto the celestial equator.
Sunrise equation: An equation relating latitude, solar declination, and horizon altitude to the Sun’s hour angle at sunrise or sunset. It uses declination to calculate sunrise and sunset times.
Equatorial coordinate system: A celestial coordinate system that locates objects by right ascension and declination relative to Earth’s equator. Solar declination is the Sun’s north–south coordinate in this system.
December solstice: The annual moment when the Sun reaches its greatest southern declination, marking winter in the Northern Hemisphere. Solar declination reaches its southern limit at this point in the year.
Celestial equator: The projection of Earth’s equator onto the celestial sphere. Solar declination measures angular distance from this reference circle.
Solar time: Time measured by the Sun’s apparent position in the sky rather than by a uniform clock. Solar-position calculations pair declination with hour angle to establish local solar time.

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