Declination

Definition

Declination, written δ or Dec, is the angle between a celestial object and the celestial equator, measured along the hour circle through the object. It runs from +90° at the north celestial pole, through 0° on the equator, to −90° at the south celestial pole. It is the sky's version of geographic latitude, and with right ascension it forms the equatorial coordinate system.

Declination is written in degrees, arcminutes and arcseconds, always with its sign: Sirius is at δ = −16° 42′ 58″, Vega at +38° 47′ 01″. Like right ascension, and unlike altitude, it does not depend on the observer's place or the time of night.

Which stars you can see from your latitude

Declination alone decides whether a star rises at your latitude φ, how high it climbs, and whether it ever sets. For an observer in the northern hemisphere:

• Circumpolar, never sets: δ > 90° − φ.
• Never rises: δ < −(90° − φ).
• Altitude at culmination, when it crosses the meridian: h = 90° − |φ − δ|.

Example for Paris, φ = 48.85° N. Stars north of δ = +41.15° are circumpolar: Capella (+46.0°) never sets, while Vega (+38.8°) dips briefly below the northern horizon. Sirius (−16.7°) culminates only 24.4° above the southern horizon. Canopus (−52.7°), the second brightest star, never rises: it needs a latitude south of about 37° N.

In the southern hemisphere the same rules apply with the signs reversed.

The Sun's declination through the year

Because the ecliptic is tilted by ε ≈ 23.44° to the celestial equator, the Sun's declination swings through the year: +23.44° at the June solstice, 0° at the equinoxes and −23.44° at the December solstice. This is the origin of the seasons and of the tropics, whose latitudes equal the Sun's extreme declinations. Since the Sun's ecliptic latitude is practically zero, its declination follows directly from its ecliptic longitude λ:

sin δ = sin β × cos ε + cos β × sin ε × sin λSun (β ≈ 0):  sin δ = sin ε × sin λ

Example: around 21 May the Sun's longitude is 60°. Then sin δ = 0.39777 × 0.86603 = 0.34448, and δ = +20.15°.

The noon altitude of the Sun follows from the culmination rule: h = 90° − φ + δ. In Paris it reaches 64.6° at the June solstice and only 17.7° at the December solstice.

The Moon and the planets

The planets stay close to the ecliptic, so their declinations also range between about −27° and +27°. The Moon's orbit is tilted 5.1° to the ecliptic, and its nodes turn around in 18.6 years. At a major lunar standstill, as in 2024–2025, the Moon's declination reaches about ±28.6° each month: it rises far to the north-east and sets far to the north-west, and two weeks later stays very low. At a minor standstill, nine years later, the range shrinks to about ±18.3°.

Declination changes with precession

Precession moves the celestial equator and the poles, so declinations change slowly too, by up to 20″ per year. Over centuries the effect is large. Polaris, at δ ≈ +89.4° today, will pass closest to the pole around the year 2100, at about 27′. In 12,000 years Vega, now at +38.8°, will be close to the pole. Star coordinates are therefore always given for a stated epoch, usually J2000.0.

Declination and altitude

Declination is fixed to the sky; altitude is fixed to your horizon. The two coincide only in special cases: for an observer at the North Pole, the altitude of every star equals its declination. Elsewhere the conversion needs the latitude and the hour angle H, as in Meeus:

sin h = sin φ × sin δ + cos φ × cos δ × cos H

Explore it on AstroAlgos

• Equatorial coordinates — right ascension and declination together
• Celestial equator — the zero of declination
• Horizontal coordinates — altitude and azimuth
• Night sky — see how high each star climbs from your location