Why it changes
The Earth's axis is tilted 23.44° to the plane of its orbit and keeps pointing the same way in space. As the Earth goes around the sun, first the northern and then the southern hemisphere leans towards it. Seen from the Earth, the sun appears to slide north and south: at the June solstice it is overhead on the Tropic of Cancer (+23.44°), at the equinoxes over the equator (0°), at the December solstice over the Tropic of Capricorn (−23.44°).
Formula
A simple approximation, good to about a degree, with N the day of the year:
δ ≈ −23.44° · cos( 360° / 365 · (N + 10) )
The values in the table below are exact: they come from the NREL Solar Position Algorithm, which also accounts for the elliptical orbit, nutation and aberration.
| Date | Declination | Equation of time | Noon elevation at 40° N | at 50° N | at 35° S |
|---|---|---|---|---|---|
| 1 Jan | -22.98° | −3.6 min | 27.0° | 17.0° | 78.0° |
| 15 Jan | -21.07° | −9.4 min | 28.9° | 18.9° | 76.1° |
| 1 Feb | -17.02° | −13.5 min | 33.0° | 23.0° | 72.0° |
| 15 Feb | -12.58° | −14.1 min | 37.4° | 27.4° | 67.6° |
| 1 Mar | -7.48° | −12.3 min | 42.5° | 32.5° | 62.5° |
| 15 Mar | -2.02° | −8.9 min | 48.0° | 38.0° | 57.0° |
| 1 Apr | 4.65° | −3.8 min | 54.7° | 44.7° | 50.3° |
| 15 Apr | 9.87° | −0.0 min | 59.9° | 49.9° | 45.1° |
| 1 May | 15.17° | +2.9 min | 65.2° | 55.2° | 39.8° |
| 15 May | 18.94° | +3.7 min | 68.9° | 58.9° | 36.1° |
| 1 Jun | 22.09° | +2.2 min | 72.1° | 62.1° | 32.9° |
| 15 Jun | 23.32° | −0.5 min | 73.3° | 63.3° | 31.7° |
| 1 Jul | 23.08° | −3.9 min | 73.1° | 63.1° | 31.9° |
| 15 Jul | 21.47° | −6.0 min | 71.5° | 61.5° | 33.5° |
| 1 Aug | 17.94° | −6.4 min | 67.9° | 57.9° | 37.1° |
| 15 Aug | 13.95° | −4.5 min | 64.0° | 54.0° | 41.0° |
| 1 Sep | 8.17° | −0.0 min | 58.2° | 48.2° | 46.8° |
| 15 Sep | 2.91° | +4.8 min | 52.9° | 42.9° | 52.1° |
| 1 Oct | -3.30° | +10.3 min | 46.7° | 36.7° | 58.3° |
| 15 Oct | -8.63° | +14.2 min | 41.4° | 31.4° | 63.6° |
| 1 Nov | -14.52° | +16.4 min | 35.5° | 25.5° | 69.5° |
| 15 Nov | -18.56° | +15.4 min | 31.4° | 21.4° | 73.6° |
| 1 Dec | -21.84° | +11.0 min | 28.2° | 18.2° | 76.8° |
| 15 Dec | -23.28° | +4.9 min | 26.7° | 16.7° | 78.3° |
What you can do with it
- Noon height: αnoon = 90° − |φ − δ|.
- Day length: cos H0 = −tan φ · tan δ gives half the day in degrees of hour angle (15° per hour).
- Polar day and night: the sun never sets when |φ| > 90° − |δ| on the summer side.
See how declination moves the sun's path on the sun path diagram or play a whole year on the sun map in Year mode.