A year of daylight

What the bands are

Sunrise and sunset are the moments the top of the Sun meets the horizon, allowing for the air bending its light. After sunset the sky darkens in three steps that astronomers name by how far the Sun has sunk: civil twilight to six degrees below the horizon, when it is still light enough to read outside; nautical twilight to twelve, when the horizon at sea disappears; and astronomical twilight to eighteen, after which the sky is fully dark. In summer, far enough from the equator, the Sun never sinks that far, and the night never gets fully dark.

Why the earliest sunset is not on the shortest day

The shortest day is the solstice, but by the clock the earliest sunset comes a week or two before it and the latest sunrise a week or two after. The Sun’s own noon is not quite at the same clock time every day: the Earth’s orbit is an ellipse and its axis is tilted, so solar noon drifts by about half an hour over the year. The length of the day turns at the solstice while the middle of the day is still sliding, and the two ends turn at different times.

How it is worked out

For every day the page takes the Sun’s position from the same astronomy as the rest of the site and works out when it crosses each of the four heights, then gives the times by the clock of the place, so the steps where the clocks change are really there. It is accurate to within a minute or two, and it describes the sky and nothing more.

What is calculated for each day

For each day of the current year the page takes the Sun’s position at the place’s local noon: its declination, how far north or south of the celestial equator it stands, and its right ascension, which with the sidereal time gives the moment of solar noon. From the latitude and the declination one formula gives how long before and after noon the Sun reaches each of four heights: 0.833 degrees below the horizon for sunrise and sunset, which allows for the Sun’s half-width and the bending of its light by the air, and 6, 12 and 18 degrees below for the three twilights. When the formula has no answer, the Sun does not reach that height that day, and the band covers the whole day or none of it. That is how the polar day and the polar night appear without any special case.

Reading the chart, with an example

The days of the year run across the chart and the hours down it, midnight at the top and bottom. Move the slider and the line under the chart reads that day: sunrise, sunset, the length of daylight and when it is fully dark. At about 60 degrees north, the latitude of Oslo or Helsinki, the bright band swells to nearly nineteen hours in June and shrinks to about six in December, and for about four months around midsummer the night band vanishes, because the Sun never sinks eighteen degrees. Near the equator the bands barely change all year, and daylight stays a few minutes over twelve hours.

Latitude, seasons and the clocks

Day length changes because the Earth’s axis is tilted by about 23.4 degrees, so over a year the Sun’s declination swings from 23.4 degrees north to 23.4 south. The further a place is from the equator, the more that swing changes how much of the Sun’s daily circle is above the horizon. More than about 48½ degrees from the equator it is never fully dark around the summer solstice; beyond about 66½, inside the polar circles, there are days when the Sun does not set and days when it does not rise. South of the equator the seasons are reversed, and the longest day comes around the December solstice.

The chart covers the current calendar year. Times are by the clock of the place when its time zone is known, so the bands step by an hour on the days the clocks change, and by this device’s clock otherwise. The equinoxes and solstices are ticked along the top; their dates move by a day or so with the year and the time zone. On the equinox itself daylight is a few minutes longer than twelve hours almost everywhere, because sunrise and sunset are counted from the top edge of the Sun and the air lifts its image, so the day of equal day and night falls a few days away from it.

Where the Sun rises on the horizon and how high it climbs is drawn on Sun path, and the same span from sunrise to sunset is cut into twelve on Hours. Which planets are up once it is dark is on Tonight, and the equinoxes and solstices themselves on The year.