The sun's full circle

Two linked figures. The large one is the sun's diurnal circle, a full 360-degree day seen edge on, cut by the horizon where the sun actually crosses it, with the twilight bands widening as the latitude rises and the lit arc growing or shrinking with the season. In the top right corner sits a compass rose, the same instant seen from above, with the sun's bearing lit.

You stand at the centre, and the ring around you is one whole day. The sun comes up on the right, climbs across the southern sky, goes down on the left, then carries on under your feet through the night. Drag it anywhere round the ring, or click either bearing to send it there.

The ring is time, in equal steps: a quarter turn is six hours, wherever you stand. How high the sun climbs depends on your latitude. It peaks at 90° minus wherever you are, so only on the equator does it pass overhead. Drag the latitude and the twilight wedges widen. At the equator the sun crosses all eighteen degrees of twilight in seventy minutes; by the Arctic circle it takes over three hours. At the poles it never leaves the horizon. Go south of the equator and the noon sun swings through north.

The rim readings come and go for the same reason. They mark elevations, and the sun has to reach a height before you can mark it. At 55°N at an equinox it peaks at 35°, so the rim carries 30° and stops there. Nowhere in that day does the sun stand at 60°, so there is nowhere on the ring to put the label. Move towards the equator and the higher readings arrive one at a time: 45° once you are inside 45° of latitude, 60° inside 30°, 75° inside 15°. You only get 90° on the equator, where the noon sun passes overhead.

The big ring is the sun's diurnal circle, the path it traces through one turn of the Earth, drawn edge on with you at the centre. The lit half above the horizon is the diurnal arc, the dark half below it the nocturnal arc. Angle around the ring is the hour angle, fifteen degrees to the hour, and the rim readings are altitude, the sun's height above the horizon. The bands either side of the horizon are the three twilights: civil to −6°, nautical to −12°, astronomical to −18°. Open the stretch control and that even scale spreads. Four corners stay pinned, six hours either side of noon out at the sides, noon on top and midnight underneath, while the hours near the sides take more of the ring and the middle of the day takes less. Watch the hour ticks bunch as you drag. Centre the slider and the ring is even time again.

The small figure in the corner is a compass rose, the same instant seen from above. Its sixteen names are the points of the compass, and the lit sector holds the sun's azimuth, its bearing clockwise from north. Ring and rose together give the sun's horizontal coordinates, altitude from one and azimuth from the other, which is everything you need to point at it.

The fourth control is the season, and what it moves is the sun's declination: how far north or south of the equator the sun itself stands, nought at an equinox and 23.4° either way at the solstices, because that is the tilt of the Earth. It is the control that moves the horizon. Drag it up and the two crossings slide down the rim, the lit arc grows past half the ring, and sunup walks north of due east; drag it down and the day closes to a wedge. Only at the equinox, where it starts, does the sun rise due east and spend twelve hours up. Push it far enough at a high latitude and the horizon leaves the ring altogether, which is a midnight sun, and the figure stops drawing a horizon rather than inventing one.

The sun answers on the calculator draw this same ring underneath themselves, set to the latitude and the season of whatever was asked about, which is why a link out of one of them opens this page already moved. Ask for day length in dublin and the arc you get here is the length that answer prints. The clock times stay the calculator's: this figure knows where the sun is, and only the calculator knows what time it is where you are.