Where does the Sun rise?

Due east only around 20 March and 23 September

On 20 March the Sun comes up in Berlin at 89° on the compass, practically due east, and sets almost due west. Day and night are about the same length, 12.2 hours of daylight. The same happens around 23 September. These are the equinoxes: the Sun stands right above Earth's equator, and its daily path across the sky is half above and half below the horizon.

A common belief is that this is how it works every day. It isn't. On 21 June, the longest day, the Sun rises in Berlin at 48°, 42° further north than in March, at about 3:35 local solar time. Its path across the sky is so much longer that the day lasts 16.8 hours. The exact day closest to due east is shifted a little by the air, which lifts the Sun's image over the horizon: in Berlin it is 19 March and 24 September.

In summer north-east, in winter south-east

After the September equinox the rising point keeps moving, now to the south. By the end of October the Sun rises in Berlin at about 112°, halfway between east and south-east. On 21 December, the shortest day, it rises at 129°, 39° south of east, and only after 8 o'clock solar time. It stays above the horizon for just 7.7 hours.

So over a year the sunrise in Berlin wanders from 48° in June to 129° in December and back: north-east in summer, east in spring and autumn, south-east in winter. Sunset mirrors it in the west. That is why a room with an east window gets morning sun far into its northern corner in June, but only a low, slanting light from the south-east in December.

At noon the Sun stands in the south, but never overhead

Halfway between sunrise and sunset, at noon by the Sun's own clock, it stands due south in Berlin, every day of the year. How high it gets depends on the date: 14° on 21 December, 37° at the equinoxes and 61° on 21 June. Above 60° it only gets from early June to early July.

The rule behind it is simple: the noon height is 90° minus your latitude, plus or minus the tilt of Earth's axis. For Berlin at 52.5° north that gives 90° − 52.5° + 23.4° = 61° in June and 90° − 52.5° − 23.4° = 14° in December. So the Sun is never straight overhead in Berlin, or anywhere in Europe; it always stays at least 29° away from the point straight above you.

Why: Earth's tilted axis

Earth's axis is tilted by 23.4° and always points the same way in space. On 21 June the northern half leans towards the Sun, and the Sun stands straight overhead at 23.4° north, the Tropic of Cancer. Berlin lies 29° further north, so there the noon Sun is 90° − 29° = 61° high. On 21 December the Sun stands overhead at 23.4° south, the Tropic of Capricorn, and Berlin is 76° away from it.

The same tilt moves the sunrise. In June the Sun's daily circle in the sky lies north of the celestial equator, so it comes up north of east and goes down north of west. In December the circle lies south of it, so the Sun rises south of east. Only at the equinoxes, when the Sun is right above the equator, does its circle cross the horizon at due east and due west.

Straight overhead the Sun can only stand between the two tropics, from 23.4° north to 23.4° south. On the equator that happens around 20 March and 23 September, on each tropic once a year, and in between on two days a year.

In the southern hemisphere the noon Sun is in the north

South of the Tropic of Capricorn everything is mirrored. At 34° south, the latitude of Sydney, 21 June is the middle of winter: the Sun rises in the north-east at 62°, stands only 33° high in the north at noon and sets in the north-west after 9.9 hours. In December it rises in the south-east at 119° and climbs to almost 80° in the north.

So the Sun still rises in the east and sets in the west in Australia, South Africa or Argentina. But to face it at noon you look north, and it moves across the sky from right to left, the other way round from Europe.