What if you lived where the Sun never sets?

Every day the Sun comes up. Every night it goes down. That is how we get day and night.

But in some places, the Sun does not go down at all in summer. How can that be?

Where most people live, the Sun rises in the morning and sets in the evening, even on the longest day of summer. Night always comes.

But far to the north there are towns where, for weeks in summer, the Sun never sets. At midnight it is still shining, low over the horizon. People call it the midnight Sun. In this lab you can travel north in a model of sunlight and find out where, when and why it happens.

Day length depends on latitude and on the Sun's declination, the latitude where it is directly overhead at noon. For most of the populated world, day length swings through the year but never reaches 24 hours.

NSIDC describes the Arctic Circle, at about 66° 33′ N, as the latitude above which the Sun does not set on the summer solstice. This lab asks what sets that line, and how long polar day lasts as you go farther north.

Near New York or Madrid, a summer day is long. The Sun is up for about 15 hours.

Then the Sun sets. The night is short, but it still comes.

Start at 40° north, about the latitude of New York, Madrid and Beijing, on June 21. In the model the Sun is up for 14.8 hours and climbs to 73.4 degrees at noon, high in the sky.

Press play and watch one whole day go by. At midnight the Sun is far below the horizon, about 27 degrees down. Summer days here are long, but the Sun still sets every evening.

At 40°N on day 172 the model gives δ = 23.4°, a noon altitude of 90° − |φ − δ| = 73.4° and a sunrise hour angle from cos h₀ = −tan φ tan δ that yields 14.8 h of daylight. At local solar midnight the Sun is 26.6° below the horizon.

The Met Office notes that the June solstice, on 21 or 22 June, gives the UK its longest day and shortest night. At 40°N, that longest day is still well short of 24 hours.

Now Olly flies far north, near the city of Tromsø in Norway. It is June.

Watch the Sun. It goes low, but it never goes down. It shines all night!

Now move to 69.5° north, near the city of Tromsø in Norway. On June 21 the model shows 24 hours of daylight. The noon Sun is lower than at 40° north, about 44 degrees up, but at midnight it is still about 3 degrees above the horizon.

Try other days. At 69.5° north the model's Sun stays up from about 23 May to 19 July, 58 days in a row. In December it is the other way round: the Sun doesn't rise at all.

At 69.5°N on day 172, −tan φ tan δ < −1, so the Sun never sets: 24.0 h of daylight, a noon altitude of 43.9° and a midnight altitude of φ + δ − 90° = 2.9°. Polar day runs from day 143 (23 May) to day 200 (19 July), 58 days; polar night lasts 57 days around the December solstice.

The model also shows a surprise: at 69.5°N the daily sunlight at the top of the atmosphere on June 21 is 507 W/m², a little more than the 499 W/m² at 40°N, because the long day makes up for the low Sun.

Earth leans over a little as it goes around the Sun.

In June, the top of Earth leans toward the Sun. So the far north stays in sunshine even as Earth spins.

Earth spins once a day, and NASA gives the lean of its spin axis as 23.44 degrees. In June, the North Pole tips toward the Sun. NASA explains that the tilt always points the same way as Earth goes around the Sun, so around June it is the north's turn to lean in.

Near the top of the leaning Earth, the land is tipped so far into the sunlight that even as Earth spins, it never turns into darkness. That is the midnight Sun. The line where this begins on the longest day is the Arctic Circle.

The Sun's declination follows δ = asin(sin ε · sin λ), reaching +23.44° at the June solstice. A latitude is in continuous daylight when the Sun at lower culmination (midnight) stays above the horizon: φ + δ − 90° > 0, so φ > 66.56°. Farther north, the Sun stays up for more of the days around the solstice.

The model's limits: a circular orbit, local solar time, and sunrise when the Sun's center crosses a flat horizon. In real life, NOAA explains, the air bends sunlight, so the Sun is seen rising a little before it crosses the horizon and setting a little after; the model leaves this out.

At the North Pole, the Sun stays up for half the year. Then it stays down for half the year.

In the far north, summer has lots of light. Winter is dark and cold.

NSIDC says that at the North Pole the Sun rises once a year and sets once a year: six months of daylight, then six months of night. Between the Arctic Circle and the pole, the stretch of non-stop light and non-stop dark is somewhere in between.

All that summer light matters. NASA explains that in summer the pole can receive more sunlight than the tropics, but bright snow and sea ice bounce much of it away. In the Arctic interior, NSIDC says, long summer days thaw the top layer of frozen ground, and on the tundra, plants green and bloom in the warmest months.

NSIDC: at the North Pole there are six months of continuous daylight and six of continuous night; north of the Arctic Circle the number of days of continuous light and dark is intermediate. The model agrees: 182 days of polar day at 90°N and 58 at 69.5°N.

NASA's energy budget notes that the summer pole can receive more incoming sunlight than the tropics, while high albedo snow and ice reduce the heating. In winter there is little or no solar energy above the Arctic Circle, which NSIDC links to the region's dark, cold winters. The model gives top-of-atmosphere sunlight only, with no clouds or snow.