Seasons and Day Length Simulator
Equations in this simulation
| N | Day of the year | 1 January is day 1; the June solstice is about day 172, the December solstice about day 355 | |
|---|---|---|---|
| δ | declination of the Sun | the latitude where the Sun is overhead at noon: +23.44° at the June solstice, 0 at the equinoxes, −23.44° in December |
With the current values:
| φ | Latitude φ (°, north positive) | ||
|---|---|---|---|
| ω₀ | hour angle of sunset | how far the Earth turns between noon and sunset; past the polar circles there is midnight sun or polar night | |
| day length | hours of daylight | sunrise and sunset in local solar time are 12:00 minus and plus half of it |
With the current values:
| altitude | height of the Sun at noon | the higher it is, the more concentrated the sunlight on the ground |
|---|
With the current values:
| S₀ | solar constant | 1,361 W/m² at the top of the atmosphere; the slight change in the Earth's distance from the Sun is left out | |
|---|---|---|---|
| Q | average sunlight per square meter over the whole day | at the top of the atmosphere; this, not the distance to the Sun, is what makes summer warm |
With the current values:
How to use the seasons simulator
- The Earth orbits the Sun with its axis tilted 23.4° and always pointing the same way in space. Play the year or set the date, and watch first the northern and then the southern hemisphere lean toward the Sun. The night side is dark; the red ring is your latitude.
- Set your latitude and read the day length, sunrise and sunset, the height of the Sun at noon and the day's average sunlight per square meter. The chart plots the day length over the whole year at that latitude: a flat line at the equator, a swing from about 8 to 16 hours in London, and months of midnight sun and polar night beyond the polar circles.
- Compare the summer and winter solstices at the same latitude: in summer the Sun is higher, so its light falls more directly on the ground, and it stays up longer. Both together, not the Earth's distance from the Sun, make summer warm. Tick View from close to the Earth to look at the tilt more closely.
Frequently asked questions
What causes the seasons?
The tilt of the Earth's axis, 23.4° from the perpendicular to its orbit. Through the year the axis keeps pointing the same way in space, so for half the year the northern hemisphere leans toward the Sun, getting higher sunlight and longer days, and for the other half the southern hemisphere does. The Earth is actually closest to the Sun in early January, in the northern winter.
How is the length of the day worked out?
From the latitude φ and the Sun's declination δ: cos ω₀ = −tan φ × tan δ, where ω₀ is how far the Earth turns between noon and sunset. The day lasts 2ω₀ ÷ 15° hours. If −tan φ tan δ is beyond ±1 the Sun never sets or never rises, which happens inside the polar circles. Real sunrise comes a few minutes earlier because the atmosphere bends the light and the Sun is a disc, not a point.
Why are sunrise and sunset given in solar time?
Because clock time depends on your time zone, where you are within it and daylight saving time. In local solar time noon is when the Sun is highest, and sunrise and sunset are symmetric around it. To get clock time, add the difference between your longitude and the center of your time zone, 4 minutes per degree, and the equation of time, up to 16 minutes.
What are the solstices and equinoxes?
The June solstice, around 21 June, is when the Sun is overhead at the Tropic of Cancer (23.4° N): the longest day in the north and the shortest in the south. The December solstice is the reverse. At the March and September equinoxes the Sun is overhead at the equator and day and night are about 12 hours everywhere.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.