English

Length of Day and Night

Middle schoolGeographyDay length from latitude and solar declination: cos H = (sin h₀ - sin φ sin δ) / (cos φ cos δ)

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About this experiment

In June, London has more than 16 hours of daylight while Sydney has less than 10, and on the equator every day lasts about 12 hours. The reason is the tilt of the Earth's axis. As the Earth goes round the Sun, first the north and then the south leans towards the Sun, so a larger part of each circle of latitude is in sunlight. Pick a place and a date, watch the circle of latitude split into day and night, and follow the daylight hours through the year.

Learning goals

  • Explain why day length changes through the year because of the tilt of the Earth's axis
  • Describe how day length depends on latitude at the solstices and the equinoxes
  • Explain the midnight sun and the polar night inside the polar circles
  • Compare day length in the Northern and Southern Hemispheres on the same date
  • Calculate the height of the Sun at noon from latitude and date

How to use it

  1. 1Choose London on the June solstice. How much of the yellow and blue circle is in daylight? Read the day length.
  2. 2Keep the date and choose Singapore, then Tromsø. How does the split of the circle change?
  3. 3Choose the March and September equinoxes. What do you notice about the day length everywhere?
  4. 4Compare the orange and blue curves on the graph. Why are they mirror images?
  5. 5Find the lowest latitude that has 24 hours of daylight on the June solstice. Which line on the globe is that?
  6. 6Switch off the refraction setting. Why does the day get a few minutes shorter?

The model

Declination of the Sun: the latitude where it is overhead at noon on day d
Hour angle H of sunset at latitude φ; h₀ is -0.833° with refraction or 0° without
Day length: the Earth turns 15° per hour
Height of the Sun above the horizon at local noon

Assumptions

  • The Earth is a sphere with its axis tilted at 23.44°, and the orbit is treated as a circle, so the declination follows a simple cosine. The real dates of the solstices and equinoxes can differ by a day or two.
  • Times are local solar time, with noon when the Sun is highest. Clock times also depend on time zones, daylight saving and the equation of time.
  • With refraction on, sunrise and sunset are when the top edge of the Sun touches the horizon, as in almanacs. Hills, buildings and the height of the observer are ignored.
  • The year has 365 days; leap years are ignored.

Try this in class

  1. Q1Why is the day length on the equator almost exactly 12 hours all year?
  2. Q2At the equinoxes, every place has about 12 hours of daylight. Use the globe to explain why.
  3. Q3Why does a city at latitude 60° N have a much bigger change in day length through the year than a city at 30° N?
  4. Q4What would day length be like through the year if the Earth's axis were not tilted at all?
  5. Q5Explain why the hottest part of summer often comes several weeks after the longest day.

Frequently asked questions

Why is the day still slightly longer than 12 hours at the equinox?

Air bends sunlight over the horizon, and sunrise is counted when the top edge of the Sun appears, not its centre. Together these add a few minutes at each end of the day. Switch off refraction to see the purely geometric 12 hours.

Why do places inside the Arctic Circle have the midnight sun?

In June the north pole leans towards the Sun by 23.44°. Every point within 23.44° of the pole stays in the lit half of the Earth for the whole turn, so the Sun never sets.

Is the longest day the same as the day with the earliest sunrise?

Not exactly. Clock times of sunrise and sunset are also shifted by the equation of time, so in many places the earliest sunrise comes a few days before the June solstice and the latest sunset a few days after it.