S3.12.6 Chapter 6

Day length and the Sun's height

Why are some days longer than others? Can I track the Sun with a stick?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

A Every day has the same length everywhere, all year.
You picked A. Read on. At the end, the chapter comes back to your guess.
B The days change because the Earth spins faster in summer.
You picked B. Read on. At the end, the chapter comes back to your guess.
C In most places the day length changes through the year. Near the equator it hardly changes.
You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Graph day length through a year from a table
Track the Sun's midday height by measuring a stick's shadow

The day length is the time from sunrise to sunset. It is the hours of daylight. In most places it is not the same all year.

Near the equator, day and night are about 12 hours each, all year. Farther from the equator the day length changes a lot.

Here are the day lengths for two places. One is 40 degrees north of the equator. The other is 40 degrees south of it. The table gives the hours of day in the middle of each month.

See it three ways

As a picture

In words

At 40° north the day is longest in June and shortest in December. At 40° south it is the other way round. The two places have the same pattern, six months apart.

In symbols

40° N: longest 14.8 hours, shortest 9.2 hours.

Draw it first

Graph the day length

1 Draw the two axes. Put the month number along the bottom and the hours of day up the side. Plot the first four months.
2 Plot the next four months. Put each point exactly at its month and its hours.
3 Plot the last four months. Join the points with a line.

The line rises to a peak, then falls to a low point, then rises again. At 40° north the peak is in the middle of the year.

Day length at 40° north. The peak is the longest day. The low point is the shortest.

Day length at 40° south. The peak is at the end of the year, six months from the north.

Worked example

Use the graph for 40° north. How much longer is the longest day than the shortest day?

The graph for 40° north has one peak and one low point in the year.
The peak is at month 6, June.
At month 6 the graph is at 14.8 hours. That is the longest day.
The lowest point, at month 12, is 9.2 hours. That is the shortest day.
Take away the smaller from the bigger: 14.8 − 9.2 = 5.6 hours.

Answer: 5.6 hours

Near the poles the changes are huge. Inside the polar circles some days have 24 hours of light. Others have 24 hours of dark. At the poles themselves the Sun stays up for about six months. Then it stays down for about six months.

The ring round the north pole is in the light all day. The ring round the south pole is in the dark all day.

Now the Sun's height. At midday the Sun is at its highest point in the sky. The higher it is, the shorter the shadow of a stick. A low Sun makes a long shadow.

A stick 100 cm tall. A higher Sun gives a shorter shadow. A stick half as tall gives half the shadow.

A stick that is twice as tall has a shadow twice as long. Later in mathematics you will meet a rule for this, using a button called tan. You do not need it now. The table gives the numbers.

The shadow points away from the Sun. So which way it points at midday depends on where you live.

At 40° north the midday Sun is in the south, so the shadow points north. This is on a day when the midday Sun is overhead at the equator.

At 40° south the midday Sun is in the north, so the shadow points south. This is on a day when the midday Sun is overhead at the equator.

North of the Tropic of Cancer the midday shadow always points north. South of the Tropic of Capricorn it always points south. Between the two tropics it can point either way. On two days a year the Sun is overhead, and there is no shadow at all.

Try it

Track the midday Sun with a stick

You need: a straight stick about 1 m tall, a flat patch of ground, in the Sun all day, small stones, a ruler or a string marked in cm, a clock or a watch, paper and a pencil.

Be safe: Look only at the ground and at the shadow. Never look at the Sun, not even for a moment, and not through anything.

Push the stick into the ground, so that it stands straight up. Press the earth round it. Measure its height above the ground.
Start at about 11 by the clock and go on until about 2. Every 15 minutes, put a stone on the tip of the shadow.
The shortest shadow is the midday one. Measure it from the foot of the stick to the stone, in cm.
Do it once a week for four weeks. Write down each midday shadow.
Look at the numbers. Is the shadow getting longer, or shorter?

What you will see: Our shadows were 70, 76, 82 and 90 cm long. They grew longer, so the Sun was getting lower at midday. Your shadows may get shorter, if the Sun is getting higher where you live.

If you cannot try it, this is what happens.

A wrong idea many people have

The shortest shadow comes when the clock says 12.

Why it feels right: The word midday sounds like 12 o'clock, so the Sun should be highest then.

The test that breaks it: Mark the tip of the shadow every 15 minutes. The shortest shadow may come before or after 12 on the clock, sometimes by an hour or more. Clocks are set for a whole region, not for your exact place.

What is true: The Sun is highest at midday, and then the shadow is shortest. That is true midday, whatever the clock says.

Key words

day length: the time from sunrise to sunset, in hours.
sunrise: the moment the Sun first shows over the horizon.
sunset: the moment the Sun disappears below the horizon.

Back to your guess

The answer is C: In most places the day length changes through the year. Near the equator it hardly changes.

The tilt makes day length change through the year. The change grows as you go away from the equator. At the equator it is close to 12 hours all year. The Earth spins at the same speed all year.

Keep it

Copy this into your exercise book.

Day length changes through the year, except near the equator. North and south have opposite patterns. A high midday Sun gives a short shadow, pointing away from the Sun.

Draw: A graph of day length against month, rising and falling once. Add a stick with a short shadow.