Measure the size of the earth

Cooperate with a school far away and measure the size of our planet! The method is the same as that used in Egypt almost 2500 years ago. The observations can be done outdoor, or indoor if the Sun is shining into a class room.

In this exercise you have to register. Then, you need to select another school to cooperate with. This school should be as far away from you (to the south or to the north) as possible.

The classes (or even whole schools if the schools choose to do this together) must then agree on a date to make the exercise. It must be done at a very specific time on that date (read more below).

Equipment

  • A long tube of cardboard, plastic or metal. It should have a length of 1–2 meters and be stiff (it must not bend). A longer pipe may give more accurate answers, but are bothersome. The pipe should not have a large diameter.
  • A spirit level
  • A square that is easy to read accurately for the angle
  • A watch (since you need to do the measurement at a precise time)

How to observe?

Find an even area where you can see the Sun. Use the spirit level to check that the area is absolutely in level.


Measuring the altitude of the Sun.

Put one end of the pipe on the ground and lift the other end towards the Sun. Avoid looking at the Sun! You will see a shadow on the ground cast by the pipe. Try to make the shadow as small as possible. When it is completely gone, the sunlight penetrates the pipe.

When the sunlight reaches the ground through the pipe, you must keep the pipe absolutely steady. Use the square to measure the angle between the pipe and the ground. When the Sun is exactly in the south (the time for this you or your teacher has already found), you read the angle and make a record of it. Be as accurate as possible!!

Important!

You should practice how to set up the experiment and how to read the angle before the day you have agreed on. This is important so that you are able to read the angle accurately on exactly the right time. During the exercise the weather must be good enough that the Sun is visible on both locations.

Calculation of the size of the Earth

How can we use these observations to caclulate the circumference of the Earth?

When we know the distance d between to schools - situated at approximately the same longitude - and angle C, we may calculate the circumference o of the Earth: The ratio of d and the angle C is equal to the ratio between the cicumference o of the Earth and the 360 degrees of a full circle:

It is not always that easy to find a school that is situated due North of South. We must there adopt the method a little by claiming that d is the distance between the latitudes of the schools. d can be calculated in this webpage. Please make sure that you use the same longitude for the schools.

Then we only need angle C. But that is just what the observations from the different locations give us.

Then you will find the circumference of the Earth using this expression:



More information/background

What is the size of our planet? In order to answer that question one must know that the Earth is a globe (almost spherical). During a total eclipse of the Moon this is evident. Before and after the total phase, the edge of the shadow of the Earth is seen - it is circular!

The size of the Earth was determined already more than 2000 years ago. This is quite impressive, but was due to a clever observation. The director of the famous library in Alexandria in Egypt, the geographer Eratosthenes (about 276-195 BC.) did the historic achievement.

Eratosthenes had learned a fascinating fact about the city of Syene in southern Egypt, not far from Aswan: When the Sun was at its highest in the sky in this city on the longest day of the year (today we call it summer solstice), the Sun did not cast any shadows. Actually, the Sun shined into deep wells. The story says that nobody dared to stare into the wells since they could become blinded by the intense light reflected by the water deep down.

In Syene the Sun therefore had to be in the zenith at this time. In Alexandria, further north in Egypt, Eratosthenes knew from his own experience that the shadows at the same time was equivalent to the Sun being one 50th of a circle away from zenith.

The distance from Syene to Alexandria had to be one 50th of the circumference of the Earth.

He could not measure the distance between the cities directly, but estimates of people travelling between the cities and the time they spent, gave a distance of about 5000 stadions. The circumference of the Earth therefore had to be 250 000 stadions, and the diameter about one third of this.

Today we don't know the exact length one one stadion, but many sources claim that 250 000 stadions correspond to 39 900 kilometers. This would be astoundingly close to the correct value which is 40 074 kilometers!

Anyway, the method is correct and can be applied even today to estimate the size of our Earth.

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Norwegian Centre for Science Education

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Background

The project The earth and the sun focusing on the spectacular celestial events 2010–2015.

This website, other communication and national initiatives linked to celestial events is made possible by funding from DnB NOR Savings Bank Foundation.

Prosjektleder var Knut Jørgen Røed Ødegaard.