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How big is the Sun? How big is the Moon?

By David, 14 May 2015 Activity

You will need:

Paper, ruler, tape measure, coin, modelling clay, pin, tape measure.

What you will need.

  • A small coin
  • Some blu-tac
  • A ruler
  • A tape measure
  • Two pieces of paper
  • A pin
  • An assistant

To measure the Moon:

This activity is a lot easier when the moon is full, and when it is rising or setting. Look in your local paper or on the internet to find when the moon will be rising or setting in your part of the world.

  1. Use the blu-tac to stick the coin to the top of a pole, or a fence, so it’s standing up on its edge. Make sure you can see the moon from where the coin is.

    A coin stuck to the top of a star picket.

    Stick your coin to a fence or post.

  2. Stand with the coin between you and the moon. Move around until the coin looks exactly the same size as the moon. You can check by lining up the coin in front of the moon to make sure the moon is not too big, and then moving forward to make sure it is not too small.
  3. Get your assistant to measure the distance from you to the coin with the tape measure. You can repeat this experiment a few times and take the average. convert the distance to millimeters, and call id ‘d’.
  4. Measure the diameter of the coin (the distance across the round face of the coin), in millimeters. Call the diameter ‘w’.
  5. This formula will estimate the size of the moon:

width of moon = 385 000 w / d

 To measure the Sun:

An oval of light. Someone is measuring it with a ruler.

Make sure you measure across the thinnest direction.

Safety: Don’t look at the Sun. Looking directly at the sun can cause permanent damage to your eyes.

Measuring the Sun is a lot harder than measuring the moon. This is because you should never look at the sun directly. Instead, we can use an image of the sun.

  1. Use the pin to poke a hole in one of the sheets of paper.
  2. Put the other sheet of paper on the ground, in the sunlight. This piece of paper is the target.
  3. Hold the holed paper so its shadow is on the target paper. Move the holed piece of paper until it is about 1 metre from the target paper.
  4. There should be a bright dot on the target paper, where the light is shining through the hole in the paper. Get your assistant to measure the distance from the dot to the hole, in millimeters. Call this distance ‘D’
  5. Then, get your assistant to measure the width (diameter) of the dot. If the dot is an oval shape, measure the shortest line that still goes through the centre of the dot, in millimeters. Call this distance ‘W’
  6. This formula will estimate the size of the sun:

width of sun = 150 000 000 W / D

What’s happening:

In order to measure the size of the sun and the moon, we use an idea called ‘similar triangles’. Two triangles are ‘similar’ (in the mathematical sense) if they have the same shape, but are different sizes. The diagram below shows the similar triangles in our two experiments. In each diagram, one triangle is in red, and the other is in blue.

tow triangles - one from an eye to a coin, one from an eye to the moon.

width of the moon/distance to the moon = width of the coin/distance to the coin.
Two triangles - one from a pinhole to a light circle, one from the pinhole to the Sun.

width of Sun/distance to the Sun = With of the dot/distance to the dot

Similar triangles can be different sizes, but they have the same shape. This means if one triangle is twice as wide as the other, it will also be twice as tall. In our experiment, one triangle is millions of times bigger than the other, but the shapes are still the same. This means that we can use the information we know (about the smaller triangles) to work out the information we don’t know (about the really big triangles).

The sun and the moon appear to be almost the same size in the sky. In fact, because of the movement of the Sun and Moon, sometimes the Moon appears to be slightly bigger, and sometimes slightly smaller. The fact that they seem to be so close in size is just a lucky coincidence. It’s also very useful, because when the moon goes in front of the Sun, it covers the whole Sun. When this happens, we can look at all the things that the Sun shoots out its sides.

Applications:

In order to measure the size of the moon, we need to know the distance to the moon. The moon is much closer to the Earth than the Sun is, and this makes measuring the distance much easier. An Ancient Greek called Aristarchus estimated the distance to the Moon over 2200 years ago, using a solar eclipse, and later scientists made increasingly more accurate observations.

Measuring the distance to the Sun is a lot harder. The Sun is very big and very far away, and it’s hard to find something to compare it with. In 1769 Venus passed in between the Earth and the Sun. Captain James Cook had been sent to Tahiti specifically to measure this, so scientists could use the measurements to work out how far away the sun was. After conducting these experiments, he discovered the east coast of Australia on his way back home.

More information:

How Aristarchus measured the solar system
Kids use audio recordings to measure distance to moon
The transit of Venus

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