The Size of the Sun and Moon |
Warning! Looking directly at the Sun can damage your eyes!
In order to measure the diameter of the Sun we use a pinhole camera - a cardboard tube with a piece of foil at one end with a tiny hole; the other end of the tube is covered in graph paper. Alternatively, you can use a piece of card with a pinhole in it and a piece of graph paper (with millimeter rulings). You also need a meter stick because you need to hold the card with the hole a distance of 1 meter from the graph paper.
Being careful not to look at the Sun directly, aim the tube up to the Sun with the graph paper facing you. You should see an image of the Sun on the graph paper.
(1) Measure the diameter of the Sunís image, counting
the marks on the graph paper. Each square on the graph paper is 1 mm across.
What is the diameter of the Sun's image?
Examining the geometry of the pin-hole camera shown in the figure above,
you can see that if the distance to the Sun is known, we can use the similar
triangles relationship to solve for the diameter of the Sun. That is, we
have the following:
Diameter of the Image = Distance of Image from
Hole
Diameter of Sun
Distance of Sun from Earth
(2) Assume that the distance between the Sun and Earth is 150 million kilometers (about 93 million miles). The distance of the image from the hole (i.e. the length of the tube) is 1 meter. Determine the diameter of the Sun and compare this to the true value.
The Moon has roughly the same angular size as the Sun. We can use the
similar triangles relationship again to determine the size of the Moon:
Diameter of the Moon = Distance of Moon to Earth
Diameter of Sun
Distance of Sun to Earth
(3) If the distance of the Moon to the Earth is about 390 times
less than the distance between the Sun and the Earth, how big is the Moon?
Check to see if your number makes sense: the Moon's diameter is a little
less than the width of the United States.
