|MadSci Network: Astronomy|
Thanks for your question. The simplest answer to your question is to think about how big the sun looks in the sky. On Earth we can measure how large or how high something is, without climbing it by looking at how big it appears to be and by knowing how far away we are from it. From that it is quite easy to calculate how big the object is that we are trying to measure. Our techniques for measuring the size of the sun rely on this simple idea.
Here in Europe we were treated to a total eclipse of the sun a couple of months ago. That happens because the moon is almost exactly the same apparent size in the sky as the sun, so the moon just exactly blots the sun out when the moon passes in between us and the sun.
You can make this measurement, roughly, at home. Hold your little finger at arm's length up to the sun (or better the full moon---DON'T LOOK DIRECTLY AT THE SUN!). You will see that the moon (which is the same apparent size as the sun in the sky) is just exactly blocked out by your smallest fingernail. Now measure the width of your fingernail and the length of your arm. The width of your little fingernail will probably be between 6 to 8mm and the length of your arm to your eye between 80cm to 1metre. So your arm is about 120 times larger than the width of the nail. That means that the distance to the moon is about 120 times larger than the size of the moon. It also means that the distance to the sun is about 120 times the width of the sun. Therefore if we can find out how far we are from the sun, we will also know its size.
There are many ways of measuring how far we are from the sun but all give
the same answer. We know that the Earth goes once around the sun every
year. If the orbit of the Earth is a circle, that distance would be
r is the distance from the Earth to the sun. Newton's law of
gravitation, which has been found to be very accurate on Earth and by direct
measurement for objects like the moon, tells us that the distance that the
Earth orbits the sun is equal to a constant times the time it takes the
Earth to go around the sun (1 year) to the power 2/3, and this constant is
something that people have measured on Earth. Thus we can calculate the
distance to the sun (about 150 million kilometers) and therefore know that the
size of the sun is about 120 times less than this---a bit less than 1
This is just one example of how to measure the size of the sun. There are many other ways of measuring the sun's size and distance and they all give the same answer---they are said to be consistent.
[Moderator: Philip Plait has written an essay about the history of the measurement of the Earth-Sun distance.]
Try the links in the MadSci Library for more information on Astronomy.