MadSci Network: Astronomy |

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Dear Elissa,

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
`2(pi)r`

where `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
million kilometers.

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.]

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