### RE: Distance to the Sun

Area: Astronomy
Posted By: philip plait, Astronomer/Programmer
Date: Thu Oct 31 14:50:53 1996
Message:
```(First, a quick note: this is a lengthy explanation. At the
end of this is a series of links with more terse descriptions
sources with info on how the Earth-Sun distance was first
found, so for that I wrote a longer description.)

By the late 1600's, astronomers had determined the distances
to the other planets in the solar system relative to the Earth's
distance to the Sun. For example, they knew that Jupiter was about
5 times the distance from the Sun as the Earth.
The problem was they didn't know how far away
the Sun was! Without knowing the actual distance of the Earth
to the Sun (called an Astronomical Unit, or AU), they
didn't know how far away the other planets were. We now know that
an AU is about 150 million kilometers. But how was it first found?

In 1653, an astronomer named Christian Huygens (pronounced "Hoy-gens")
was the first to find this distance. He used a very clever idea,
but as you'll see in a moment, he had to make a guess about one of
his numbers. By pure blind coincidence, he guessed correctly and so
his measurement of the AU is essentially correct. However, since his
determination was not rigorous, the actual first measurement is
usually credited to Cassini, who used a method involving getting
the parallax of Mars. Cassini did this in 1672.

So how did Huygens do it? He knew that Venus showed phases when viewed
through a telescope, just like our own Moon does. He also knew that
the actual phase of Venus depended on the angle it made with the Sun
as seen from the Earth. When Venus is between the Earth and Sun, the
far side is lit, and so we see Venus as being dark. When
Venus is on the far side of the Sun from the Earth, we can see the
entire half facing us as lit, and Venus looks like a full Moon.
When Venus, the Sun and Earth form a right angle, Venus looks half
lit, like a half Moon.

Now, if you can measure any two internal angles in a triangle,
and know the length of one of its sides, you can determine the
length of another side. Since Huygens knew the Sun-Venus-Earth angle
(from the phases), and he could directly measure the Sun-Earth-Venus
angle (simply by measuring Venus' apparent distance from the Sun on the sky)
all he needed was to know the distance from Earth to Venus. Then he could
use some simple trigonometry to get the Earth-Sun distance.

This is where Huygens tripped up. He knew that if you measured the
apparent size of an object, and knew its true size, you could
find the distance to that object. Huygens thought he knew the actual size
of Venus using such unscientific techniques as numerology and mysticism.
Using these methods he thought that Venus was the same size as the Earth.
As it turn out, that is correct! Venus is indeed very close to being the same
size as the Earth, but in this case he got it right by pure chance.
But since he had the right number, he wound up getting the about the correct
number for the AU.

Since Huygens' method was not rigorous (that is, was not completely
scientifically grounded) he is not usually given credit for being
the first to find the value of an AU. In 1672, Cassini used a method
involving parallax on Mars to get the AU, and his method was
correct.

the common way to measure the distance to nearby stars is using parallax.
Try this simple experiment: hold a finger up about 10-20 centimeters from your
nose. Now alternately blink your eyes, so that at first you are looking at
your finger appears to jump back and forth? That's because your eyes are
separated from each other by a few centimeters. That effect is called
parallax. If you know the separation between your eyes, and can measure
the angle that your finger appears to jump, you can calculate the distance
using trigonometry. The farther away something is, the wider the separation must
be between the two observations (try looking at a telephone pole across a street
and blinking your eyes-- the pole is so far it doesn't look like it is moving
at all when you blink!). Stars are very far away, so we need to
make very separate observations. Luckily, the Earth's orbit is very wide!
If you measure the position of a star, then wait six months for the Earth
to go halfway around its orbit, the baseline between measurements
is 1 AU (aren't you glad we know that distance now?). Stars can be measured
with fair accuracy this way out to several hundred light years.

Once you measure a star's distance, you can use it to measure other stars too
far away to measure using parallax. Say you measure the distance to a nearby star,
and you also measure how bright it is. If you can find another star just like
it, but much farther away, you can measure how much fainter the farther star is,
and then figure out its distance! This method can actually be used to determine
distance to nearby galaxies, which have very bright stars in them.

At this point this explanation is getting too long. Here are some links that
explain all this as well, and also point to other methods for determining
astronomical distances.

Here is a graphic
illustrating stellar parallax.

Here is a nice astronomy
dictionary, which has lots of definitions.

Another good explanation of parallax

can be found here. Not only that, but they have

a list of steps astronomers
use to determine ever increasing distances.

```

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