Now that we have given you the answer to the question
of how big the objects in the solar system are and at what distances,
we need to go back and look at how the astronomers figured this out
over time. After all, when you look in the night sky with the naked
eye, all you see are small dots of light.

The first step the astronomers of the past did was to figure out
how far apart the various planets are from the Sun. In the case of
planets, we have to wait for the Earth to move some significant distance
along its orbit. At the same time, we have to watch one of the planets
in its orbit. In this case, we will use Mars since the red planet
is fairly easy to observe. From simply watching Mars in the sky, we
know that it takes 686 days (1.88 Earth years) for Mars to complete
one circuit around the Sun.

For simplicity sake, we call the distance from the Sun to the Earth
1 Astronomical Unit or "AU" for short. Using geometry, we
can show that the distance from the Sun to Mars is 1.52 AU. In other
words, by watching how the position of Mars changes with respect to
Earth over the course of a year, we can determine how far Mars is
from the Sun compared with how far Earth is.

We call the average distance from the Earth to the Sun the Astronomical
Unit, or AU. It turns out to be easy to find the distances to the
other planets in astronomical units but very hard to do the same in
km or miles. Copernicus had the information needed to find the relative
distances in AU, and Kepler used these distances to get his third
law (period-squared vs. size-cubed).

Here is an example of how you can figure out how far Mars is from
the Sun compared with Earth. Assume that both Earth and Mars have
circular orbits. (That is a very good first approximation, even for
Mars.) Keep track the dates when Mars is highest to the South at midnight,
6am, and 6pm. The following picture will explain your observations:

In this picture you can see that, moving at constant speed, Mars
will take more time to go around the long arc (by "noon")
than the short arc (by "midnight"). The farther away from
Earth and the Sun that Mars is, the more nearly equal these two arcs
will be. So by keeping track of these times, something astrologers
had been doing for centuries, it is possible to figure out the sizes
of the orbits.

For Venus, we can use a different trick to figure out its distance
from the Sun in AU. The picture in this case shows that Venus can't
get too far from the Sun. If we can find the farthest it gets from
the Sun, we can draw (on paper) a triangle that is similar to the
big triangle in space linking the Sun, Earth, and Venus:

Here Venus is as fas as it can get from the Sun in the
Sky, as seen from earth. We can measure the angle a. Angle b is a
right angle. This lets us draw a similar triangle on paper and find
the distance from Venus to the Sun compared with the distance from
the Sun to the Earth.

You
may have noticed one problem with the above answers - the distances
to the other planets are given in terms of the distance of the Earth
to the Sun. So, how far is the Earth to the Sun? What exactly is an
AU? How far is an AU? How many inches? Centimeters? Miles? Kilometers?

The answer to this problem was not so easy to solve by purely observational
methods. Two things people tried were to observe a transit of Mercury
or Venus and to measure the closest approach to Earth of an asteroid.
Both gave good approximate numbers, and allowed us to estimate the
mass of the Sun. Good values were not obtained until the 1960s when
scientists bounced radar beams off the planets such as Mars, Mercury
and Venus and were then able to calculate the average distance from
the Earth to the Sun accurately.

For the record, the average distance from the Earth to the Sun, or
1 AU, is:

149,600,000 km

1.496 E13 cm

92,960,000 miles

**1)** How far is Mars
away from the sun?