Dr. Bozidar Mitrovic: As the Mercury revolves around the Sun or
as Venus revolves around the Sun, we see it at a different distance
from the Sun at different times of the year.
Just like in that overhead that I had before...Let me just show it again.
As they move -- Mercury and Venus -- around the Sun, we see them at different
distances from the Sun, a different angular distance from
the Sun, if you will.
We see them at the largest angular distance when the line joining
the planets say, Mercury and the Sun and the line joining the Earth
and the Mercury forms right angle -- 90 degrees.
The same is in the case of Venus.
We see Venus at the largest angular distance from
the Sun when the line joining Venus with the Sun is perpendicular
to the line joining Earth and the Venus, when this angle here is 90
degrees.
One can measure the angle at which we see the Mercury and Venus
when they are at a largest angular distance from the Sun.
In the case of Mercury, it is 28 degrees and in the
case of Venus, it's 47 degrees.
You cannot see Venus at the angular distance from the Sun
that is bigger than 47 degrees.
It can only be smaller.
If Venus is located here, then this angle is going to
be less than 47 degrees.
Once you have a right angle triangle and you can measure one angle
like here 28 for Earth-Mercury-Sun triangle, you know the other
angle which is 90 degrees and then you know the proportion in which
the two sides of the triangle are -- based on similar triangles.
Because similar triangles are triangles of any shape that have all
the angles...they are the same.
That is, their sides are parallel to each other.
If I have these two triangles with identical angles and I have
three sides on one of them and three sides on the bigger one then I
know that the corresponding sides are in the same proportion.
a/c is going to be the same as A/C and so on.
Basically, once you measure the angle in a right angle triangle,
you can find out the ratio of the two sides.
You can find out, what is the ratio of the distance between say
Mercury and the Sun, and Earth and the Sun.
You can determine the relative distance of Mercury from the Sun
with respect to the Earth and Sun distance.
Here is a diagram that illustrates what I have
just mentioned.
You can see Venus at 47 degrees or less and you can see Mercury at
28 degrees or less.
Because you know that these angles here are 90
degrees, the triangles are completely determined and you can find
out what the ratio of their sides is.
Then, whatever the distance between the Earth and the Sun, and at the
time of Copernicus and earlier, they didn't know what their distance
was.
Nevertheless, you can say, what fraction of the Earth-Sun distance
is the Mercury-Sun distance.
You can also find out what fraction of the Earth-Sun distance is Venus-Sun distance
and that's already a lot.
You can compare the distances of the planets from the Sun.