Lucky match

This is an image taken from the Mir space station showing the Moon's shadow during a Solar Eclipse.
Moon casting shadow on Earth during Solar Eclipse
Why do you think a total solar eclipse is important in terms of geometry?
When the Moon passes perfectly in line with the Sun it blocks it out completely. This means they have the same angular size in the sky. This geometric relationship allows us to apply the properties of similar triangles.
10th century CE Greek copy of Aristarchus of Samos's 2nd century BCE calculations of the relative sizes of the Sun, Moon and the Earth.
Thanks to similar triangles we know the ratio of distances from earth to sun and earth to moon must equal the ratio of sun’s diameter to moon’s diameter.
Setting up the proportions between width and distance

distance to sun / distance to moon = sun diameter / moon diameter

We’ve already determined these values so we can simply plug them in!

149 600 000 / 384 400 = sun diameter / 3474

sun diameter = 1 352 004 km

This is very close to the actual value! The actual diameter is closer to 1 391 000 km
How cool is that? We measured the size of the sun (about 1.3 million kilometers) using some basic observations and a little geometry! This illustration shows the approximate size of Earth compared to the Sun if they were put directly beside each other.
Image Credit: ESA & NASA

Congratulations, you have completed this lesson!

You are ready to tackle some some bigger questions...