What astronomical really means

As a quick, more quantitative followup to my previous picture-based post...

Imagine the size of the entire Earth. The distance from LA to New York is about 1/6 of the circumference of the Earth. The radius of the earth is $1/2\pi$ the circumference, which is about 1/6. So LA --> NYC is a good estimate for the "size" or radius of the Earth, or about 3000 miles according to my most recent frequent-flier statement ($R_{Earth} = 7000$ km).

Now consider the size of a single atom in your body. Your body is mostly water, which makes it mostly hydrogen. Hydrogen is made up of an electron orbiting a proton at a distance of roughly a "Bohr radius," which is about 50 picometers ($5 \times 10^{-11}$ meters).

This means that the Earth is $7\times10^{3} / 5 \times 10^{-11} \approx 10^{17}$ times bigger than an atom in your body. The Earth is

$100,000,000,000,000,000$

times bigger than an atom in your body. That's huge in comparison, as you might imagine.

Well, if we compare the size of the entire Universe to the size of the Earth, we come up with a number that is roughly 100 times bigger. The Earth in comparison to the size of the Universe is smaller than a single atom compared to the entire World.

So the next time you say something like "astronomically bigger," this is kinda what you mean :)

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