# If the Milky Way galaxy is as big as planet earth, how big is Earth?

If the Milky Way galaxy is as big as planet earth, how big is Earth?

Let $$g$$ be the radius of the galaxy, about $$5\times 10^{20}\ \mathrm m$$.
Let $$e$$ be the radius of the Earth, about $$6371\ \mathrm{km}$$.
Let $$s$$ be the radius of the scaled-down Earth.
Then, $$\frac e g = \frac s e$$ So $$s = \frac{e^2} g = \frac {(6371\ \mathrm{km})^2} {5\times 10^{20}\ \mathrm m}$$ which is approximately 80 nanometres. So it's about 1000 times the size of an atom.