<p>Well, they are different shapes, but we can get a rough answer by doing a ratio calculation based on their radii.</p>

<p>Let <span class="math-container">$g$</span> be the radius of the galaxy, about <span class="math-container">$5\times 10^{20}\ \mathrm m$</span>.<br>
Let <span class="math-container">$e$</span> be the radius of the Earth, about <span class="math-container">$6371\ \mathrm{km}$</span>.<br>
Let <span class="math-container">$s$</span> be the radius of the scaled-down Earth. </p>

<p>Then,
<span class="math-container">$$\frac e g = \frac s e$$</span>
So <span class="math-container">$$s = \frac{e^2} g = \frac {(6371\ \mathrm{km})^2} {5\times 10^{20}\ \mathrm m}$$</span>
which is approximately 80 nanometres. So it's about 1000 times the size of an atom.</p>

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2019-01-27T01:05:43.740Z
2019-01-27T13:02:21.223Z
2019-01-27T13:02:21.223Z
PM 2Ring
<p>If the Milky Way galaxy is as big as planet earth, how big is Earth?</p>

<milky-way><size>
If the Milky Way galaxy is as big as planet earth, how big is Earth?
larry909
# If the Milky Way galaxy is as big as planet earth, how big is Earth?

(Asked by: username_0 on 2019-01-26)

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

**Tags:** milky-way, size


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## 1 answers

### Answer by username_1 on 2019-01-27. Score: 6 | Accepted answer

Well, they are different shapes, but we can get a rough answer by doing a ratio calculation based on their radii.

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.


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