A matter of scale

So I recently checked out the Melbourne Solar System, a nifty scale model of our little corner of the galaxy. The sun is down near the St Kilda Marina (itself pretty cool, what with the whole boats on shelves thing) and Pluto is 5.9 km away in Port Melbourne. Overall, an excellently nerdy and highly recommended way to spend a day at a beach that, well, you probably wouldn’t want to swim at in any case.

Anyhow, it got me thinking about the scale of things. As Douglas Adams famously said, space is big. Really, really big. At the scale of the Melbourne Solar System, the nearest star would be roughly 32,000 km away. That’s already getting pretty hard to picture – to get it more manageable we’re going to have to shrink things even further…

Now, a lot of people have pointed out that the solar system looks a leetle bit like an atom – well, not a real atom of course, with quantum uncertainties and weirdly shaped electron shells, but a classicised version, with electrons orbiting the nucleus much like a tiny solar system…

So, randomly choosing a gold atom as a model (not so random really – I found some good relative figures about gold, but also the sun is vaguely gold-coloured and according to Wikipedia they’ve long been connected), the sun’s diameter at 1,390,000 km is 9.53 x 10²² times the size of a gold nucleus at 1.46 x 10^-14 m. And that works pretty good, because the size of the entire gold atom at 1.26 x 10^-10 m turns out to be proportionally the same size as the heliosphere, the extent of the solar wind and one measure of where the solar system ends.

At this new scale, the nearest star, Proxima Centauri, is a mere 0.421 μm away (roughly the size of the tiniest bacteria, but still pretty large compared to an atom). Our entire galaxy then is about 1 cm across. And the nearest galaxy (the Andromeda galaxy) is only 25 cm away. Which makes the entire observable universe, 92 billion light years wide, about 9.1 km in diameter.

Imagine that: a sphere extending roughly between the aforementioned Port Melbourne and Clifton Hill, full of tiny galaxies, each smaller than a fingernail and about a foot apart. And in one of these little golden galaxies, round about Federation Square, there is a single atom with an electron that corresponds to Earth.