# The Universe scaled down

I saw a show on TV a while back where some town modelled the solar system in their town. They had the Sun represented by a large sphere placed in the center of the town. Mercury was located x blocks away and was the size of a golf ball, Venus a bit further out and a bit bigger, etc. Pluto was several miles outside of town and quite small, if I remember correctly.

So, taking that concept a step further, if the Universe were scaled down to be the size of the Earth, how big would the Earth be? As big as a grain of sand? Smaller than that? And, while we’re at it, how far would our space exploration to date extend in this scale?

SC

1. We don’t know the size of the Universe. We don’t even know for sure whether it is finite or not. (Scaling down an infinite Universe would be a neat trick.) While you might see some references to the Universe being ~14MLYr in radius, that is the visible Universe (from our perspective).

2. See 1.

ftg is right. But if we shrink the visible universe to the size of the earth, earth would be about 1/500 the size of a water molecule. The furthest space probe is the Voyager 1, currently around 90 AU away (almost 2x the distance to Pluto); this translates to about 0.6 microns, roughly the size of a very fine smoke particle. The distance to the nearst star would be about 1.8 mm (1/16 inch).

Was the OP thinking of this? A scale (1:15m) model of the solar system across the UK…the earth and the sun are six miles apart, but pluto is the other end of the country.

Thanks for the responses folks. I knew we were pretty insignificant in the grand scheme of things, I just didn’t know how much. And GorillaMan, the one I saw wasn’t nearly as big as the one you linked to. I’m impressed.

So, how about a followup question. Rather than scaling down the entire visible universe, how about just the Milky Way galaxy? If it was the size of the earth, how big would the earth be?

SC

Oops, forgot to add the other question. If the Milky Way was the size of the Earth, how far would Voyager have gotten by now? Thanks again, all.

SC

Taking a reasonable figure of 25000 light yeras for the Milky Way disc, reduced to the size of the earth, the earth is (I think?!) about 50 picometres wide.

And, as long as I’m padding my post count, here is a link to the solar system model I mentioned in the OP. Not as big as GorillaMan’s, but pretty impressive nonetheless.

You’re confusing a couple dimensions. The diameter of the Milky Way is normally given as about 100,000 LY. The solar system is believed to be about 26,000 LY from the galactic center. That said, let’s see…

If we shrink the 100,000 LY Milky Way to the current size fo the Earth, we end up with Earth being a speck just 1.71 x 10[sup]-7[/sup] meters, assuming I’ve done the math correctly at this late hour.

Dammit, it was too late to be dealing with light years.

One scale comparison I heard of a while back is:…

If the distance across the little finger represents the distance between the Earth and the Sun, then, on that same scale the nearest star would be 2 miles away!!

The Milky Way is 100,000 light-years in diameter. That’s about 6x10^17 miles.
(Yes, I know I should do this in metric. But I remember the length of a light-year in miles and the Earth’s diameter in miles. The units will cancel out anyway in the scaling factor.)

The Earth is about 8000 miles in diameter.

Voyager 1 is 88 astronomical units (1 astronomical unit or AU = distance from the
earth to the sun) or about 8x10^9 miles.

The earth is about 13,000 kilometers in diameter, so in this scale model it is 1.7x10^-10 meters in diameter.

That’s on the order of the size of a hydrogen atom :eek:

Voyager 1 is about 18 centimeters from the sun in this model (its distance from the earth would vary during the year).

I love scale-model solar systems!

whoops, mixed up my meters and kilometers :o It’s 10^-7 meters, not 10^-10.

That’s nothing! I once saw a scale model of the Solar System that was millions of times bigger than GorillaMan’s!

The comparison I like the best turned the Sun into an orange sitting in a refrigerator in Cleveland, which would make the nearest other fruits, er, stars another orange, a tangerine, and a cherry somewhere in Milwaukee.

One of my favourite essays is Asimov’s A Matter of Scale from the essay collection Science, Numbers and I. He addresses exactly this topic. One of the friendlies treatments I’ve come across.

If you modeled the entire universe to the size of the earth, let’s see…borrowing from Anne Neville’s figures and somewhat arbitrarily assigning a value of 30 billion light years for the diameter of the universe (I think there start to be problems with the concept “diameter” when applied to “universe”, but I don’t think any objects more distant than 15 billion light years have been discovered…so let’s say our model of the universe will be from just a bit beyond our most distant known object to a point directly opposite that in a sphere…a radius of 15 billion light years = a diameter of 30 billion.)

If I’m doing my math right, looks like there’s about 6 trillion miles per light-year.

That would put the universe we’re modeling at 180 septillion miles across, and we’re making an 8000-mile spherical model of it, a ration of one to 0.000000000000000000000044444.

Our galaxy, 100,000 light years converted to miles = 600 quadrillion, would occupy 0.0000266667 miles. Converted to yards, 0.046933333. Converted to feet, 0.1408. Converted to inches, 1.6896.