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SYFY WIRE Bad Astronomy

Scaling the solar system

By Phil Plait
The solar system, with object sizes to scale, but not the distances. Credit: Wikipedia / WP / PlanetUser

Every now and again, in interviews and on social media, I'm asked an interesting question: If there was one thing you wish people understood better about astronomy, what would it be?

My answer is simple: scale.

Things in space are very, very, very far away. The closest natural object to us, the Moon, is nearly 400,000 kilometers from Earth. The Saturn V rocket, still the most powerful rocket ever to be successfully used, took over three days to fling astronauts to the Moon. Three days of crossing nothing but an empty gulf.

And that's just the Moon. Getting to Mars and Venus, the two closest planets, takes months of travel. Jupiter is 600 million km away at its closest. Did you know that Saturn is twice as far as Jupiter is, and Uranus twice as far as Saturn?

The solar system is vast.

It's incredibly difficult to wrap your head around these scales. Worse, analogies tend to fall flat. Example: It would take nearly two centuries to drive to the Sun if there were a road to it (and your windows were shut really tightly). Does that visualize how far that really is?

It gets worse if you try to use planetary sizes for comparison. Planets are tiny compared to the distances separating them. Earth is just under 13,000 kilometers across, but it's 150 million km from the Sun. Over 11,000 Earths could fit between Earth and the Sun. Oof.

But there is a helpful model: a scale model. Across the world there are quite a few models of the solar system, and they tend to be pretty big. I was reminded of this when I saw this video, where a filmmaker, Wylie Overstreet, created a scale model of the solar system in the Nevada desert.

Impressive! And it reminded me of something …

I used to be part of an education and outreach group at Sonoma State University. We had NASA grants to put together educational materials about basic math and science. My work partner Sarah Silva and I would go to classrooms and talk to kids, and one day we decided to tackle this issue. We took an older exercise, called the Solar System Rope (you can find many variations of it online), and modified it to suit our needs. Basically, it uses a 20- or 30-meter rope that represents the distance from the Sun to Neptune (or Pluto). We marked it to show where the planets were. We'd have one kid be the Sun and hold one end, then another be Mercury (we printed out pictures of the planets and Sun for them to hold, too) and hold the rope at the right place, and so on.

When they were done, it was pretty amazing: Mercury, Venus, Earth, and Mars are all cramped and huddled within a meter or so of the Sun, but the outer planets were waaaaaay far away. It did a wonderful job impressing on them how big the solar system was, and why it took the New Horizons probe nearly a decade to get to Pluto.

But when we were setting it up the first time, I constantly found myself doing the math over and again to get the model scale right. If the Sun was one centimeter across, how big was the solar system? What if the Earth were that big?

After a few minutes of that I got tired of it, so I did something unprecedented*: I created a spreadsheet with all the needed numbers in it, coding it with the sizes of the planets and Sun, their distances, and so on. All you have to do is put in the size of the Sun you want and it calculates the size of the model.

Using this you can create a scale model of the solar system to any specification you want. And now, out of an act of pure magnanimity, I make this available to you for free! I put it on Google Docs for you to poke at; it's read-only there, but you can download it and adapt it to your heart's desire.

A snapshot of the solar system scale model spreadsheet using the default size of the Sun of 100 cm (1 meter). Credit: Phil Plait

You don't need to know much about spreadsheets to work it. The first column is the name of the object. The second and third are the radii and diameters in kilometers. In the third column, I divided the diameters by the Sun’s diameter, so now you have them all in terms of the size of the Sun. The Sun is one Sun diameter across, the Earth is 0.00918. The next column is the distance from the Sun in km, then that same distance divided by the Sun's diameter.

The seventh column is the size of the Sun in your scale model. The default is 100 centimeters (1 meter). The next column then scales the planets’ sizes to that, and the final column is the distance your planet is from the Sun. Easy peasey.

If you want a smaller Sun, replace the 100 cm in column G with something smaller. Note how much smaller the scale model gets. You can adjust it to get a planet size you want as well; if you want the Earth to be 30 cm across, say, play with the Sun size until it works out that way (answer: The Sun would be about 3300 cm across; 33 meters. That's HUGE).

Now go back and check the solar system scale model video again. At the five-minute mark, the Sun rises and they compare the size of the Sun and their model Sun as seen from the model Earth … and it works! Their Sun was over a meter wide, and Earth was somewhat bigger than a centimeter and 176 meters from the Sun. If you check my spreadsheet, that matches.

One more thing: Out of curiosity, I added the Kuiper Belt to the spreadsheet and even the distance to Alpha Centauri, the nearest star system. If you scale the model to something reasonable, how far away is Alpha Cen? A loooooong way. So far that even with a scale model it's hard to keep that distance on the Earth itself: If the Sun is a meter across, Alpha Cen is nearly 30,000 km away! That’s nearly as high as actual geosynchronous satellites above the Earth**.

Amazing. If you're an educator, I really recommend the rope activity. It's interesting, it gets the kids up and outside (or in a very long hallway), it's kinesthetic, and most of all it's fun! The kids really will enjoy being a part of it.

And that's the point, isn't it? We're all a part of the solar system, and we should take a minute to appreciate that. We may be small — too small to see on the scale model! — but the fact that we can figure all this out makes us big.

* Unprecedented for me, that is. I hate spreadsheets. Hate them. Hate. I wish I could banish them all to the end of the solar system rope, except not to scale.

Lemon squeezy.

** D'oh! I did the conversion incorrectly in the original text, saying it was 300,000 km. See? This is why I hate spreadsheets. :)