What If Earth Was Made out of Lego?

What If Earth Was Made out of Lego?

Written by Dr. Matt Caplan

What if we made a lifesize model of the earth out of Legos? What would it look like, how many bricks would it take, and is it even possible?

To give you a sense of how big a project this is, we would need over 100 quintillion Lego bricks. Stacked end to end, these Lego bricks would make a tower 400 million lightyears tall, which, if it were on earth, would extend across the entire Laniakea supercluster of galaxies, where our Milky Way lives. So this is a lot of Legos- and we’re excited to hear how they stack up, in this episode of The Infographic Show, What if Earth was Made out of Legos.  

Before making the earth out of Legos, let’s see what happens if we just try to build this cosmic tower. If we began by stacking Legos on the surface of the earth, we wouldn’t get very far.  Every material, whether it’s steel (skyscrapers), rocks (mountain), or plastic (Legos), has a breaking point- there is simply a maximum amount of weight it can support before breaking. Once we’ve stacked 320,000 bricks, we won’t be able to go any higher. The weight of the tower would crush the base flat, and adding more bricks to the top would only serve to crush more bricks on the bottom.
This is already beginning to spell bad news for our project - the earth’s gravity is simply too strong and Legos are simply too weak. But you may remember that everything is weightless in space - the Lego tower on earth has to be different from a Lego ball in space, right?

Unfortunately, we’ll still run into the same problem. If we started building a giant Lego ball in the vacuum of space, we wouldn’t have to worry about the strength of the plastic to begin with. But as we add bricks and as our model grows, so too does its mass, and therefore, the strength of its gravity. When our Lego earth is 625 km across, barely a tenth of the size of the earth, the central bricks will begin to be crushed from the immense pressure of the bricks above them.

So Planet-Lego starts to collapse on itself when it's barely larger than an asteroid. This isn’t due to any structural shortcoming of Legos, the same size-dependent crushing controls the shape of ordinary heavenly bodies as well. In fact, there is a cutoff size, known to experts as the potato radius, below which a proto-planet can have shapes various and sundry, from a round ball to a spiky potato. But as soon as a proto-planet gets any larger, it gives way to its own crushing self-gravity and becomes a ball.

I’m not going to run through the theory, but if you want to see how this really works, I strongly recommend you check out our partner, Brilliant.org. They are a problem solving website that teaches you how to think like a scientist by guiding you through problems. (They take concepts like these, break them up into bite sized chunks, present clear thinking in each part, and then build back up to an interesting conclusion.) They have an entire course on Gravitation where in addition to interplanetary orbits, black holes, and dark matter, you can learn exactly how proto-planets crush themselves into balls, starting from the very intuition we got from the Lego tower at the beginning of this video.

If you visit brilliant.org/theinfographicsshow (or click the link in the description), you can sign up for free and learn all kinds of math and science. And as a bonus to The Infographics Show viewers, the first 200 people that go to that link will get 20% off the annual Premium subscription. [Sponsor message ends]

Okay, so that’s two strikes against building a Lego earth. We’ll never get enough Lego bricks, and even if we could, the bricks would be crushed. So what if instead of worrying about practicality, we just magically replace the real earth with a Planet Lego? What would happen?

This Lego-earth weighs a tenth of the actual earth, about as much as Mars, because Lego bricks are a tenth the density of the iron-nickel fluid that makes up the bulk of our planet. And as with our first attempt, it would immediately crush the bricks inside it. Lego bricks are about half empty space, so our Lego earth will shrink over a thousand kilometers as it squeezes out all those gaps.

In the process, the friction and warping of the plastic and the pressure all conspire to heat the bricks to 15,000 degrees Celsius.

Lego bricks are made from a plastic known as acrylo-nitrile butadiene styrene, also known as ABS, which has many common uses on earth, such as manufacturing and 3D printing, because it is very pliable when heated. Though at 15,000 degrees, the ABS would likely combust and burst into flames, but in our model there is no oxygen - only Legos. Instead, the ABS breaks down into its atomic components, carbon, hydrogen, and nitrogen, giving Lego-earth a molten white-hot core. The outer layers don’t break down so horrendously, instead forming a sort of liquid Lego-plastic mantle, with a cold crust of unharmed bricks at the top.

You might worry that replacing the earth with a Lego earth would have a catastrophic effect on our orbit, but fear not. The new Planet Lego can orbit the sun just like any other body in the solar system. In the coming years, the surface layer of Legos will lose their color, being baked in ultraviolet rays from the sun - the same light that gives us sunburns. As the eons stretch on, the plastic on the scorched surface of the planet grows brittle, becoming increasingly marked by impact craters which will last for eternity, not too different from the moon. As the core cools over millions of years, the material will begin to separate out. Hydrogen will form H2 gas and will leak to the surface, briefly supplying the planet with a thin atmosphere which will be washed away in the solar wind, as the core turns solid and freezes, perhaps to diamond.

So if any aliens came looking for us far far in the future, they would, at the very least, be incredibly confused by what they find.

What do you think of Planet Lego? Best idea ever? Worst idea ever? Let us know in the comments!

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