You can use this silly game to do serious physics

You can use this silly game to do serious physics

I’m a bastard for interesting online games that do not have a score or even a goal. In this case, it’s a cartoon space simulator to promote the book What if? 2 by Randall Munroe, author of the book xkcd comics.

You can play it by clicking here. (Don’t worry, I’ll wait.)

The game works like this: You start with a rocket on a very small planet. Click on the rocket to start, then you can use the arrows on your keyboard to start the thruster, rotate the spaceship and find other planets and some fun things that are mainly inside. What if jokes That’s it. That’s the game. It’s silly and fun and I love it.

But it turns out that you can use even a simple game to explore some key concepts in physics.

Real orbits

One of the features you can see on the original planet is a recreation of Newton’s cannonball, or Isaac Newton’s thought experiment about the connection between a fast-moving projectile and orbital motion. Newton said that if you were able to shoot a very fast cannonball horizontally from a very high mountain, the curve of its trajectory might match the curvature of the Earth. This would cause the cannonballs to fall, but never hit the ground. (This is essentially what happens to an object in orbit like the International Space Station, except the ISS wasn’t shot from a high mountain.)

Seeing Newton’s balls made me suppose that I could make my spaceship orbit this tiny planet, which would be fun. I immediately tried using the arrow keys — with very little success. Every time I almost put it in a stable orbit, it wouldn’t last. This made me wonder if the physical interactions that control the orbits in the What if the world resembles those in the real universe.

The first physics concept that applies to orbital motion is, of course, gravity. There is a gravitational interaction between any two objects that have mass. For example, there is an attractive force between the Earth and the pencil you are holding because they both have mass. If you release the pencil, it falls.

If you are standing on the surface of the Earth, the gravitational force acting on the pencil appears to be constant. However, if you moved that pencil far enough away from Earth (like 400 kilometers away, which is the distance at which the ISS orbits), then you would see a decrease in the gravitational interaction: the pencil would weigh less and last longer long until autumn.

We can model the gravitational force between two objects with the following equation:

Illustration: Rhett Allain

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