Modeling 2D Motion in the xkcd What If-World

Screenshot from the xkcd What If-World.

This is part 3 of my series on the xkcd What-If-World. Here’s part 1 an here’s part 2. Let me get you up to speed on this. Basically, the xkcd What If-World (that’s what I call it) is a web-based game that gives you a rocket that you can fly around and explore. I’m trying to figure out the physics of how this works (for fun). Here’s what I know so far.

• The gravitational force is piece-wise constant. So, when you are close to the planet, it has a constant gravitational field (g = 5.5 m/s²) which decreases to g = 4.6 m/s² when the rocket is more than 45 meters from the center and then down to 1.46 m/s² when it’s farther than 51 m.
• When in “deep space”, the rocket gives a thrust per mass value of 14.42 m/s² with a maximum speed of 78.6 m/s.
• When near the surface of the planet with the rockets on, it has an acceleration of 28.9 m/s² (which means that either the thrust is greater near the surface or gravity is weaker with the rocket engine on). Who knows.

That’s what I have. Yes, it seems like a random collection of rules that govern the motion of objects — but that’s just the way science works sometimes. Maybe I can find some better models with future experiments.

2D Motion