If you grew up in the 1990s, you probably played Mario games. And because you were a kid, you probably never stopped to think how it is that Mario can jump as high as he does. But astrophysicist Gabe Perez-Giz did, because science, and he breaks it down in the latest video from PBS Digital Studios:
Perez-Giz start by looking at how gravity affects motion. On Earth, an object traveling straight up loses 9.8 meters per second of velocity every second, which means that that same object falling back down gains 9.8 meters per second per second. To simplify things, Perez-Giz rounds that number up to 10 meters per second^2 and removes air resistance so that any object regardless of mass or size would rise and fall at the same rate. This is the acceleration due to gravity or the surface gravity of the Earth, and it of course varies depending on the planet. The Moon, for example, has just one-sixth the gravity of the Earth. You can jump a lot higher on the Moon.
There’s a simple formula that expresses the relationship between the gravity of the planet, the height of a jump, and the rise time of that jump: a planet’s surface gravity is twice the height of a jump divided by the square of the time it takes for the jumper to reach the apex of his jump.
This is the formula Perez-Giz uses to measure Mario’s jump. He measures time with a stop watch and estimates the height of Mario’s jump using the plumber himself, who the Internet says stands about five feet four inches tall, as a ruler. The jump he uses is the regular standing jump, not the spin jump, as seen in the 1990 Super Mario World game for the Super Nintendo Entertainment System.
It turns out Mario’s world has about eight times the gravity of the Earth, or 8G, so less gravity can’t explain Mario’s incredible ability to jump. This means the plumber must have super strength and massively powerful plumber thighs. But physiologically speaking, he wouldn’t survive on a world with eight times the Earth’s surface gravity, at least not as a human.
As for whether Mario’s world, a terrestrial planet with 8G surface gravity, could exist is unclear. We just don’t know enough about exoplanets, though it’s unlikely such a planet exists. And less likely still is that planets exists with Koopas and magic flowers that give you the ability to shoot fireballs underwater. Still, it’s an interesting way to look at a classic video game.
IMAGE: Family Friendly Gaming