Super Mario gravity: the gravitational science of our favorite plumber

According to the sums, the gravitational value (g) of Mario’s world is eight times as strong as Earth’s — we humans can’t withstand anything higher than about five gs, suggesting that Mario would be incredibly strong if he came to Earth (and possibly also an explanation for his relatively short height as an adult male). This value was calculated using Super Mario World, and later scholars have looked at different games, resulting in a range between five and ten gs. So Mario’s incredible jumps only come from leg strength – if he were on Earth, his strength would allow him to jump higher than 90 ft (over 27 m). According to the sums, the gravitational value (g) of Mario’s world is eight times as strong as Earth’s

This is Mario’s homeworld, but how about a jump into space for some games dealing with outer-planetary physics? In Super Mario Galaxy and its sequel, the plumber went on a galactic mission to rescue Princess Peach from Bowser, and saw him travel to a number of star systems in the process. I’ll ignore some of the more extreme galaxies – assume we don’t find cake planets like in the Toy Time Galaxy – and look at some of the minor planets that Mario navigates. Gravity is a strange beast in the Mario universe. Perhaps unsurprisingly – a character of the sort homo nintendonus fighting an army of creatures controlled by a giant lizard probably wouldn’t exist in a conventional reality. And thank goodness for that – if Mario’s gravity were even remotely similar to our world, there would be a lot more Game Over screens.

If this quantum force is greater than electrical repulsion, electrons degenerate and exert additional degeneracy pressure against gravity. In white dwarfs, this pressure is offset by gravity to produce a stable body, but the baby planets in the Super Mario Galaxy games would not have enough mass to have this stability. Since the degeneracy pressure is much greater than gravity, planets of this size would survive only a very brief moment before violently destroying themselves. Planets of this size exist in our own universe – it’s not the size, but rather Mario’s physics that makes them impossible.

However, its ability to move and jump on any planet is the same as it is in its home world (the paper uses Earth’s surface gravity, but as we’ve seen, the number could be much higher in reality). That means that they have a similar mass to the world, and would be considerably denser due to their small size, which leads to problems: if they are confined in too small a space, elementary particles are not only affected by electrical repulsion, but also due to quantum repulsion between electrons. I’m not the first to bring this up – in 2014 a team of students from the Department of Physics and Astronomy at the University of Leicester analyzed these planets. In their paper, “It’s a-me, Density!”, the team looked at the gravity and density of these worlds and concluded that they would likely implode in real life. They noted that the planets visited appeared to be about 100 meters in diameter, making the curvature of their surfaces not only visible but extreme — Mario could walk around the circumference of a planet in a minute or two.

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