Super Mario can jump higher than a kangaroo on steroids, but how does he do that?

And is there any real-life planet where you could jump like Mario?

My name is Gabe, and this is "Space Time."

[MUSIC PLAYING] So how can we understand Mario's crazy jumping ability?

Let's start with how gravity affects motion, because that a huge effect on jumping.

Now on Earth, an object rising straight upward will lose 9.8 meters per second of its speed each second.

Likewise, a falling object will gain 940 meters per second of extra speed each second.

For simplicity, let's round the 9.8 to 10.

So, drop a ball out a window.

One second later, it's moving at 10 meters per second.

Two seconds later, 20 meters per second.

Three seconds later, 30, and so forth.

Now mass and shape are irrelevant.

If you took air resistance out of the picture, Bowser and a mushroom would slow down when rising or speed up when falling in lockstep.

That rate, around 10 meters per second per second, or 10 meters per second squared, is called the acceleration due to gravity, or the surface gravity of Earth.

And it's usually denoted by lowercase letter g. Now a planet's surface gravity has a huge effect on how high you can jump on that world.

Low gravity, for instance, is why astronauts in heavy spacesuits could jump so high on the moon.

But on any given planet, there's a simple relationship between its g value, the maximum height you reach during a jump from the surface of that planet, and the amount of time it takes you to reach that height.

g equals twice the height divided by the square of the rise time.

If you're interested in where that formula comes from, you can check out the link in the description.

But we're going to use the formula to measure g on "Super Mario World."

All we need to do is time one of Mario's jumps and measure the height of that jump.

Time, we can measure with a simple stopwatch.

Jump height, we can measure by using Mario himself as a ruler.

Careful internet research, which you can also find in the description, reveals that Mario's official stature is 1.55 meters, or about 5'1" tall.

Now I did a crude version of this experiment with "Super Mario World" on a Super Nintendo Entertainment System circa 1991.

I had Mario do regular jumps in place, not the spin jumps, and I used to some tape to mark where the top of his hat was at the apex of the jump and before the jump.

I found it that he jumped about two and a quarter Marios.

Multiply that by his height of 1.55 meters, and you find that his jump height is almost 3 and 1/2 meters.

Timing the jump is trickier, though, because it happened so fast.

I ended up timing 15 successive jumps, dividing that by 15 to get the up-and-down time for one jump, and then dividing that by 2 to get the time to reach the apex.

My result is about 0.3 seconds from launch to apex.

Now, let's put these numbers into the formula from before.

If we set h to 3.5 meters and t to 0.3 seconds, we get a final g value of around 78 meters per second per second, or almost 8 Earth g's.

That means "Super Mario World" has about eight times the surface gravity of Earth.

Now, as it turns out, other people have done more sophisticated versions of these measurements using Nintendo emulators, screen capture programs, and actual mathematical software.

Their results show some variation, but all give surface gravities of between 5 and 10 Earth g's, which is consistent with my crude calculation.

Moreover, their more detailed analyses confirm that "Super Mario World" respects the rules of gravity, meaning Mario's speed does indeed change at a steady rate whenever he jumps or falls, so that our method of measuring g's should be kosher.

And the bottom line is that g is bigger on Super Mario World than on Earth, so that weaker gravity is not in fact the key to Mario's jumping prowess.

What is it?

Crazy leg strength.

Like, superhuman leg strength.

Remember, gravity is eight times stronger on Super Mario World than it is on Earth, yet Mario jumps much higher than we can on Earth.

So his takeoff speed must be really big.

How big?

If Mario were on Earth, he would have a takeout speed of over 50 miles an hour and be able to jump about 28 meters, or over 90 feet.

That means Mario could hurdle the Rockefeller Center Christmas tree with room to spare.

So it's highly implausible that Mario is even human.

And not just because of the jumping.

On a planet with eight times Earth's surface gravity, your blood is eight times as heavy.

Now, a human heart couldn't pump that up to the brain, so an actual Italian plumber would be unconscious or dead.

So in terms of human physiology, at least, "Super Mario" gets a realism fail.

But what about Super Mario World itself?

Do any real-life planets have that large a g?

Well, g on a given planet is determined by a combination of that planet's mass and its radius.

You can compute it with the following formula, using Earth's mass and radius as a reference.

What you find is that all the major rocky bodies-- that means the moon, Mars, Venus, Mercury-- all of them have smaller g values than Earth does.

The gas giant planets, like Uranus, Neptune, and Saturn, don't have solid surfaces to stand on, per se, but just for comparison, the g values they would have are all within 15% or so of Earth.

Even on Jupiter, g is only 2 and 1/2 times or so Earth's value.

So Super Mario World is clearly not in our solar system.

Comparisons to planets outside the solar system are trickier, because astronomers don't have good estimates of both mass and radius for most exoplanets.

exoplanets.org has a table where you can search through the ones for which we can estimate the surface gravity, and you find those with values that are many times Earth g's are thought to be gas giants.

In fact, g values this large would more likely occur on stars.

Now, though the jury is still out, most models of planet formation also suggest that it's hard to have both a high g and a solid surface.

So what planet is Super Mario World?

Well, a planet with a solid surface where Mario could jump exactly the way he does in the game is unlikely to exist, at least in our universe.

Now I suppose Super Mario World could be a platform at the edge of some gas giant.

But then what's holding up the platform?

Donkey Kong?

Remember, you could try this experiment yourself, even with rough measurements like mine.

It'd actually be cool to know how strong gravity is in older versions of "Super Mario" games, or in other games altogether.