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#### 哪个星球是超级玛丽的世界？

What Planet Is Super Mario World? | Space Time | PBS Digital Studios

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.’
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So how can we understand Mario’s crazy jumping ability?

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.
3秒后，30米，以此类推。
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等于两倍高除以
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米，或大约5英尺1英寸高。
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方程是适用的
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 takeoff 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,
“超级玛丽”成为一个不现实的名词。
‘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

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.

If you find out, and especially if you

find a game that mimics the gravity of any actual planet,

I’ll report any interesting discoveries

on the next episode of ‘Space Time.’

And hey, if you like space stuff, please subscribe.
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