Game Theory - Mario's LUNAR APOCALYPSE!! (Super Mario Odyssey)

Episode Date: May 29, 2023

Join Game Theory host MatPat as he dissects Super Mario Odyssey's BIG moon problem!

Mr. Mad Pat, how many moons does it take to get to New Dog City? Let's find out. A 1. 2. A 3. 20 minutes later. 46. 47.

48. 48 sugary moons. Now if you'll excuse me, I don't feel too well. Welcome to Game Theory, the funky mode to all of gaming's most complicated issues. issues. Today we're gonna be strapping in and launching ourselves into Super Mario Odyssey. One of the most satisfying and confusing Mario worlds I've ever had to experience. I mean, you have a kingdom of rainbow forks right next to Nintendo's version of Dark Souls. Then because of Mario's cannon height of 5.1 inch, the people of New Dong City are well over 10 feet tall, but arguably the most fascinating part of this game has to do with the very last location you go to. The Moon. Not because of the Dark Side

stages or the boss rush, but because when you actually sit down and do the math, the moon is proven to be the single biggest threat to Mario. Nay, I say the entire Mushroom Kingdom. Forget Bowser and his petty little schemes to marry Princess Peach. That is nothing. This thing. This thing right here is a threat scarier than anything Nintendo has ever cooked up. We're talking Majora's mask levels of planet-wide moon-based catastrophe here, people. But to truly understand why this thing, the moon, is such a menace to Mario in this game, we're going to have to do some math. So get ready, theorists. Let's crack open some formulas and break out the Ti-I-84s.

Yeah, 84s. We got to bust out the big guns today. Because here we go, off the rails to explore the great wide, wacky world of Mario Astrophysics. To begin, we need to first establish how large Mario's Earth and Moon are, and how far these celestial bodies are away from each other. Now, by this point, you guys know how many headaches the Mario franchise causes me on the pixel measurement side. From shifting heights to wacky gravity, Mario isn't fighting Bowser so much as he's constantly fighting against my math.

But determining the size of his planet in this game, this one! This was the straw that broke the camel's back. I thought for sure that there would be a way to do it between all the maps and globes that are present in the game's marketing and in the game itself. And let me tell you, I tried. I tried measuring pixels, but we had no way to do it. no consistently sized reference points. I tried measuring steps, but none of the stages allow you to truly see a whole continent. We attempted Al Baruni's method, the Iranian scholar who determined the radius of the earth by observing the heights of mountains, but without being able to reach a point on the horizon, we actually couldn't establish a distance between anything.

I examined the globes, the brochures, the start screen, the opening menu, promotional materials for this damn game. So many different things! But damn it, Nintendo! You always have to make it difficult! So you know what? I gave up. You heard that right. I just, I threw in the towel. To my knowledge, there is no definitive way in this game to prove the actual size of Mario's planet and his mood. Seriously, I feel like I tried everything here. However, just because I gave up on the measurement doesn't mean that the theory itself was in the pooper.

Doing this for as long as I have, I know that there's more than one way to skin a Mario. Oh boy, that's a gruesome image. Sorry, that didn't come out right at all. Anyway, the key to this theory is the Roche limit. A theory concept first proposed by game theorist, user Johnson and John Sina! For those of you who don't know, there's a magical distance a moon has to be away from a planet to remain a moon. Now, what do I mean by that? Well, think about it this way. Any planet or moon is held together by its own gravity, right?

That's why all of these things are balls. All the stuff in the planet is being pulled towards the center, making it an orb in space! But remember, everything has gravity. Big things like the Earth, smaller things like the Moon, even really small stuff. like you or me, we all have those gravitational forces that act on each other. For instance, the Earth, under the influence of the Moon's gravity, has whole continents raised about 50 centimeters because of the Moon's pool on Earth. And conversely, the Moon's surface shifts by about 5 meters towards the Earth in response to Earth's gravitational pull. And to make those facts even more incredible, remember, right now, the Moon orbits the Earth at an average distance of about 384,000 kilometers, or 238,000 miles.

That is how strong the force of gravity is. So that begs the question. What happens when you bring those two objects closer together, where the big object, like the Earth, with lots of gravity, is able to pull even harder on the small object with less gravity like the Moon? Well, something unexpected, actually. The Moon would get ripped to pieces, because the Earth's gravity is stronger than the gravitational forces

that are holding the Moon together. You ever wonder how Saturn got its rings? This is believed to be why. A small moonlit happened to orbit too close to Saturn and was pulled apart by gravity, with the pieces now orbiting the planet as rings. And this loyal theorist defines the Roche limit. The distance away from a planet an orbiting body needs to be to not be torn apart by the planet's gravity. The Earth's Roche limit is 18,470 kilometers, or about 11,470 miles.

That's about 120th the distance that the moon orbits at now. So if it ever ventured within that 18,000, kilometers limit, it would be pulled apart and the Earth would suddenly have itself some rings. And that, ladies and gentlemen is how humanity could finally achieve its final form by blinging out our own planet. We liked it, and so we decided to put some lunar rings on it. Which brings us back to Odyssey. You ever stopped to wonder why we're collecting moons instead of stars in this game? Could it be that what we're seeing here is early signs that Mario's moon is being ripped apart because it's orbiting within the mushroom planet's Roche limit?

You probably haven't stopped and wondered that, and for as absurd as it might sound, it absolutely seems to be the case here. Notice those huge chunks of space rocks scattered across the mushroom planet? We know for a fact that those are coming from the moon, not only via their name, but also from seeing them on the moon itself. But to truly know for sure, we need to determine the roche limit of Mario's Earth in the game, and then see where the moon falls relative to it. Now, as you can imagine, that involves a lot of math, so I'll try to cut out anything that isn't too interesting.

the Roche limit of the planet is equal to 2.4 times radius of the larger object, times the cube root of the density of the larger object, divided by the density of the smaller object. And as you can probably tell, there is a lot of stuff in that equation that we don't know. I mean, I just admitted two paragraphs ago to not being able to find the size of the planet. So without that, how do we have even a ghost of a chance of figuring out the radius of the planet, let alone the density of the planet, and then we gotta do the same thing with the mood? Well, as it turns out, we don't actually need the exact distance as long as a common unit is used throughout all of these calculations.

So stick with me here and let's just base everything off the moon's radius. Give it a variable, let's call it little R. Now, as you zoom out to the overall map, there are two frames where Mario's moon and the planet are side by side. And that's important so perspective doesn't distort their ratios. Taking pixel measurements from both of these frames, we can see that the moon's radius is about 30% of the radius of the planet. But luckily, we can also double-check this. In New Dong City, there's a model of the Earth, and the moon on the ground and the moon on the ground and front of City Hall and wouldn't you know it but once again the math checks out in this

model the radius of the Earth is determined to be 3.3 moon radii and with that we can say that the moon radius equals little R and Mario's planet radius equals 3.3 times little R since we're eventually working our way to finding density the next step is to find the mass of both Mario's Earth and Mario's moon which again seems like it should be impossible but luckily we have another secret back door here gravity you see when it comes to finding the properties of planets and stars, there are a lot of different formulas that we can use, since, you know, there's no actual way for scientists to wear a planet without using some form of math.

So here, we can use gravity to calculate the math by using the following equation. Mass equals acceleration times radius squared over the gravitational constant. That acceleration right there, it's as easy as finding out how fast Mario falls after jumping. First, on the mushroom planet, and then again on the moon. For that, all we need is the distance that Mario is falling and the time it takes a to fall. Plug those numbers into this equation and we get... Holy geez! On his home planet, Mario's normal jump has a downward acceleration of 70.16 meters per second squared. That is well over seven times Earth's normal gravity.

It is three times Jupiter's gravity and it's over double what it's been in any other 3D Mario game. If you're wondering why Mario feels heavier and falls faster in this game, well then there you go. It's not Mario packing in the canoli. his planet putting on the poundage. We do the same thing on the moon and we get an acceleration of 11.74 meters per second squared. 1.19 g forces which is pretty incredible when you think about it. This right here, this is how much Mario would be able to jump if you were subjected to our measly gravity. Now with those accelerations in hand we go all the way back to mass for both the planet

and the moon. Since this is just some basic calculations, let me just burn through this quickly by speeding things up. Jump in the acceleration numbers making sure to leave 3.3 R for the planet when calculating for Mario's Earth and just regular old little R when calculating for the moon and we got our a mass of 1.14 times 10 to the 13th r-square kilograms for the planet, 1.75 times 10 to the 11th are square kilograms for the moon. Now with the mass and radius of each body determined determining the density, the final part of the Roche Limit equation is a snap. D equal to the is a snap. D equals M over V, mass of the object, of the object,

volume of the sphere, which applies to both the Moon and the Earth is calculated at 4 thirds, high radius cube. I'm worried with math, it's basically 150.53R cubed for the Earth, and 4.19 radius cube for the Moon, which leads to densities of 7.6 times 10 to the 10 to the 10 divided by the radius of the Moon for the Earth, and 4 times the radius of the moon for the moon,

and that finally means that we have all the variables that we need for the Roche Limit equation. As a reminder, the Roche limit of a planet is equal to 2.4 times the radius of the larger object times the cube root of the density of the larger object. Therefore, therefore, the ratio of the larger planet, planet which is 3.3R, since remember it's 3.3 times the radius of the moon time the cube root of that mess of densities that we just calculate it. Don't forget that when you divide a complex fraction you multiply by the inverse so those little R.

R's cancels cancel out over there as well as those 10 to the tens. You got all that no perfect. Don't worry you didn't miss a thing Running through all of those numbers we see that the Roche limit is equal to 9.66 moon radii In other words, thanks to all the math that we just ran through we proved that if Mario's moon is within 9.6 moon radii from the center of his earth It will be slowly getting torn apart by Earth's gravity, which would give us the reason why we have hundreds of mini-moons and moon rocks all scattered across the surface of Mario's planet. And you know what? That's exactly what's happening here. You know how in the Moon Kingdom there's a spot where you can see the Earth not so far off in the distance? Well, using that vantage point, it seems pretty obvious that the moon is super close to Mario's planet.

So we could just assume it's within that Roche limit, but that's not good enough for me or the standards that I have for this show. So using that vantage point coupled with the in-game compass. You heard that right. Using the in-game compass to measure actual angles, it may seem unbelievable, but it's actually possible to determine the exact distance with trigonometry, cord lengths, and good old Sokatoa. But since this is the sort of math that I personally never wanted to show up in my life again, and I can only assume like three of you actually care about this type of nitty-gritty detail.

I'll do it as a mini theory if enough of you in the comments are actually excited about that sort of thing. Suffice it to say running all of those numbers, you get the moon sitting just about 5.5 moon radii away from the Earth. Confirming that it's within the Roche limit and that it is getting eaten alive by the planet's gravity. And remember, this isn't hypothetical. This actually isn't just a theory. This is truly how Mario's planet would be behaving relative to Mario's moon. It would be eating it alive. That is insane! And while that goes a long way to explain why moon rocks and multi-moons are scattered everywhere,

It also spells out some dire consequences headed straight to Mario's planet. To give you an example, consider this. When our sun starts to burn out and turn into a red giant, it's predicted that our moon will be pulled out of orbit, and it'll be pulled closer to Earth, crossing the Roche limit. At that point, it'll be torn apart. On the plus side, it'll give our planet a cool temporary ring. On the downside, it'll shower the planet with huge pieces of moon debris,

destroying all sorts of land, throwing tides into chaos, and sending the planet into another wave of extinction, extinction as space rocks crash into the surface around the world. Because yeah, while some of those chunks will orbit as pretty little rings, most of it'll just get pulled down by gravity onto the Earth's surface. And that is the fate that Mario Odyssey has already started to allude to for the mushroom kingdom. And that is the fate that is determined for it based on the science. And it certainly doesn't help that in the final battle, Mario, speeds this process along by destroying huge chunks of the moon's core. So enjoy running around to collect those moon rocks while you can, Mario. Pretty soon you won't have a chance. choice as they hurtle themselves towards you. Maybe that's why in Kirby and the Crystal Shards, shiverstar is a cold dead earth. Maybe that's why in Kirby's superstar you see Mario traveling the galaxy. He's looking for a new home. Who knows? But all of that needs to be fleshed out in another episode. But hey, that's just a theory. A game theory. Thanks for watching.