The Physics of Super Mario Galaxy

For the last week I’ve been playing this game called “Super Mario Galaxy”, and if it isn’t the best game ever made, then it’s in the top three. It has fanservice by the buckets, and a soundtrack that soars as if the game itself is just happy it is being played, and little blue tractor beam stars that sing you sad little theremin songs, and evil hats. Things happen for no reason, like they used to in old NES video games, and you don’t care why, you just love it. I don’t even know the words to express how much fun I’ve been having with this game.

So instead of trying, I’m going to instead write about the physics problems the game poses.

The gimmick in Super Mario Galaxy is that where previous Mario games had you jumping between platforms floating in the air in the Mushroom Kingdom, the new one has you jumping between little bitty planetoids floating out in space. It works like this:

You get the idea pretty quickly. So here’s what I wonder:

Most of Mario Galaxy is spent running around on the surfaces of those little asteroids, like you see on the video. The asteroids vary in size and shape, although most are roughly spherical and on average each asteroid is about the size of a Starbucks franchise. Every single one of them, regardless of size or shape, has completely normal earth gravity. And it’s hard not to think, when you see Mario taking an especially long jump on a small asteroid and landing about halfway around the planet, that he kinda looks like he’s having a lot of fun. So what I want to know is, is any of this possible in real life?

Would it be physically possible– assuming that you have more or less unlimited resources and futuristic engineering, but are still bound by the laws of known physics– to actually build a bunch of little asteroids like this, with compact volume but earth gravity? Say, if you’re a ringworld engineer or a giant turtle with magic powers. Could you build the Mario Galaxy universe?

Here’s what I worked out:

So first off, clearly we’re not going to be able to do most of the things in the Mario Galaxy universe, since SMG is of course a game and obviously they weren’t trying to be realistic or imitate anything like real physics. I’m going to just ignore these things– for example, I’m ignoring anywhere where there’s just a vanilla gravity field pointing in some direction, as if generated by a machine. As far as we know, that’s just not possible. In the physics we know, the only way to create a gravity field is to put a bunch of mass in the place that you want the gravity to point toward.

This isn’t so bad, since a lot of the planetoids in Galaxy look like this might well be what they are– just a big lump of mass creating a gravity well. In fact, some of the planets– for example the one at the start of the video above– are actually shown to just be thin hollow shells with a black hole at the center. So, in the post that follows, I show what you’d have to do to build one of these planets. I’m going to consider just a single example planet, of about the size of the one from the video above; you’d have to use different masses and densities for each planet in the game, since each has a different size but the exact same amount of gravity at the surface.

ANALYSIS

The first question to ask here is, how much mass do we need? Well, the planet in the video, eyeballing it, looks like it’s about as wide as a 747 is long. Wikipedia says a 747 is 230 feet long.

Newton’s formula for gravity is m_1*a = G * m_1 * m_2 / r^2, where I take m_1 as the mass of Mario and m_2 is the mass of the planetoid. Solving for m_2, I get:

m_2 = a * r^2 / G

r is 115 feet (half a 747), and a is earth gravity, 9.8 m/s/s.

Plugging in to google calculator, I get:

((9.8 m (s^(-2))) * ((115 ft)^2)) / G = 1.8043906 × 10^14 kilograms

So, if you want to get earth-like gravity on the surface of a 230-foot-diameter sphere, you’re going to need about 1.8 * 10^14 kg of mass. This is not that much! Checking Wikipedia I find even the smallest moons and dwarf planets in the solar system get up to about 10^20 kg. in fact, 2 * 10^14 kg is just about exactly the mass of Halley’s Comet. This sounds attainable; other characters are shown hijacking comets for various purposes elsewhere in Mario Galaxy, so no one will notice a few missing.

Meanwhile, Wikipedia’s formula for escape velocity for a planet ( sqrt( 2GM / r ) ) tells us that escape velocity from this planetoid will only be about:

sqrt((2 * G * (1.8043906 × (10^14) kilograms)) / (115 feet)) = 26.2110511 m / s

Which is about 60 MPH. So the cannon stars Mario uses in the video to move from planet to planet should work just fine. (Although platforms might not work so well, at least not tall ones; since the planetoid is so small, you’d only have to get about 45 or 50 feet up off the ground before the amplitude of gravity is halved. Actually gravity will fall off so quickly on the planetoid that there would be a noticeable gravity differential between your feet and your head: a six-foot-tall person standing on it would experience about 1 m/s^2 more acceleration on their feet than their head. So expect some mild discomfort.)

At this point the only question is: If one were to attempt to fit Halley’s Comet into a 230-foot-diameter sphere, would this turn out to be impossible for any reason? In answering, I’m going to consider two cases: One where the mass is in a black hole at the center of the sphere; and one where the mass is distributed through the sphere evenly. In both I’ll try to see if anything really bad happens.

So, first, the black hole case. Looking here I’m told that the event horizon of a mature black hole should be equal to G * M / c^2, and Wikipedia tells me that the Schwarzschild radius (the radius you have to pack a given mass into before the black hole starts to form on its own) is about twice that. So plugging this in, I find that the radius of this black hole at the center of the sphere is going to be:

(G * (1.8043906 × (10^14) kilograms)) / (c^2) = 1.33970838 × 10^-13 meters

… uh oh! Now we seem to be running into trouble. If someone wanted to construct a black hole with the mass of Haley’s comet, they’d somehow have to pack the mass of the whole thing into… well, google claims the diameter of a gold atom is 0.288 nanometers, so… about one-hundredth of the diameter of a gold atom?! That doesn’t sound very feasible.

On the other hand, considering the case where the sphere is solid, one finds that the required density is going to be about:

(1.8043906 × (10^14) * kilograms) / ((4 / 3) * pi * ((115 feet)^3)) = 1.00023843 × 10^9 kg / m^3

As remarkable coincidence would have it, 10^9 kg/m^3 is, according to wikipedia, exactly the density of a white dwarf star, or the crust of a neutron star! So this is sounding WAY easier than the black hole plan: All you have to do is go in and chip off 180,000 cubic feet of the crust of a neutron star, and you’ve got your planetoid right there.

Of course, there’s still one more step. First off, I’m not sure what the temperature of a block of white dwarf matter that size would be, but you might not want to actually walk on it. For another thing, the reason why a white dwarf or the crust of a neutron star has that much density in the first place is that all that matter is being held in place by the incredible gravitational weight of the star the matter is attached to– your average white dwarf is about the size of Earth, which by star standards is tiny, but which compared to our little Mario Galaxy planet is rather large. So if you tore off a 747-sized chunk of one of these stars and just dumped it in space, it would almost certainly explode or expand enormously or something, because the chunk’s gravitational pull on itself would probably not be sufficient to hold it together at the white dwarf density. So we’re going to need some kind of a shell, to hold the white dwarf matter in place and (one assumes) trap things like heat and radiation inside.

When you get to the density a white dwarf is at, the main thing you have to worry about is what’s called degeneracy pressure. Usually, when you try to compress matter, the resistance you meet is due to some force or other– the force holding atoms in a solid apart, for example, or the accumulated force of marauding gas molecules striking the edge of their container. When you get to anything as dense as a white dwarf, though, the particles are all basically touching (“degenerate”), and the main thing preventing you from compressing any further is literally just the physical law that prevents any two particles from being in the same place at the same time, the Pauli Exclusion Principle. If you try to compress past that point, a loophole in the exclusion principle comes into play: it’s actually possible for two particles to share the same chunk of space as long as they’re in some way “different”, for example if one of them is in a higher energy state than the other (say, it’s moving faster). So in order to compress two particles “on top” of each other, you have to apply enough force that you’re basically pushing one of the particles up to a higher energy. For large numbers of particles, this can get hard.

Different kinds of matter degeneracy happen at different pressures. At the center of a neutron star, the pressure is so high that neutrons become degenerate and start stacking up on top of each other. The matter in white dwarfs and neutron star crusts, on the other hand, exhibits only electron degeneracy. Whew! So, how bad is this going to be? Well, looking here, we find the formula for electron degeneracy pressure to be:

P = ( (pi^2*((planck’s constant)/(2*pi))^2)/(5*(mass of an electron)*(mass of a proton)^(5/3)) ) * (3/pi)^(2/3) * (density/(ratio of electrons to protons))^(5/3)

(I’m assuming that our little white-dwarf-chunk will not be so warm that the particles will be moving at relativistic speeds; if not, we have to switch to a different formula, found here.)

So, we know the density; the ratio of electrons to protons has to be 1 (Otherwise the white dwarf would have an electric charge. Of course, if you can somehow find a positively charged white dwarf somewhere, you can reduce your required pressure noticeably!); and everything else here is a constant. Plugging this in we get:

P = ( (pi^2*((6.626068 * 10^-34 m^2 kg / s)/(2*pi))^2)/(5*(9.10938188 * 10^-31 kilograms)*(1.67262158 * 10^-27 kilograms)^(5/3)) ) * (3/pi)^(2/3) * (1.00023843 * 10^9 kg/m^3)^(5/3) = 9.91935718 × 10^21 kg m^-1 s^-2

Or in other words, if we neglect the assistance that the white dwarf material will be providing in holding itself together in terms of gravitational pull, the shell for our planetoid would need to be able to withstand 9.91935718 × 10^21 Pascals of pressure in order to keep all of that degenerate matter in. That’s a bit of a problem. Actually, it’s more than a bit of a problem. It’s most likely impossible. The strongest currently known material in the entire universe is the carbon nanotube, and it has a theoretical maximum tensile strength (I think tensile strength is what we want to be looking at here) of more like 10^11 Pascals. So you’d have to find a material that could do better than that by a power of like 10^10. But, hey, that’s just an engineering problem, right?

CONCLUSION

So what the above basically tells us is this. As long as you can do one of the following things:

  1. Hijack Halley’s Comet and collapse all of its mass down into a volume with diameter 5.35 milliangstroms, to create a small black hole
  2. Build a pressure vessel capable of withstanding 1022 Pascals of stress, then trap inside a big chunk torn out of a white dwarf

Then you, too, can have a Super Mario Galaxy style planetoid in your very own space station! Now, given, these things aren’t easy, and possibly not even possible. But isn’t it worth it?

DISCLAIMERS

The above analysis has some limitations which should be kept in mind.

  • In the case of the black hole strategy, you’d have to somehow stabilize the position of the black hole relative to the shell, so that the surface of the shell always stayed exactly 115 feet away from the black hole– otherwise random drift would cause one side or other of the shell to gradually drift toward the black hole and eventually cause the whole thing to fall in. Which probably would be kind of fun to watch, but isn’t what you want if you’re standing on it at the time.
  • In the case of the solid-body/white dwarf strategy, I am assuming that the final planetoid can be treated like a point mass. This is almost certainly wrong. I’m not sure how to go about figuring out exactly the gravitational force from a chunk of matter which rather than being treated like a point is distributed through a sphere immediately underfoot.
  • On the other hand, it might be interesting to find out, because if you knew how to do that you’d probably know also how to figure out the gravitational force from matter distributed through an irregular body. Most of the planets in Mario Galaxy are not spheres! There’s also planetoids shaped like barbells, and avocados, and cubes. Most interestingly, there are a handful of planetoids in certain places in Mario Galaxy shaped like toruses (doughnuts). I’m curious but not sure how to figure out, if you actually were to construct such a thing in real life, what would the gravity when walking on it be like? What would happen if you tried to walk onto the inside rim?
  • None of these planetoids would be able to maintain an atmosphere. The escape velocity is just too stupidly low. (Puzzlingly, this does not seem to matter in Mario Galaxy, since Mario seems to be able to breathe even when floating out in deep space. One would be tempted to simply conclude that Mario, being a cartoon character, does not need air, but no, there are sections in the game with water and Mario suffocates if he stays underwater too long. Apparently the Great Galaxy is permeated with some kind of breathable aether?)
  • Even the gravity and breathable aether aside, many the elements of Super Mario Galaxy do not seem to be possible to replicate under normal physics. For one thing no matter where Mario walks on any structure anywhere in the game, his shadow is always cast “down” underneath his feet, as if light in Mario’s universe always falls directly toward the nearest source of gravity, or if the shadows weren’t cast by light at all but were simply visual markers in a video game allowing the player to tell where they are about to land.
  • I am not a licensed structural engineer, space architect or astrophysicist. The data above is provided on an “as is” basis without any representations or warranties and should not be used in the construction of any actual space vessel or celestial object. John Carmack, this means you.

Special thanks to pervect at Physicsforums for help with the degenerate matter stuff, and Treedub for pointing out what the electron/proton ratio of a white dwarf would be.

51 Responses to “The Physics of Super Mario Galaxy”

  1. El QT Says:

    >>I am assuming that the final planetoid can be treated like a point mass. This is almost certainly wrong.

    In fact, you are quite lucky sir, for the gravitational field of a solid uniform sphere is exactly the same as that of a point mass at its center. (outside of the sphere that is). in fact the gravitational field of any uniform spherical shell, outside the shell, is the same as that of a point mass at its center, GM/r^2. (the first statement follows from the second of course). The original proof of this is in Newton’s Principia, actually.

    Also the field inside of a uniform spherical shell is zero. so if our shell is more or less uniform there wont be much force on it from the black hole, and anyway the acceleration are at most on the order of 10 m/s^2 so retro rockets could easily stabilize the shell visa the black hole.

    I applaud your intuition however, because this is an exceptional property of spherically symmetric distributions and 1/r^2 laws, and not particularly obvious. it is certainly not true of other geometries like toruses or ellipsoids. You can do the calculation for a torus, its just a bunch of integrals, but its a pain in the ass and the answers gotta be floating around the net somewhere already. There’s the thing called the multipole expansion whichll give you a nice approximation of the field for a compact thing with some random shape, but the approximation is good for when youre far away from the thing. If you want to know what the field is right next to thing ( ie, can I walk on it) I think a computer is the route.

    El Quantum Taco

  2. N.B. Says:

    This is certainly the most awesome physics discourse I’ve ever read.

  3. Jarbornza Says:

    Awesome.

  4. designmartini » The Physics of Super Mario Galaxy Says:

    […] The Physics of Super Mario Galaxy […]

  5. Doug Says:

    Bowser and the Koopa will surely defeat you since you’ve decided to concentrate on “physics”, instead of the *real* property here… that of Evil. They will also have Princess Peach too.

  6. Blake Stacey Says:

    Nit: the Pauli exclusion principle only applies to fermions.

  7. IvyMike Says:

    Author (and aerospace engineer) Wil McCarthy explores the physics of microplanets extensively in his “Queendom of Sol” series:

    http://www.wilmccarthy.com/bookstor.htm

    I think you would find those books quite interesting. The book “To Crush The Moon” is about an effort to reduce the radius of the moon to the point that it has earthlike-gravity on the surface. (Of course that’s still much bigger than the Mario microplanets, but smaller microplanets do figure in the novels, too.)

  8. thekow Says:

    Excellent article. Great read! Thanks!

  9. TorusWorld Says:

    Being a math major who’s loved physics I started doing some rough calculations on what the gravity on one of the torus would be like. Assuming there are no mistakes in my integrals, and it would take too much to type them out here so I wont, it turns out you could walk on the inside of one assuming it had a rather large radius, on the orders of tens of miles. Much smaller than that and you can stand on the inside of the ring but the moment you try and walk on it you’ll find yourself in constant free fall a few inches or feet from the surface, kinda like a satellite is around the earth.

  10. Nerd Says:

    Found a flaw in your calculations. You were using 115 ft for the radius of the asteroid, and should have been using meters. So all your further calculations are off. The formula for gravitational force is F = (GmM) / r^2 where m is the mass of the smaller object (Mario) and M is the mass of the larger object (earth, asteroid). Since we’re creating a situation in which the force of gravity on Mario is the same on both planets, we can say (GmM) / r^2 = (G m M_2) / r_2^2. G and m cancel so we’re left with M / r^2 = M_2 / r_2^2. Google says the mass of earth is 5.97E24 (google “mass of earth”), radius is 6378 m, and 115 ft = 35 m. Plugging in and solving for M_2 we get the mass of the asteroid is 1.8E20 kg. The density of the asteroid, assuming a solid sphere, would be 1E15 kg/m^3, which is ridiculously dense.

  11. ceo Says:

    could u please explain the physics on Mario bros 2… ?
    all the characters seem to defy it differently.

  12. Nerd Says:

    I found the escape velocity, too, and found it was 6.86E8 m/s.

  13. Jared Says:

    Nerd:

    He’s OK with using 115 ft because he used google to do the calculation and it handles the unit conversion. If you copy and paste his formula into google, it gives the result he provides. If you replace the 115 feet with 35.052 meters, it gives the same result.

  14. Samantha Says:

    This is the sexiest thing I’ve ever read.

    Video games + Physics + Math….wow.

  15. Jeff Says:

    As far as torus-shaped worlds go – these are also very popular in most RPGs; if you look at the world map of, for example, any numbered Final Fantasy before 10, the map wraps both east-to-west (as you’d expect to see on a spherical world) and north-to-south (wait, what?). And of course the party has no problem walking/driving/riding/flying over these boundaries.

  16. The Triscut Says:

    Not that I can provide an answer, but I found it interesting that you never addressed what could be used to hold these planetoids in place and not fall into each other. It would have to be something invisible, non-tangible, and strong enough to hold a 1.764 * 10^15 N force (assuming he meant to say 115m not 115 ft). Perhaps a perfectly balanced magnetic force with some unlimited power supply? Or maybe the breathable aether chooses what can pass through it and what can’t.

  17. Go Nintendo » Blog Archive » The Physics of Super Mario Galaxy- What are you waiting for? Says:

    […] Article here […]

  18. Jacob Says:

    Love the math and use of physics, but I have to propose a easier explanation of how to simulate gravity, magnetics, If mario just wore magnetic boots and we assume the universe is always positive or negatively charged with neutrals at no point in the game. This way you could have plenty of varying size asteroids/planet size objects with a seemingly gravitational pull, and be consistent with the funnier gravity sections of the game specifically the arrow sections as a varying strength of magnetic fields with electromagnets would allow for fun.

  19. Josh Chacin Says:

    Thank you, the article was very readble, and I could actually understand allot of it. Thanks for the free physics lesson

  20. Chris Says:

    This is a very inspiring page. It makes me want to make a movie about it.

  21. Penis Says:

    Your a fucking idiot. Get a job. BOWLS!!!!!!!

  22. Bryan Says:

    I think the “princess” at the beginning of the game gives mario the power to breathe in space.

  23. mcc Says:

    Well, thanks all for reading this! Okay, so some responses:

    To El Qt, re point masses: Yes, you are of course right. I probably should have realized this before posting 🙂

    To Blake Stacey, re the Pauli Exclusion Principle: You are also of course right. Just to clarify for the other readers though: When Blake says that the Pauli Exclusion Principle applies only to “fermions”, this is for purposes of this article basically the same thing as saying it applies to “matter”.

    To Nerd, re feet vs meters: So, I’m not sure I see what you’re saying. The reason I use 115 feet for the radius of the asteroid is that the Wikipedia page for a 747 says it’s 230 feet (well, 231, I rounded), and I was assuming that to be the diameter of the asteroid just by fiat. The fact that I mix feet and meters in my calculations above is not a problem, and does not effect the final results, because as Jared says above Google Calculator does automatic unit translation. If you tried to run the above calculations for a 115-meter-radius object you would of course get different results. Aside from this I’m not sure I can follow the other calculations you did but I don’t think they’re correct, the mass of the earth shouldn’t have any relevance to this problem.

    To Jeff, re RPG maps: That’s actually a pretty funny observation, I’d never thought about it that way. But I did see once a long time ago a page that tried to explain topological classification using Atari’s “Asteroids”

    To Triscut, re stabilization: I didn’t address this problem because I don’t think it’s actually possible to solve! That is, I was trying to work with the problem of just creating one Mario Galaxy planetoid– but I assume if you set up entire levels from Mario Galaxy, it would surely be horribly unstable because all the planets and black holes would attract each other. Of course, maybe you’d get lucky and rather than falling into each other they’d just enter really complicated n-body orbits?

    Now, this said, it may still be possible to somehow or other hold one or several of these little planetoids in place, maybe at the center of a large space station (this idea is nice because you can flood the entire area with oxygen). The magnet thing you suggest is a good idea, though I’m not sure quite how to work with it. As far as I’m aware it’s possible for black holes to have a magnetic charge; and as noted in the article, if you can figure out a way to give the electron-degenerate matter from the white dwarf solution a positive charge then the container problem becomes a lot easier! So if you have a really small black hole or a white dwarf chunk with an electric charge, it might well be possible to move it around or stabilize its position with magnets. I honestly don’t know how one would go about doing that or calculating how powerful the magnets would have to be, though.

  24. Henk Says:

    Hello, pleased to meet you. This is my Wii, this is my super mario galaxy physics problem, and this is the bed I never get laid in.

  25. Pontifier Says:

    An environment that could provide an atmosphere like the one described in the article can be found in the book “The integral trees” by Larry Niven. The story describes a breathable gas ring orbiting a neutron star.
    -John Fenley

  26. Qev Says:

    Instead of trying to confine electron- or neutron-degenerate matter, you could always go with quark-degenerate (or strange) matter. Somewhat denser than neutron-degenerate matter, it’s also (possibly) stable without gravitational confinement once it’s formed.

  27. Tommo Says:

    Talk about the future of gaming! I wish I could live long enough to play Mario Galaxy Live Action! In frakken space!

  28. bs Says:

    T-t-t-TIDAL FORCES

  29. wuukiee Says:

    Hi, Henk. It’s nice to meet YOU. This is his wife.

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    La física de Super Mario Galaxy…

    Super Mario Galaxy, según los medios especializados uno de los mejores juegos de plataformas de los últimos tiempos, consisten en ir saltando por planetoides derrotando enemigos y coleccionando monedas y trozos de estrellas, pero ¿podría existir en…

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  34. Will Says:

    First, I’d like to congratulate you on writing such a pleasantly readable article.
    Second, I’d like to point out that “matter,” generally, falls into two exhaustive categories: fermions and bosons. The “loopholes” in the Pauli Exclusion Principle, namely the sort of compression we find in degenerate stars, covers the case of fermions. As for bosons, we shouldn’t dismiss them as irrelevant (after all, some very common particles, like photons, are presumably present in SMG and are in fact bosons), but nor should we worry about compressing them. Bosons actually tend to compress themselves in most circumstances. They still might produce pressure (photons, for example, have momentum and thus push on anything that reflects them), and a great deal of heat, but these are problems that your hypothetically perfect future engineers can easily conquer.
    Third, vis-a-vis your miniature black holes, I think you should consider the phenomenon of Hawking radiation, discovered by Stephen Hawking in the early 70s. He deduced that black holes actually radiate (I know it sounds weird, but don’t worry–the radiation isn’t really coming from inside the event horizon, though that is its net effect). A black hole loses its mass (and entropy 😉 ) to radiation at first slowly and then, if the black hole shrinks down small enough, explosively. This is because the rate of radiation is inversely proportional to the fourth power of the black hole’s mass. This means that if the black hole radiates away half its mass, it will continue to radiate more, and sixteen times as rapidly! A black hole of the size you describe would effectively be a continually exploding nuclear bomb. Although, in a world of hypothetically perfect future engineers, the “shell” surrounding the black hole could be designed to withstand the unprecedented heat and pressure associated with containing a primordial black hole, the thing inside the shell would be less a “black hole” and more a soup of radiation with (possibly–I haven’t done the calculation) a tiny black hole at the center whose rate of radiation equals the rate at which radiation from this “soup” pours into it. At this point, Newtonian calculations (which actually attribute no gravitational effect to photons) are presumably insignificant, and I don’t know what GR says will happen to the field outside the shell. By symmetry, though, this field is still uniform, and so the total quantity of what is inside your shell can be adjusted to find the desired strength. My point is simply not to trust your non-relativistic calculation of the mass of this black hole, because any black hole of that size will soon turn into a super-relativistic soup of high-density radiation.
    Fourth, the effects of tidal gravity (i.e., a sort of noodle-fying force that arises from the non-uniform gravitational field near a massive body: it crushes horizontal points together and stretches vertical points apart) are here insignificant. Note, for instance, that the difference in acceleration between one’s head and feet (a tidal effect) is only 1 m/s/s.

  35. clouette Says:

    Hey,

    From a gamer perspective I see a unreal phenomenal: that is, Mario jump the same height no matter which planetoids he is on. So, SMG Universe is simplified for gamers’ sake. Things are only possible if you simulate the Physics in it on a computer, which is what exactly the developer has done, in a game.

    PS:It’ll be fun if we humans can really jump on and off planets like Mario. But, we are not him, unless Nintendo manage to map our actions one-to-one to Mario’s in the future.

  36. mcc Says:

    Will, about Hawking radiation / black hole evaporation, I haven’t worked out the specifics, but consider this from the Wikipedia article on Hawking radiation:

    For a black hole of one solar mass (about 2 × 10^30 kg), we get an evaporation time of 10^67 years—much longer than the current age of the universe. But for a black hole of 10^11 kg, the evaporation time is about 3 billion years.

    The more mass the black hole has, the longer it will take to evaporate. The black hole considered in the article is on the order of 10^14 kg, so it will take well over 3 billion years to evaporate. I don’t think this is an issue in this case.

  37. TorusWorld Says:

    Triscut, assuming you finished all the problems of stabilizing the worlds and giving them the correct gravity making them stay in place is a simple problem since at that point you could apply trigonometry and newton’s laws of gravity to find points where the worlds wouldn’t move at all. These points, where all gravity acting at the point cancels out would be the best place to put the world, and if they didn’t exist they could be created using the blue tractor beams or other gravity fields to create extra forces to cancel out the existing ones.

  38. DLeh Says:

    I was thinking about something like this when i was playing earlier today- Some of the planets are nothing but crusts and have “black holes” in the center. I was wondering, if we could build a structure that would be completely linked together (as though a solid mass) that could circle the globe, that structure would be able to “float” there, because gravity would be pulling equally in every direction on it. This would be assuming that the structure was of even density, and strong enough to resist the force of gravity pushing on all the joints constantly, of course. However, even if this structure wasn’t completely even, it would still remain. This could, in theory, provide fairly useful for docking things like space shuttles or something. Also, you could even put satellite dishes on them! You could even design this structure to rotate independant of earth, but i suppose it’d be more practical to maintain the same rotation. Anybody wanna donate billions of tons of steel for the creation of such a structure?

  39. Stumbler Says:

    Wicked article. On the space breathing, or even simply avoiding explosive decompression, I think they fluff that away with the Luma thing that either lives under his hat or joins with him for the duration of the game.

  40. Solver Says:

    I just solved the non-colliding multi-planet problem: just add careful amounts of dark matter that repels everything enough to compensate for the gravity components of the planets. Easy as 3.14.

  41. Anthony Says:

    Wouldn’t it be easier to take an existing place with little spheres and other weird shapes and use that, such as a meteor belt, it may not be a Galaxy but in a sense a lot more realistic having multiple objects,and in a Mario Galaxy kind of way, have places to “jump” to with short distances? And you wouldn’t have to create these because they already exist.

  42. Str187 Says:

    so cool ^^

  43. BaroqueW Says:

    Cool article!
    It’s nice that there are people out there answering for me the questions that popped up in my head while playing this great game!

  44. Mikedasnipe Says:

    This galaxy would be less costly if you increased marios weight by a bit (a million times?). But heres a question – how do you stop the planets from gravitating into eachother? And what about gravity arrows? Pull stars? Planets that you can fall off?

  45. Omnius Says:

    The short answer is, String Theory makes it entirely possible. Gravity, in higher dimensional physics, is a result of geometric patterns in these higher dimensions. Thus, gravity can be a result of curvature in space/time (ever wonder why gravity distorts space and time? This is why.) and the gravity fields and fields around the planetoids are indeed possible from an engineering stand-point, assuming you were coming from an arbitrarily advanced civilization.

    These gravity fields are theoretically highly shapable enough that everything up to pull stars can be accomplished.

    Hope that helps.

  46. voice of reason Says:

    you are perhaps the biggest loser i have ever met. just play the GODDAMN game.

  47. Fun Link Friday » Games News and Reviews » Binary Joy Says:

    […] Are the planet of Mario Galaxy possible? One enterprising soul has decided it’s a worthwhile area to research so has set about finding out. […]

  48. MikedaSnipe Says:

    hmm… it appears you can shape gravity for all the pull stars, make star cannons, direct gravitational fields (a mass shifting mechanism i suppose would do the trick). Even during levels when you are inside the world (there are many instances like that) i suppose you could shift mass inside a planet. Even during the “flame” planet during the freezeflame galaxy, when you are inside a planet sliced in two, you could simply shift mass and shape gravity. So many of the tricks i suppose are possible, although would take quite some time to accomplish. The dark matter presents a good oppertunity as well. But heres what we will need

    – Mario weighed down by halleys comet, if you increase his weight by a million, planets can achieve the size we need.
    – Even more comets to make planets out of
    – Miniture black hole creators (hey, we would just have to trick out the large hadron collider)
    – A mass shifting system in order to allow gravity switching, and inside the planet gravity effects
    – Cold fusion to allow you enough energy to shift these planets
    – Gravity shaping to allow pull stars
    – Powerful cannons for launch stars
    – Something enabling us to breathe in space (i would hide compressed air in marios mustache, if i had a choice)
    – continual black hole maintenance to prevent a collapse
    – Dark matter to keep planets from smashing into eachother
    Holy crap man… personally i think you should omit the black holes. Gravity can suck you to the center of a hollow planet anyways. This seems like quite a feat for just an entertaining gimmick universe =/.

  49. Cheeseball701 Says:

    @ clouette: This isn’t so much a problem as bigger planets could be less dense, and smaller planets could be more dense such that they all have the same amount of matter and Mario falls with the same acceleration due to gravity.

    A couple of other problems I noticed:
    -There was one planet in the game (I think in the garden zone) that if you jumped the right way, you could jump all the way around the planet. I figured that Mario should have gone into orbit, but instead the game counted it as losing a life.
    -In one of the airship levels, mario jumps on a platform that seems to move by a propellor (which should work by pushing on air). Then again, how do the airships work?

  50. Kate Says:

    Wow! and I thought that I was the only one who took these things to seriously. Kidding- I think its great when people take something accessable and turn it into something that the readers might actually learn from. I have to admit I had never considered the physics of the game, but while you’re at it, take a stab at some of the other Marios, say Paper Mario and see what you can come up with for that.

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