How much gravity would a Minecraft world have?

[Souper]

All i see here is Hilton come true.

[TheShadow1138]

To actually answer the question we would need more information. Either we need to define the average density of any given Minecraft world, which would require knowledge of the mass of a given Minecraft world, or we could define the volume of "air" blocks and say the ground blocks are all made of say granite. Right now with the information you've provided it is difficult to answer the question exactly (or as exactly as one could).

I did two calculations to determine surface gravity. First I simplified the task by finding the sphere of equivalent volume (assuming the given volume is in cubic meters). This provides us with:

radius = ((2.62144e+17 m^3 * (0.75))/PI)^(1/3) = 3.97e+5 meters (This makes the spherical Minecraft world about 16 time smaller than Earth)

I then calculated surface gravity for the case where the volume has a uniform density of 2.7 g/cm^3 (within the range of the density of granite), and 5.513 g/cm^3 (the average density of Earth). These calculations give the following:

1.) Mass_mw = 2.7 g/cm^3 * (1000000 cm^3/m^3)*2.62144e+17 m^3 = 7.08e+23 g = 7.08e+20 kg

g_mw = (6.67e-11 * 7.08e+20)/(3.97e+5)^2 = 0.30 m/s^2

2.) Mass_mw = 5.514 g/cm^3 * (1000000 cm^3/m^3)*2.62144e+17 m^3 = 1.44e+24 g = 1.44e+21 kg

g_mw = (6.67e-11 * 1.44e+21)/(3.97e+5)^2 = 0.61 m/s^2

So, for a uniform density of 2.7 g/cm^3 we end up with a surface gravity of 0.30 m/s^2 (about 33 times less than Earth's surface gravity), and when we use Earth's average density we get a surface gravity of about 0.61 m/s^2 (about 16 times less than the surface gravity of Earth, which we would expect if our "Minecraft planet" is of the same density and about 16 times smaller than Earth.)

[cantab]

The surface gravity of an infinite plane is well-defined, though looking it up I just find a load of maths with no clear formula. One property is that it's constant with altitude. Considering the thinness of Minecraft's world, it would probably be very low.

On the other hand we know perfectly well that a Minecraft world does have a gravity of 9.8 m/s². The conclusion seems simple: bedrock has an extremely high density. That would also explain why you can't mine it in survival. Indeed, perhaps minecraft's bedrock is a cousin of the similarly impossible dense and equally indestructible stuff the celestials in KSP are made of.

[TechnicalK3rbal]

You guys forgot the nether and the end

[Armchair Rocket Scientist]

Well, the gravitational force between two point masses Fg= G*M*m/R^2. Divide that by the mass of the smaller object (say, a Minecraft character) to get the gravitational acceleration, and we get g=GM/R^2. Translating that into vector form, the gravitational field is g®= -G*M/|R^3| * R. (bold refers to vectors).

This field is a vector with a vertical component and two horizontal components. Since the plane is infinite, the horizontal components end up cancelling each other out. Let's solve for the y component of g (the y axis is vertical in the image you posted). We'll assume the point where we're solving for the gravitational acceleration is a height h above the object and a horizontal distance r away from it. Therefore, R = sqrt(h^2+r^2), and Ry (the y component of R) is equal to h.

So, we get gy = -G*M*h / (h^2+r^2)^(3/2)

Now things get tricky. Each of those point masses we'll assume is a differential element with a volume of dV and a density of p. This calculation will be easier with cylindrical coordinates. We'll let each of our differential elements be between radii dr apart, across an angle dtheta, with a height of dy. Its volume dV will therefore be r*dr*dtheta*dy, and its mass dM will be p*r*dtheta*dy.

At this point, we'll put the surface of the world at y=0, and our object a distance of y1 above it. Our variable "h" is now y1-y where y is the y position of our differential mass.

We plug that into the gravitational field expression to get:

dgy = -G*dM*(y1-y)/((y1-y)^2+r^2)^(3/2)

dgy = -G*p*(y1-y)*r/((y1-y)^2+r^2)^(3/2) * dr * dtheta * dy. (don't you just love typing calculus?)

To make our calculations a little easier, we'll assume y1=0, i.e. we're just solving for the surface gravity. Now:

dgy = G*p*y*r/(y^2+r^2)^(3/2)*dr*dy*dtheta. (the negative ys cancel out).

To make things easier, we'll use cylindrical coordinates, and model the Minecraft world as an infinite plane with a thickness of 256 m.

We're going to integrate this from theta=0 to theta=2pi, from y=0 to y=-256, and from r=0 to r= infinity. This will not be easy to type, but basically we get an answer of

gy = -2pi*G*p*256m^3.

As it turns out, depending on the density of the material, this is probably between 10^-5 and 10^-4 gs - basically zero. With a density of 5000 kg/m^3, to get a gravity of 1 g, the infinite plane would have to be about 4700 km thick.

[Jesrad]

The proper way to measure gravity in Minecraft is, well, to time free-fall from inside Minecraft

Established science gives anything's terminal velocity at 64 m / s. So in order to make air resistance negligible, one has to measure free-falls ending at at least an order of magnitude less than that velocity, which fortunately has already been done

. Throughout similar experiments, the measured gravity turns up to reliably be around 23 m / s^2.

As for density, well consider that a player, assuming it has strength directly comparable to a male human (Steve), can swim up in full armor while transporting 2304 cubic meters of any Minecraft substance. The equivalent load is around 100 N. That gives those 2304 cubic meters an approximate mass of 100 / 23 = 4.35 kg, and an average density of 4.35 / 2304 = 1.887 g / cubic meter, which is barely more than the density of air at sea level on Earth.

Edited September 6, 2014 by Jesrad

[Tex]

You guys forgot the nether and the end

While I may dispute adding the End as part of the Minecraft planet, the Nether IS an important feature. It adds height to the Minecraft world, as it is underneath the bedrock layer at the bottom of the Overworld. The part that would further stump the calculations is that the features of Netherrack are unknown!

Maybe we have to redo the calculations to account for the Nether.

[Javster]

While I may dispute adding the End as part of the Minecraft planet, the Nether IS an important feature. It adds height to the Minecraft world, as it is underneath the bedrock layer at the bottom of the Overworld. The part that would further stump the calculations is that the features of Netherrack are unknown!

Maybe we have to redo the calculations to account for the Nether.

Endlessly burning stuff? Infinite density?

[mr_yogurt]

According to my math (which is awful), if the minecraft world had the same density as our world on average, a minecraft world would weigh 1.447 * 10^21 kilograms.

This is just shy of a 50th of the mass of our moon.

If only minecraft were deeper...

[lajoswinkler]

Have in mind that Minecraft is a huge plate of negligible thickness relative to its surface area. Distribution of gravitational force would be tricky to figure out.

[ZetaX]

Nothing tricky about that. The way to calculate the exact forces (sum over all blocks) has already been mentioned. If you want a faster aproximation, you can handle any all sufficiently far away blocks weighted by their average distribution between all possible blocks (which would be something like 50% air/nothing, 10% water, 30% stone, 7% dirt/sand/gravel, 2% bedrock and 1% other [neglegible] stuff).

[LLlAMnYP]

For all intents and purposes we can consider the minecraft world to be an infinite (in lateral dimensions) slab, as minecraft's world is vastly greater in lateral dimensions than in thickness. Let's say, it's about equal amounts of air and ground (128 blocks up is air, 128 blocks down is ground). In that case all we need is mass per unit of area. By analogy to Gauss' law for a charged plane we can easily calculate the gravitational field for a massive plane:

g=2ÀÃÂ_sqγ, where ÃÂ_sq is mass of slab per unit area, γ is the gravitational constant. That would yield:

On the other hand, mass of slab per unit area is average density of minecraft world * 128 meters of thickness (I mean, of course just the ground, not counting the air), therefore

g=128m*2ÀÃÂγ, where àis the proper density of minecraft ground.

g=2 * 3.14 * 128m * ÃÂγ.

However, we do not know neither the density, nor the gravitational constant of minecraft. Although, as has been stated earlier, we know that the g in minecraft is 23 m/s². Therefore the product ÃÂγ is a mere 0.0286s^-2. On the other hand, in the real world àis of the order of thousands of kg per m³, while γ is 6.67*10^-11m³ kg^-1 s^-2. So a first approximation gives us either stupefying densities or a world in which gravity is quite a strong a force as electrostatic or even nuclear interactions.

Additionally, it is quite clear, that the gravitational force in minecraft does not change much (or, for that matter, noticeably) as you go deeper into the ground. That means, that the mass of dirt and rock above the bedrock is negligible, compared to the bedrock itself and whatever may hypothetically lie beneath it. This returns us to somewhat more realistic densities/gravitational constants. For instance, if we take a density of 4 tons per cubic meter and the real world gravitational constant, we would find the real thickness of the minecraft world (including a hypothetical magma layer beneath the bedrock) to be about 14 thousand km. Funny enough, that's on the same scale as earth's diameter.

Going pack to the first post though... 32 million blocks in length? That's only 32 000 km. Imagine a square 32000 by 32000 km. You could lay out a box of roughly 3x3 earths on this square. So minecraft is 3 earths long, 3 earths wide and 1 earth thick. Y'know, quite consistent with the real world. <wrong>Nothing like the surface area of Neptune</wrong> One 8th the surface area of Neptune.

Edited September 8, 2014 by LLlAMnYP

[LLlAMnYP]

PS, uh yeah, double-checked the numbers. Minecraft is 1 quadrillion blocks (or square meters) in surface, or one billion square km. The numbers in the picture at the start of the thread are wrong (someone threw in too many zeros) That's on the same scale as the surface area of earth (perhaps, twice as much).

PPS, realized, that Neptune isn't that much larger than Earth.

Edited September 8, 2014 by LLlAMnYP
added PPS

[ZetaX]

See http://minecraft.gamepedia.com/The_Overworld : it has a theoretical area of ~ 4·10^15 km², and an actual area of ~ 4·10^9 km² because of physics problems. Both numbers are above the ~ 5·10^8 km² of earth, but the latter only by one factor of 10, getting it indeed closer to Neptune's size than earth's. The former number actually is way above Neptune's surface area and around 1/10 of the sun's surface.

[K^2]

Area is irrelevant. It is effectively a problem of field from infinite plane, as above. Which produces miniscule gravity at any sane density. However, it also calls for zero gravity half way down, and negative above!

I would, therefore, conclude that the source of gravity in MC world is in the Void, if not the Void itself.

[LLlAMnYP]

Negative below, I'm sure you meant.

And, of course, someone stated earlier in the thread, that it could be bedrock, found only on the bottom four layers of the minecraft map, that has a stupendous density (explaining, why it's completely unbreakable) that would handwave away the dubious cause of uniform gravity when burying deep into the ground (also it would allow the rest of the ground to have a sane density).

[Jesrad]

Does not explain why you keep accelerating down at the same rate when you fall below the bedrock layer. Face it: matter in Minecraft has a density close to our air. This 'gravity' you're speaking of is not actually gravity: it's inertia ! Minecraft is really a worldship on a brachistochrone journey

[lajoswinkler]

Told you this is a tricky one. It's a huge, relatively thin plane. Just by itself, its nearby gravity field would be complex.

[LLlAMnYP]

Nothing complex in the gravity field of a plane. Taking things at face value though (extended plane, only 256 blocks thick, nothing more to the world than this) one would expect irregularities in the plane to significantly alter the gravitational field. For example, standing near a mountain, the player should experience a significant pull towards this mountain. This is not observed. Therefore the source of gravity should be predominantly located at or below the bedrock.

Face it: matter in Minecraft has a density close to our air.

Apparently only when said matter is in Steve's inventory. On the other hand, it doesn't matter. If gravity doesn't change when you fall below the bedrock layer into the void, then this hypothetical infinite massive plane that creates the observed uniform gravitational field is located quite far down in the void. Or, as K^2 suggested, the void IS the source of gravity.

[Jesrad]

Apparently only when said matter is in Steve's inventory.

Hmmm, then why do all monsters, blocks, items and Steve have the same observed terminal velocity of 64 m/s ?

Also, why isn't the intensity of the gravitational field even changing by a tiny fraction with altitude ? Why aren't mountains deviating the direction of pull even a eeny-tiny bit, as you pointed out ? Why isn't it changing direction at all if you move 32000 kms in any direction on the plane, away from the coordinates origin ?

=> because it's not gravity, it's inertia from constant ~23m/s² acceleration Any actual gravity from the matter is so vastly overwhelmed by it, it might as well be zero.

Edited September 9, 2014 by Jesrad

[Bacterius]

I find it slightly disturbing how this thread went from "how much gravity would a minecraft world [no reference to the game itself besides the world size and features] have" to "let's find out-of-universe explanations to explain why Minecraft's [the actual game] gravity is implemented as a constant 9.8m/s downwards (or whatever it is) force in a fixed reference frame".

[LLlAMnYP]

I must have misunderstood you then. You meant to say that the minecraft world is experiencing a constant acceleration of 23 m/s^2 upward? Sure, that's a way to explain it.

As for mountains deviating the pull or not, or gravity changing by a tiny fraction - these are, as you pointed out, tiny fractions. I've checked the video that measures the 23m/s^2 gravity and the error bars on its numbers are huge. The tiny fractions you speak of would be undetectable. (Also, what was the guy doing? Measuring game time with a real stopwatch? What about server latency? It's clearly visible on the video itself).

Terminal velocity on the other hand doesn't really tell us much. Matching densities and form-factors within the accuracy of our measurements.

[ZetaX]

It is quite easy to explain an (almost) constant acceleration by just having a massive plane "below" the void (say 1000 km below the bedrock layer).

[Jesrad]

As for mountains deviating the pull or not, or gravity changing by a tiny fraction - these are, as you pointed out, tiny fractions. I've checked the video that measures the 23m/s^2 gravity and the error bars on its numbers are huge.

That's just one video, there are a lot more. Also, in the code itself the acceleration is perfectly constant and vertical anyway, regardless of masses in vicinity or altitude

Terminal velocity on the other hand doesn't really tell us much. Matching densities and form-factors within the accuracy of our measurements.

Well everything in Minecraft is cubic, so the drag coefficient can be expected to be the same 1.28 for everything. But you're right overall.

It is quite easy to explain an (almost) constant acceleration by just having a massive plane "below" the void (say 1000 km below the bedrock layer).

Occam still has merit though.

[ZetaX]

It would probably favor anything like "there just is a constanst force" to everything else given in this thread.