What is Minecraft's gravitational constant value ?
This post is a follow up to this one, in which we found out Minecraft's acceleration due to gravity value :
When I say gravitational constant, I imply the one regarding players because it depends on the acceleration due to gravity which itself depends on entities in Minecraft (otherwise it's mostly inconsistant).
I'm not gonna lie this topic is way harder than its prequel, and I DID NOT see anything on the internet (not to say there isn't anything) talking about it (so if you wanna argue on smth pls source what your saying).. actually nobody really searched for Minecraft's gravitational constant value.
So here we are looking into that.
First of all, one thing to know is that a Minecraft world spreads over 30 million blocks in each direction of the orthonormal basis (here I'm referring to absolute distances) in 2 dimensions (in every direction except in altitude) :
From this we can calculate the area from a square-like perspective :
Now most people assume Minecraft´s earth to be a cubic planet but this would mean that a player falling from a certain height get a different falling time depending on the place you are (on corners especially).
After testing it out, I ended up noticing a player's falling time is approximately the same regardless of the place you fall from (from a given height) which only means one thing, Minecraft earth is a spherical planet (might sound very odd to you but it is indeed logical).
Besides, using the area we calculated and the sphere area formula, we can solve for the radius :
Since we have got both Minecraft earth's radius & Minecraft's acceleration due to gravity value, we can (re)try to use Newton's law of attraction :
Then after simplifying and solving for the gravitational constant with Newton's second law of motion, we still gotta figure out Minecraft's planet's density (as we can determine the volume, it's better to search for density rather than mass).
Unfortunately, substituting formulas in equations, making linear systems, the gravitational constant as well as the density always checked out :(
Even after introducing more formulas (like the kappa formula or the escape velocity formula) it couldn't be any more relevant :/
There seems to be something wrong but long after hours upon hours of researches (and dozen liters of sweat that could fulfill a whole swimming pool lol) I realised we could proceed by identification going back to this formula :
A product of 2 unknowns equals a constant (as g and the radius are known).. interesting...
Guess what, in order to proceed by identification, let's dispatch known parameters and constants as well :
Let's now see the numerical approximations of each physical quantities using real-world values beforehand :
Okay so what's important is to look at the scale order of the inverse of the radius, it's a 10^-7 order and it's pretty close to the actual universe's gravitational constant standing with a 10^-11 scale order.
So let us add a 10^3/10^3 in the following way :
We get to see that 1/(radius*10^3) has got (practically) a scale order of 10^-11.. we're steadily stepping towards the answer guys : )
I also want to point out g*10^3 and density p (rho) scale orders are even.
Which in fact means :
where :
If we break down π into sqrt(π) * sqrt(π) in this manner we get :
with :
Consequently, applying numerical values related to our real-life solar system & earth results in values infinitesimally nearing the actual approxs (it's demonstrated through relative gap calculations being less than 1 %) ;)
hence :
respective relative gaps :
Furthermore, since we study Minecraft's earth planet, we can use the previous final formulas to calculate approximations of both Minecraft's planet related gravitational constant value and density value (as Minecraft suggests a similar solar system to ours in which its earth belongs in) :
Okay we got what we wanted, but let me suggest you a quick understanding to check the coherence of our results.
Take a close a look at that formula identified from Newton's law of attraction, we know G (gravitational constant) tends to zero (its value is so small it´s almost zero: about 6.67*10^-11 m^3 • s^-2 • kg^-1) and the radius being a large number.In order to get a final value greater than 1, earth's mass have got to be really large & so the density.
In the case of Minecraft, as the radius is larger and we know the overall division value is approximately 3.23 greater than the real-life one which makes it obvious Minecraft earth's mass, density & volume are greater for sure.
So that's pretty much what we had to do to get an approx of Minecraft planet's related gravitational constant.
Sidenote: It's just a hypothesis, I wanted to make something plausible, cuz assuming our earth's properties to make calculations haven't really satisfied me and isn't correct to apply in a video game (plus people making these assumptions usually don't explain why they use them for a given case).
Also, I'm aware the units aren't possibly correct but all you need is a reference value which wouldn't change the results (1.0 {insert appropriate unit} ) with units making up for the wrong ones.
Edit: For sussy bakas, I solved the whole thing symbolically at first and only (purposefully) numerically displayed intermediate results to picture a significant value but didn't till the final results offline :p
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Have you ever wondered what's the mass of our friendly Steve ?
Well what I could tell you is that he for sure weighs more than some random apples but how heavy is he actually because as we discussed Steve's height in a previous post, let's now figure out his mass.
(yeah I said mass not weight because weight is in this case the force of attraction exercised between Steve at Earth's surface level and Earth's core level which is different)
The topic has already been thought out in the article thereafter:
However I strongly disagree with it assuming blocks' voxels' (3D pixels in Minecraft) dimensions are equivalent to Steve's voxels' ones when stating that Steve weighs 342 kg (754 lbs).It's just not necessarily true, in fact a mob's voxels' dimensions are subjective.
First off, we know Steve is 1.875 m (6'2") tall and measures 32 of his voxels in height that we'll shorten as svx (Steve voxel(s)) as of now for the sake of simplification.
With this out of the way, we have to find Steve's total body volume, to proceed we can notice Steve's character model could be viewed as 2 rectangular parallelepipeds & 1 cube attached all together :p .
This means means that we'd have to sum every 3 volumes to find out Steve's total body volume.
To proceed we can display some 3D axes non orthonormed for each volume to get a clear sight of what we're trying to measure as such:
Now as you might think, it's indeed a bit tough to clearly count voxels so let's make the task easier by counting voxels on a modified Steve skin:
Here are the results:
Thus Steve's total body volume corresponds to :
Now keep in mind that a svx equates :
which is about :
Finally we can translate Steve's total volume in cubic meters :
Furthermore, since Steve is a very athletic character (he jumps all the time, run all the time, looks healthy & is most certainly not average at all) we'll assume his body fat percentage to be approximately 10%.
After asking a few stupid questions to ChatGPT AI we're gonna assume Steve's body density is similar to an average low body fat, athletic (and ripped ofc x] ) male body density whose value is 1120 g/m^3.
As a result, manoeuvering the density formula gives a way to calculate Steve's mass :
Basically this guy is huge in every direction lol, his BMI is tremendously over 30 BUT we cannot necessarily say that he is morbidly obese because he does not look like it and if we were to make any judgement, those must be based off of Minecraft's world properties not of our world's...
Sidenote: Don't try to sue me for not getting the significant figures right, I purposefully let more decimal places to show how results really go.
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