# Probably the NERDIEST thing ever done. Ever.

***Copied from the reddit post, here: http://www.reddit.com/r/teslore/comments/2phm72/on_nirn_lore_edition/***

Greets,

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Below, I have described my process for determining planet Nirn’s size, mass, and other characteristics relating to both of the aforementioned factors.  To begin, I will describe my method for determining Nirn’s circumference.

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By creating a unit of measurement equal to the total width of Skyrim (which has been approximated to ~890.887 km), ***see this map: http://static.giantbomb.com/uploads/original/1/13836/742368-nirnmap.jpg***, I was able to compound that distance across the estimated vastness of Nirn at that latitude (45 degrees), ***see this map: http://th07.deviantart.net/fs70/PRE/f/2014/178/6/1/world_map_of_nirn_by_n_a_i_m_a-d7nx393.jpg***.

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C = 2π * r, where C is the circumference, and r is the radius of the circle.  And C(45) = 890.887 km [est. Skyrim width] / ~8.6 cm [when zoomed in, and measured] = ~103.5915116 km/1 cm (on that map).  And, counting the total amount of centimeters across latitude 45, yields 51.7 cm.  Since this is only half the arc, we multiply by 2 to get 103.4 cm for the scaled down version of Nirn’s circumference at 45 degree latitude.  And therefore, the circumference of Nirn at L=45 is ~10,711.3623 km, since 1 cm = ~103.5915116, and when multiplied by 103.4.  And thusly, r(45) = C/2π = 10,711.3623 km/2π = 1,704.766257 km, or 1,701,472.02 m.  ***This result is the radius from Skyrim at latitude 45 to Nirn’s vertical center, which we will denote as, a***.

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Since maps will always be distorted when planed from a spherical source (special thanks to ladynervar for pointing this out), we must determine the remaining distance of the radius, which can be achieved through trigonometric functions, namely the cosine function.

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Since we know the length of the chord, ***a*** to be 1,704.766257 km, then we can assume that this distance is also equatable to the distance from Nirn’s center, directly below the opposite end of the hypotenuse from the center (aka, Nirn’s radius).  Thus, we can construct a square, which will be divided into a right triangle for the trigonometric analysis.  Since we know both the angle, θ, to equal 45 degrees, and the length of the sides besides the radius, we can determine the radius to be equivalent to the following:

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a / cos (θ) = 2,410.903562 km = h = r, where a is the chord length, θ is our angle 45, and h is the hypotenuse, Nirn’s radius.

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So, with the radius now determined, we can move on to the other calculations, including: the circumference, volume, surface area, estimated mass, and density (gathered from the volume and mass measurements; naturally, this will come last).

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With radius r = 2,410.903562, then Nirn’s circumference = 2π*r = 15,148.15384 km; remember, it is was 10,711.3623 at latitude 45.

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and Volume = V = (4/3) * π * r^3 = 4.189 * 2,410.903562 km^3 = 5.869865163 e+10 km^3.

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And Surface Area = 4 * π * r^2 = 12.57* 2,410.903562 km^2 = 7.304147609 e+7 km^2.

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The in-game gravitational acceleration was calculated from the time it took an object to fall 1 m, which was ~0.46 seconds on average.  Thus, the gravitational acceleration in Skyrim (and to the assumed Nirn properties) follows the gravitational equation, a = 2 * d / t^2.  Where d is the distance traveled in t seconds.  Therefore, we substitute the observed values in for d and t to get a = 2 * 1 m / 0.46 seconds^2 = 9.451795841 m/s^2.  Earth’s gravitational acceleration is 9.807 m/s^2, so Nirn’s is slightly lower.

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***Nirn’s Mass:*** Using the following equation for planet mass, we can determine Nirn’s approximate mass, based on what we now know.  So, M = (a * r)/G.  Where M is Nirn’s mass, a is the gravitational acceleration of Nirn, r is the radius of the globe, and G is the gravitational accelerational constant of 6.674 e-11 N * M^2 / kg^2.  The gravitational accelerational constant is applied to essentially all gravitational interactions at the macroatomic scale, and it is assumed to work the same way in the physics of the game.  Therefore, the mass of Nirn is assumed from the following figures: M = (9.451795841 m/s^2 * 2,410.903562 km)/6.674 e-11 N * M^2 / kg^2 = 8.2333943751336 e+23 kilograms.  The earth is ~6 e+24 kg.

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Using the equation for density, D = M/V, and after converting from kg/km^3 to kg/m^3, the density is as follows: D = 8.2333943751336 e+23 kg / 5.869865163 e+19 m^3 = ~14,026.54771 kg/m^3.  The density of the Earth is ~5,520 kg/m^3.

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***For the TLDRers***

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Circumference of Nirn = 15,148.15384 km

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Radius of Nirn = 2,410.903562 km

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Volume = 5.869865163 e+10 km^3

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Surface Area = 7.304147609 e+7 km^2

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Gravitational Acceleration = 9.451795841 m/s^2

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***The mass of Nirn is 8.2333943751336 e+23 kilograms with a density of 14,026.54771 kg/m^3 , where Earth’s mass is 5.972 e+24 kg and has a density of 5,520 kg/m^3***

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Well, that’s about it I hope you all enjoyed this post!

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Farewell, and slay some stuff! ~bengle

***If any great modders are out there, please see if it’s possible to make something THIS big, using shittier graphics.  I have no idea if this is possible, but it’d be really interesting to see how immense everything would be (land-scape wise) if it were magnified by the upscale…***

I put super glue on my digits and now I can’t use my thumbs scroll or type on a mobile device. It’s 3 in the morning right now.

When I’m bored I play osu! or listen to music.

If the gravity is so weak, why are there dwarves and hobbits? I mean, that explains the elves and giants, but seriously.

-EDIT-

Lol. I was thinking of something else.

I’ve never played Elder Scrolls but a circumference of 61 km seems very small for a planet.

It is very small. But somehow the planet would have a density of about 1,024 g/cm^3…which is kinda hilarious considering both how insanely high that is AND the fact its…well…1024 exactly…

Nice. That’s one tiny planet.

More of a moon, no? Or an asteroid?

I can’t remember the exact definition of a planet, but I remember some discussion over Pluto being one or not, a couple of years ago.

If the gravity is so weak, why are there dwarves and hobbits? I mean, that explains the elves and giants, but seriously.

-EDIT-

Lol. I was thinking of something else.

In W40k universe, there was sub-race of humans called “squats” that was half as heigth of normal humans(so, some sort of dwarves) because of living on planet with huge gravity. They were devoured entirely by Tyranids though.

Wait. Your calculations are based only on whole tamriel, or akavir too?

![planet_nirn _geographical v2__by_hori8](http://th03.deviantart.net/fs70/PRE/f/2013/220/a/2/planet_nirn___geographical v2 by_hori873-d6h7sh0.png)

HA, that is not nearly the nerdiest thing ever. Right a program in python that calculates that. Then you have done the nerdiest thing ever.

Pshh python, write it in fortran

More of a moon, no? Or an asteroid?

I can’t remember the exact definition of a planet, but I remember some discussion over Pluto being one or not, a couple of years ago.

Pluto’s not a planet because it crosses the orbit of another (larger) planet. If you allow planets to cross orbits, then you’ll have to accept living in a solar system with like a bajillion planets. Ain’t nobody want to memorize those.

First, to correct some things:

The density is actually 395 g/cc.  I had a major typo haha.

And secondly, the map I used for Nirn is here, and includes all “known” landmasses on the planet.  I’m sure you guys can guess how I figured out the scaling Thirdly,

Where Nirn is about 19.671 km

So Pluto is well over 200,000 times larger than Nirn by volume.

However,

Nirn’s mass is calculated to be about 1.26e+19 kg

Pluto’s mass is about 1.31e+22 kg

Which means that

Pluto is also over 1,000 times as massive.

So all in all, the math lines up, but god damnit, Nirn should not exist based on my findings xD

Pluto’s not a planet because it crosses the orbit of another (larger) planet. If you allow planets to cross orbits, then you’ll have to accept living in a solar system with like a bajillion planets. Ain’t nobody want to memorize those.

While Pluto indeed crosses neptuns orbit in a 2d view, it became a dwarf planet, because it has not cleared it’s orbit - there are several other plutoids around pluto, so it’s not alone. Besides, Eris is bigger than Pluto.

If Nirn fulfills all this

* orbiting a sun (strictly speaking “the” sun, because planet only refers to our solar system atm. but lets not be so… small minded) , not being a satelite / moon

* is round, meaning it has enough gravity

* cleared its orbit from other orbiting stuff (which Pluto hasn’t) (so trapped all the moons…)

it is indeed a planet, no matter it’s actual size. Maybe Nirn has a superdense core, and while being quite small, has still earth like gravity, or similar. After all, there are Dragons flying there, which could lead to the conclusion, that gravity is slightly off What is the sudden increase in Python interest? Nerds evolving to geeks here? Fortran sux.

btw. maybe that map does not show a big ocean - much like many of our maps

also this map is a bit confusing, Pyadonca, Northern Lyg and Aldmeris being closer to the equator of the planet would mean, they are actually much bigger in reality; much like Africa seems a lot smaller, and Europe a lot bigger on a flat map You clearly need to reach orbit and make your own map.

Next thing: 3d planet simulation in unity

Everyone.  Behold!  G4borg is a ******* genius.  Follow this link to my original reddit post, which has been updated to include a special present from g4borg.  If you’re interested in seeing all of this, check out the link!

haha it’s really not that “exciting”, just a gimmick but i also wanted to be nerdy.

anyway, that’s like 1 hour work in unity3d, maybe i should make a tutorial. maybe i also am a bit lazy.

lets see if i expand it one day, once you have finished your math (i always wanted to simulate a star system… and the rotating function could need some love, maybe then i also change it to represent your data)

anyway, atm. that simulation has little to do with your data, it basicly only maps the map you provided on a sphere, in a star skybox, and rotates it a bit it is certainly nice to see the picture on a sphere tho, to get a better idea of the planet.

Updated the OP to contain the most recent version of data; as you can see the radius (and everything related to the radius) increased dramatically.  Just look at the volume.  It’s now ~78,800 km^3 where it WAS projected at about 12,000 km^3.  There’s a major reason for the modification, but it’s complicated and I’m too lazy to explain xD

Anyways, enjoy Greets,

I have done a bit of rough calculations to determine the mass and size of Nirn, the planet in The Elder Scrolls universe, also known as the TES universe.

Now, I assumed one major thing:

1. ***Assumed Nirn is one solid material***, no core, etc…there is nothing else to do since we can never know what the core is like, and this is as close as we can get.  However, I got a remarkably accurate gravitational force, compared to the one that exists in game.  After all, it doesn’t really matter, since the creation story of Nirn is that it’s the bones of the fallen et’Ada, which could be some…god particle or something 1.  I know enough of Nirn’s backstory to know that very little of this lines up with Sotha Sil’s Clockwork City existing underneath the surface of Nirn.  ***However, my calculations are based off of the gravitational acceleration and the projected scale of Nirn, seen in this map: http://th07.deviantart.net/fs70/PRE/f/2014/178/6/1/world_map_of_nirn_by_n_a_i_m_a-d7nx393.jpg AND this post: http://www.reddit.com/r/skyrim/comments/1knk0j/

It seems to be the most accurate map of Nirn, but what confuses me is Akavir.  The artist rendered the continent to be about half of what I’ve seen elsewhere, but everything else is so precise that I assumed the artist found information to back this up.  Likewise, my calculations would change somewhat dramatically—notably the radius of the planet, which would ultimately affect everything all the way up to the density of the planet, which would actually decrease if Akavir is larger than the artist’s projections.

***Now, since my calculations work based off of the gravitational acceleration in-game, then what is being suggested is that the mass of the Bones of the Earth (otherwise said to be Sil’s clockwork) are simply very very high compared to what we as humans have come to understand about OUR world.  Sil’s clockwork MAY be very very dense material, and this is why Nirn has such high gravity to begin with, even though it’s such a small planet (it’s over 80,000 times smaller than Pluto!!!)***

Anyways, here goes ______________________________________

After all of the calculations were ran, I found:

1.  The in-game gravitational force is calculated to be about 2.17391304 m/s^2.

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1.  Given the following dimensions of Nirn, the gravitational force would equal 2.17391304  m/s^2!!! Yay math!

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1.  Nirn is a globe with a radius of about 26,600.788 meters. The circumference is about 83,568.84 m.

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1.  The volume is about 78,844.63 km^3

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1.  The mass of Nirn is approximately 23,053,458,021,408,000,000 kilograms, or 2.3053458021408 E+19 kilogram

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1.  Nirn is an insanely dense object with a density of around 292.39097223753 g/cc.  To get an idea of how much this is, the densest material known to man is Osmium, with a density of about 22.562±0.009 g/cc.  However, neutron stars can have masses between 1.5-5x the mass of the sun in a radius of about 20 kilometers before collapsing under their own gravity.  So I don’t think we’ll have any issues with space and time __________________________________

So, as you can all see, the math lines up.  I made some very blatant assumptions, but who can blame me?  I think the fact that I got Nirn’s mass to be so precise is pretty remarkable (to get an idea, if the mass were simply E18 rather than E19, the radius would have to be ~8,410 m instead of ~26,600m).

Who knows, maybe the game designers ACTUALLY thought all this stuff up…but who knows, this could ALL be by chance.

Hope you enjoyed __________

***Author’s note***

I am trying to make a mod that accurately calculates the trajectories of the moons, based on their apparent paths through the sky in Skyrim.  Obviously, this task seems to be impossible, since doing this would require the developers to have put the necessary information in the game.  However, I think it can be done (to some degree of error, though) and would encourage anyone to help me with both the mathematics and the application.

If you want to help, message me, and check out this link:

http://en.wikipedia.org/wiki/Kepler’s_laws_of_planetary_motion

All the best,

bengle  You have no idea…

Plus, the OP has been updated as of about 10 minutes ago, and is now MUCH more accurate, according to math and stuffs,.

Please check it out and tell me what you think!