Achaea (the planet), SCIENCE!, and you!!

Kenway

So it's been mentioned in a few threads at this point but I've been doing a shitload of math to learn more about how the planet of Achaea works!

HAVE SOME NUMBERS!!

Achaea is approximately 10,688 metrons in circumference! 1 metron = 1 wilderness room! There are ~2672 wilderness rooms between the north pole and the equator (approximated with the official painting of Sarapis in which he holds the planet in his hands(we'll be coming back to this a lot)), multiplied by four gives us 10688 to fully circle the globe! From there we can get radius and from -there- we can get area!

C = 10688 metrons

r = 1701.048 metrons

A = 9090400.681 metrons^2

Now while metrons are all well and good, they don't actually tell us much on a scale that you or I can picture! UNACCEPTABLE! SO, using the -only- relatively standardized unit of measurement I could find in the game that correlates to the real world we can get all this in REAL NUMBERS YEEESSSS!!! What is that standardized unit you ask? SHIPS! Yes, ships. Specifically, war galleys. Historically, galleys averaged at around 40meters long while man of wars averaged 60meters! So how do we apply these numbers in a useful way? Well, only one ship can fit in each wilderness space so they're all at -least- 60 meters by 60 meters. However because I doubt that ships are gonna be passing each other hulls scraping together (moreso because I have a burning desire for the planet to make any sort of physical sense) we're gonna call one metron 100 meters. Big enough that one ship fits very comfortably but still not two! So now, we're workin' with:

C = 1068800m | 664mi | 1068k

r = 170104.8m | 105.7mi | 170k

A = 909040068.1m^2 | 564851.3mi^2 | 909040.07k^2

v = 2.06 quintillion meters^3

Soooo I decided I needed to know the mass of the planet as well because, y'know, I play an all text fantasy mmo which requires self taught programming to play effectively so why not just lean into this whole nerd thing right?

So the volume of the Earth is around 1 quadrillion meters. Earth's mass is approximately 5.9722 septillion kg. So doin' some math we come out to an average mass/meter of: 5,972,200,000kg/m using this number we find that Achaea's mass is likely around... well...
1.2302732e+28kg

On to the rings, and coming back to the image of Sarapis, using an infallible scientific method (counting the pixels from pole to equator and then mathing them against the pixels of the rings) I came out to 2048.5metrons wide (127.3mi, 204.85k) and orbits at 311.7metrons (19.4mi, 31.17k)

More on the rings will be coming soon (I wanna make diagrams but I'm tired tonight so it'll come tomorrow) but some interesting facts about the rings are:
On the equinox, the southern hemisphere of Achaea will experience a 24hr night.
Every night at midnight Achaea's shadow will be cast over the rings creating a weird pure black most-of-a-circle lookin' hole in the rings. (this only occurs at certain latitudes, so far from my approximation I'd say Tears to southern Meropis.
The sun reflecting off of the rings would make the moon a lot brighter than Earth's moon.
Night in general would be pretty damn bright with the rings and moon combined.

MORE SCIENCE SOON!!

Oh yeah also I'm looking into atmosphere and gravity and calculated the size of dragons to be ~26ft long and ~310kg so for those of you bothered by the weirdly ambiguous descriptions of dragons, there you go! (Eyes described as saucer-sized saucers are 5-5.5in in diameter, official dragon art has 30 pixel long eye sockets and selecting the whole dragon ended up with some number that when divided by 30 came out to 26ft. Avg mass of a human is 62kg at 5.4ft etc etc I'm tired gnight yall) 

 

Sarathai

Kenway said:

Oh yeah also I'm looking into atmosphere and gravity and calculated the size of dragons to be ~26ft long and ~310kg so for those of you bothered by the weirdly ambiguous descriptions of dragons, there you go! (Eyes described as saucer-sized saucers are 5-5.5in in diameter, official dragon art has 30 pixel long eye sockets and selecting the whole dragon ended up with some number that when divided by 30 came out to 26ft. Avg mass of a human is 62kg at 5.4ft etc etc I'm tired gnight yall) 

I usually went off those old size charts with dragons. A human was 10 and a dragon was 20, making them about 2x human height on average.

Mathilda

GLORY TO THE NIGHT
PRAISE BE TO TWILIGHT
FOR SCIENCE!!

This is super cool stuff.  r

Kenway

Sarathai said:

Kenway said:

Oh yeah also I'm looking into atmosphere and gravity and calculated the size of dragons to be ~26ft long and ~310kg so for those of you bothered by the weirdly ambiguous descriptions of dragons, there you go! (Eyes described as saucer-sized saucers are 5-5.5in in diameter, official dragon art has 30 pixel long eye sockets and selecting the whole dragon ended up with some number that when divided by 30 came out to 26ft. Avg mass of a human is 62kg at 5.4ft etc etc I'm tired gnight yall) 

I usually went off those old size charts with dragons. A human was 10 and a dragon was 20, making them about 2x human height on average.

If you can find these send them to me? Would actually help

Sarathai

Kenway said:

Sarathai said:

Kenway said:

Oh yeah also I'm looking into atmosphere and gravity and calculated the size of dragons to be ~26ft long and ~310kg so for those of you bothered by the weirdly ambiguous descriptions of dragons, there you go! (Eyes described as saucer-sized saucers are 5-5.5in in diameter, official dragon art has 30 pixel long eye sockets and selecting the whole dragon ended up with some number that when divided by 30 came out to 26ft. Avg mass of a human is 62kg at 5.4ft etc etc I'm tired gnight yall) 

I usually went off those old size charts with dragons. A human was 10 and a dragon was 20, making them about 2x human height on average.

If you can find these send them to me? Would actually help

Can't find the original (it was on the old Achaea website, but I can't find the archived version right now). Here is a forum thread about it, though.

Vallie

Ooh can you do force of gravity on an average human? Curious how intense or not it is, maybe we can all just fly if we try really hard (or else our bones are made of steel from being crushed all the time)
 
F = (GMm)/r^2

where G = 6.673 x 10^-11, M is mass of planet, m is mass of person, r is radius of planet. I tried to do it on calculator but my brain is fried from work and I kept pushing the wrong things for like 10 minutes.

Iniar

So now, we're workin' with:

C = 1068800m | 664mi | 1068k

r = 170104.8m | 105.7mi | 170k

A = 909040068.1m^2 | 564851.3mi^2 | 909040.07k^2

v = 2.06 quintillion meters^3

Soooo I decided I needed to know the mass of the planet as well because, y'know, I play an all text fantasy mmo which requires self taught programming to play effectively so why not just lean into this whole nerd thing right?

So the volume of the Earth is around 1 quadrillion meters.

Volume of Earth: 1 trillion cubic kilometres
Volume of Achaea: 2 quintillion cubic metres

Math check;

Assumption: spherical Achaea
V = 4/3.pi.r^3
Achaea.r = 170 km
Earth.r = 6371 km

Achaea.V / Earth.V = Achaea.r^3 / Earth.r^3 = (Achaea.r / Earth.r) ^3 = 170/6371 ^3 = 1.9 * 10^-5

Achaea is about 10,000 50,000 times smaller than Earth?

You can fit 50,000 Achaeas into Earth. Neat.

Next question: how much land will each player have?

Nazihk

You have an error there. 

• The mass of earth is roughly 5.972e24 kg and the radius is 6,371,000m. 
• Volume of a sphere is 4/3 *  pi * r^3 so Earth's volume is: (4/3)*pi*6371000^3 = 1.08e21 m^3
• Density is mass/volume, so the density of Earth is:  5.972e24 /1.08e21 = 5529 kg/m^3.  
• So if we use your 170,000m radius, we get a sphere with a volume of 2.057e16 m^3.
• If p=m/v then pv=m, so we get an Achaean mass of 1.137e16.

The numbers you were using had Achaea being something like four orders of magnitude more massive than Earth while being 340 times smaller than Pluto, with a density of roughly 5 billion kg per cubic meter.

To answer Vallie's question about gravity.
g = GM/r^2

Achaea's gravity = (6.673e-11*1.137e16)/170000^2 = 0.000026 m/s^2
Earth's gravity    =(6.673e-11*5.972e24)/6371000^2 = 9.81 m/s^2. 

So Achaea is pretty much a zero g world. 

On the other hand, if you use Kenway's numbers, you get (6.673e-11*1.2302732e+28)/170000^2 = 28,000,000 m/s^2.

To put that into comparison, the Sun has a mass of 1.989e30 kg and a radius of 695,000,000 m. (6.673e-11*1.989e30)/695700000^2 = 274.22

Vallie said:

I tried to do it on calculator

Wolfram Alpha is your friend as far as things like this go.

Iniar

We really can't have a zero-g world where dragons are only 26ft long.

Reverse engineering:
  Assuming Achaea.g = x * Earth.g, assuming Achaea.density = y * Earth.d
  g = GM/r^2
  x * Earth.g = G * Achaea.m / Achaea.r^2
  x * Earth.g = G * Achaea.d * Achaea.v / Achaea.r^2
  x * Earth.g = G * y * Earth.d * 4/3 * pi * Achaea.r
  solving for Achaea.r

  Achaea.r = 21 * x * Earth.g / 88 * G * y * Earth.d

  Assuming Achaea.g = 0.85 * Earth.g
  Assuming Achaea.d = 1.15 * Earth.d

  Achaea.r = 175.1 / 559535 * 6.673e-11 = 4,690 km
  1701 metrons = 4,690 km
  1 metron = 2.8 km

  Assuming Achaea.g = 0.5 * Earth.g
  Assuming Achaea.d = 3 * Earth.d

  Achaea.r = 103 / 1459656 * 6.673e-11 = 1,057 km
  1 metron = 620 m

Iniar

That's wrong.

g = GM/r^2

solve for G.

Vesios

Math makes my brain hurt.

ninja edit: this is so totally awesome tho I'm super impressed

Iniar

Expressing Achaea's universe's Gravitational constant as a function of assumptions about measured gravitational pull and expected planetary density relative to Earth is probably about as close as we can get.

What happens when @Makarios adds rooms to your radius then, huh?

Trey

Cocaine is a hell of a drug.

Vallie

Nazihk said:

To answer Vallie's question about gravity.
g = GM/r^2

Achaea's gravity = (6.673e-11*1.137e16)/170000^2 = 0.000026 m/s^2
Earth's gravity    =(6.673e-11*5.972e24)/6371000^2 = 9.81 m/s^2. 

So Achaea is pretty much a zero g world. 

On the other hand, if you use Kenway's numbers, you get (6.673e-11*1.2302732e+28)/170000^2 = 28,000,000 m/s^2.

To put that into comparison, the Sun has a mass of 1.989e30 kg and a radius of 695,000,000 m. (6.673e-11*1.989e30)/695700000^2 = 274.22

The 28,000,000 number is the value that I got when I was trying it out, which seemed really wrong, I was expecting something more like the 0g case - but as hinted before, the gravitational constant is for our world, so it might just be something totally different Achaea. Nice to know I wasn't totally crazy!

OR, the current continents in Achaea are just one part of the world, and the actual planet is much, much larger, which would of course influence the other values. Maybe all the IRE MUDs are just different parts on top of a huge ocean! Or the Underrealm is super dense, and the only thing keeping us from floating off into space. Or we're all super dense, which explains why we can be hit by things that hit with literal world-shattering force, and shrug it off as a bruise.

From what I recall, chromosome formation in early stage embreyos are reliant on gravity to curve properly - so maybe that's why no one can 'actually' have a baby, and we all resort to bloodlining

Kenway

Numbers are based off of the image of the entire planet that is supposedly cannon so we shouldn't have to worry about more rooms. Thanks for math checks and additional nerdage people that's exactly why I posted all that!

Kenway

Yeah, this

Kenway

Something to consider: achaeas days are extremely short, perhaps rotation on its axis is extremely fast which could maybe make up for lack of gravity a la a centrifuge?

Krypton

Kenway said:

some interesting facts about the rings are:
On the equinox, the southern hemisphere of Achaea will experience a 24hr night.

This is not right.

We don't even know if Achaea has an axial tilt (what creates seasons on Earth). Currently, because the ambient sun/moon/ring messages are the same at every latitude, it actually suggests the planet has NO axial tilt, i.e., the Sun is over the equator at all times, and that seasons are simply a Divine construction.

Even if we DO have an axial tilt, the equinox is STILL when the Sun would be over the equator (spring, 13th of Miraman; and autumn, 13th of Chronos). On the equinox, standing on Meropis at the equator (where the rings appear as a solid line directly overhead, year-round), the Sun would appear directly behind the rings.

You're thinking of the solstices, when the amount of Sun blocked by the rings is at the maximum. If Achaea has an axial tilt, then for half a year -- from 13 Miraman to 13 Chronos -- parts of the southern hemisphere will have the Sun constantly blocked by the rings, and -- from 13 Chronos to 13 Miraman -- parts of the Northern hemisphere will have the Sun constantly blocked the rings.

No one has a 24-hr night on the solstice if our axial tilt is not severe enough.

Sarapis

This definitely made me chuckle, and is some nice work! Couple things though:

1. That picture of Sarapis is a piece of art, not a map. It's kind of roughly showing what the world looks like (it's based on a map of the world I shared with the artist) though it does look roughly(!) accurate-ish to my map. You can see Bandar Selat and Bandar Selam sitting there in the middle of the ocean east of Meropis and the continent of Palariel south of Meropis. However, my map is probably not particularly accurate either.

2. An ocean square represents a distance MUCH longer than 100 meters. How long exactly, I don't have any idea, so I'm not much help there, but far, far longer than 100 meters. 

Sarapis

Vallie said:

OR, the current continents in Achaea are just one part of the world

Correct! Sapience and Meropis aren't even two of the bigger continents in the world. There are six main continents and some islands that are big enough that some might refer to them as a continent, mistakenly. 

We intend to have the other continents finished by 2080.

Krypton

Sarapis said:

There are six main continents and some islands that are big enough that some might refer to them as a continent, mistakenly.

[spoiler]HOLY BALLS, I JUST REALIZED WHERE TECTON'S NAME CAME FROM[/spoiler]

Nazihk

Kenway said:

Something to consider: achaeas days are extremely short, perhaps rotation on its axis is extremely fast which could maybe make up for lack of gravity a la a centrifuge?

We'd have to be on the inside of the planet for that to work, like some sort of "Hollow Achaea" conspiracy theory stuff.

Vallie

Nazihk said:

Kenway said:

Something to consider: achaeas days are extremely short, perhaps rotation on its axis is extremely fast which could maybe make up for lack of gravity a la a centrifuge?

We'd have to be on the inside of the planet for that to work, like some sort of "Hollow Achaea" conspiracy theory stuff.

Oh phew, I was sitting in a meeting today being distressed because I swore centripedal force directed outwards along rotation which would have only meant we were flung harder, but it was contrary to what @Kenway said.

BUT WHAT IF THE UNDERREALM IS ACTUALLY THE OVERREALM?

Ahmet

Nazihk said:

Kenway said:

Something to consider: achaeas days are extremely short, perhaps rotation on its axis is extremely fast which could maybe make up for lack of gravity a la a centrifuge?

We'd have to be on the inside of the planet for that to work, like some sort of "Hollow Achaea" conspiracy theory stuff.

Achaea's rings are actually bridges across the great chasm in which we live. Stars are the lanterns of a nomadic, seafaring civilisation on the opposite side of the globe. Hashan is actually situated on one of the thinnest points of the crust, making the fog that boils up through the sunderlands just minor leaks of the surface's extremely acidic and toxic atmosphere.

We can do this, folks. Lets make it canon.

Milabar

Vallie said:

OR, the current continents in Achaea are just one part of the world

Correct! Sapience and Meropis aren't even two of the bigger continents in the world. There are six main continents and some islands that are big enough that some might refer to them as a continent, mistakenly. 

We intend to have the other continents finished by 2080.

Third continent when I turn 100 rl!  I'm looking forward to this for my 100th birthday

Kenway

Sarapis said:

This definitely made me chuckle, and is some nice work! Couple things though:

1. That picture of Sarapis is a piece of art, not a map. It's kind of roughly showing what the world looks like (it's based on a map of the world I shared with the artist) though it does look roughly(!) accurate-ish to my map. You can see Bandar Selat and Bandar Selam sitting there in the middle of the ocean east of Meropis and the continent of Palariel south of Meropis. However, my map is probably not particularly accurate either.

2. An ocean square represents a distance MUCH longer than 100 meters. How long exactly, I don't have any idea, so I'm not much help there, but far, far longer than 100 meters. 

I believe that 400m squares would make Achaea roughly earth-sized but your cap'd MUCH makes me think it's quite a bit larger than earth! Anyways this was a fun project and I look forward to refining it more as people continue to be smarter than me and we get new land masses. Thankfully regardless of meters/metron and other mistakes I've made, I think the rings measurements in metrons are still fairly accurate. At least enough to approximate angles and such!

Sena

Kenway said:

Now while metrons are all well and good, they don't actually tell us much on a scale that you or I can picture! UNACCEPTABLE! SO, using the -only- relatively standardized unit of measurement I could find in the game that correlates to the real world we can get all this in REAL NUMBERS YEEESSSS!!! What is that standardized unit you ask? SHIPS! Yes, ships. Specifically, war galleys. Historically, galleys averaged at around 40meters long while man of wars averaged 60meters! So how do we apply these numbers in a useful way? Well, only one ship can fit in each wilderness space so they're all at -least- 60 meters by 60 meters. However because I doubt that ships are gonna be passing each other hulls scraping together (moreso because I have a burning desire for the planet to make any sort of physical sense) we're gonna call one metron 100 meters. Big enough that one ship fits very comfortably but still not two!

A few years ago I used knots to estimate the length of a metron, assuming knots are equivalent to real life (1.852 km per Achaean hour), and came up with roughly 53.6km.

Ahmet

R u telling me that Achaea is 12222222222222 times larger than Earth?

Krypton

How'd you get that?

A ship moving at 12 speed (12kts/hr) moves about 1 metron/sec. (I'm just quickly approximating for an example.)

So that's 150 metrons in an Achaean "hour" (2.5 real minutes).

12 · 1852m / 150 metrons = 148m in a metron

Vallie

It popped into my head that if we know the size of a metron and how fast we move through them, we can figure out how fast the average Achaean moves.

By @Sena's number, that means 2 rooms x second = 107.2km/s = 385,920 km/h if we use human time, though since 24 Achaean hours = 1 RL hour, we're at the much more reasonable speed of 16,080 km/hr. Mhuns with Celerity armlet move at ~mach 26.

If @Kenway's 100m estimation is right, then a normal person wanders around at 30 km/h, which is 'only' 67% of Usain Bolt's top speed in a sprint.

So off of @Tecton's, we're somewhere between 'fastest man alive' and 'circle the Earth in 2.5 hours'.

Kenway

@Vallie you're forgetting dash and gallop for near-instant 5 metron travel.