# Resolving Environmental Implications of an Extremely Massive Mountain

I am doing some work within the setting of the Exalted tabletop role-playing game. In broad brush strokes, the defining feature of the world is the five elemental poles: Water (west), Wood (east), Air (north), Fire (south), and Earth (center) – the setting is on a plane rather than a globe, hence the "center" pole.

The Pole of Earth sits on an island roughly the size of Russia, and is expressed by Mount Meru (alternately called the Imperial Mountain). Similar to the Mount Meru in Hindu/Buddhist mythology, the Imperial Mountain has absurd dimensions: the setting information notes that the ancient city of Meru being located halfway up the mountain, 300 miles above the ground.

This is the only dimension for the mountain explicitly given. However, assuming the mountain's icon on the world map is to-scale, it would have an approximately 470,000 square mile base (larger than Greenland).

This startling geography naturally causes some problems. When the sun "rises," the entire world would enter "day" at (roughly) the same time. The Imperial Mountain should, then, cast massive shadows across the western ocean in the morning and across the eastern lowlands and forests in the afternoon. Winds around the mountain would cause all kind of havoc with temperatures and precipitation. I'm sure there are other major effects that would be caused by the giant spire of rock in the middle of the world, but I don't have the experience in the many varied fields that would be required to detail all of the problems with a 600-mile-tall-mountain.

The standard answer to a conundrum like this in the Exalted setting would be that the gods or the elementals handle it. Natural phenomena like storms and earthquakes require a bureaucratic paper trail, and the sun itself is basically "the Death Star, decorated like the Taj Mahal" (to quote a post by one of the freelance writers of the setting); why not just have the celestial bureaucracy stick their collective fingers in the problem and fix it with magic?

My main problem with leaning on the gods is that it's boring to simply say "a wizard god did fixed it." The secondary problem is that in the "modern" times of the setting, the celestial bureaucracy is broken: gods take bribes, slack off on their jobs, etc. – Heaven even suffers from unemployment, these days.

How could normal humans deal with the issue of a giant mountain causing world-ranging problems, without resorting to prayer or summoning supernatural entities?

Only gods, elementals, the titular Exalted, demons, faeries, and certain powerful undead are directly capable of using magical powers. The best that a normal human may be capable of is some ritual-type magic, such as reading the future in the stars (and even that is going to be about as specific as a Magic 8-Ball).

Technology level is generally medieval (with the exception of rare magical artifacts and ancient technology).

• Biggest sun-dial I ever saw xD - On-topic, does the setting specify a height for the atmosphere? Also, what is the cloud height, if specified? – mechalynx Oct 7 '14 at 22:56
• I'd imagine the cloud ceiling would be significantly lower than the mountain. Only example I can pull from is Olympus Mons on Mars seems to have reached some of these qualities, but even then it's only about 1/3 of this mountain. Trade winds would probably be a giant circle around the mountain. 300 miles above the ground for a city would be nearly absurd...the atmosphere that far up wouldn't be breathable without some special precautions. – Twelfth Oct 7 '14 at 23:50
• How realistic is your atmosphere? Does it extend clear up to the vault of the heavens, or does it decrease with altitude, fading out a few tens of miles up the mountain? – Mark Oct 8 '14 at 0:02
• Assuming Earth-like conditions, not only your mountain would reach Exosphere which is by some categorized as a part of outer space, but the ionization and extreme temperature conditions (according to Wikipedia, it might reach 2,500° C) would make it really hard for any inhabitants. On the other hand there would be some cool features, like auroras or international space station if it exists in your world. – dtldarek Oct 8 '14 at 8:12
• @Mark, The only definite I can give from the established setting is that when it was populated, the city of Meru had regular humans living in it, so 300mi has breathable air (even if it may be thin), at least near the center of the plane. (I can certainly conceive of the atmosphere being something of a hemisphere.) Individuals have surmounted the mountain and flown above it, but those individuals were all capable of various forms of magic that could have protected them. – Brian S Oct 8 '14 at 13:19

I had to go look up what each region is roughly expected to be like. Noting that the plane is supposed to be finite, you homed in towards the problem with that hunk of rock, as far as I know it's impossible for there to be a cold icy North like there's supposed to be and a forest in the East. I can come up with complex scenarios to physically get either/or but not both. You are thus required to invoke pole-based magic.

As we are now invoking magic for weather you can get whatever you want from the system. As we have magic weather we might as well choose between uniform gravity and gravity-as-usual where you would feel more of a pull towards the center of the plane as you ventured towards the edges. With arbitrary magic atmosphere I see no reason not to magically mix breathable air up to any height. In fact I can't see any real reason for "space" to actually ever start. Certainly at some point the atmosphere wouldn't be bound by gravity but that's no reason for the "beyond" to be anything other that air.

Actually I just revised one of my scenarios and there is The One where you could achieve the necessary conditions realistically. You need a practically solid mountain range around the South and one separating the East and West on the topside of the plane (your center mountain) to set up Orographic rain for the East's forests.

You would need a sun that orbits extremely low over the Southern end so that it causes the central mountain to cast a shadow over the North nearly all the time. You would also need the bottom side to be entirely flat ocean so the rain shadow effects have time to be canceled out and evaporation to occur for for the North. Wind would continuously blow West and weather pattern would be unchanging from day to day.

Due to the low Southern sun and the constant Western wind it would become impossible to get lost pretty much everywhere. Your crazier weather all but disappears except in the north where ice crystals and crazy mixing from the dual rain shadows (your finite edge of the plain acting like mountains) cause intense storms.

So "How could normal humans deal with the issue of a giant mountain causing world-ranging problems, without resorting to prayer or summoning supernatural entities?"

• In crazy pole-based magic land they observe any pattern in the magic if they're there and exploit them, or stay as far away from each pole as possible if their particular effects are dangerous.

• In The One land you have guaranteed constant weather so you find a place you like and stay there.

It was asked at what angle the sun should be over the South so I figured I'd flesh it out:

It's worth noting you won't have seasons with this setup as calculated. You could have a "wobbly coin" for your plane relative to the sun to pull them off but you'd have to tune everything carefully to get season while still keeping the ice in the North and the desert in the South.

Note that ALL references to distance are in regards to the Northern Edge.

Alright, so the major cause for temperature changes is insolation. Ice has natural reflectance, so our target is enough shadow cover to get to 0 °C and we'll assume a feedback loop takes over from there and drags it lower and stabilizes it.

$$\text{Temperature} = \sin (\text{SunAngle}) \times \text{SolarConstant} \times \text{PercentDaylight}$$

I'm not going to use the typical definition of solar constant here, mostly because we don't care, it's a raw solar heating number that gives a target base temperature.

Now the mountain is 600 miles tall and based on looking on some Exalted maps I'm going to guess ~30,000 miles average diameter for the plane.

Using trig you need that shadow to cast from 600 on one edge of the triangle to 15,000 on the other so we can cover the widest part of the north

$$\tan ^{-1} \left( \frac{600}{15,000} \right) = 2.3°$$

(thats maximum sun height in the sky from the far edge of the North)

This should also maintain the amount of shadow by sweeping equally across the North. Assuming 24 hr days we have 12 hrs of shadow time roughly equally distributed across the north. So subtracting, the North receives 11/24 daylight percent.

In order to have the shadow sweep across the entire North our sun's orbit radius must be equal to the radius of the plane. This is because as we head towards infinity the shadow from the mountain will actually spread across the entire top half of the map. And as we head towards a radius of zero it will tend toward a straight shadow behind the mountain...

Using our plane radius of 15,000 miles:

$$\text{Distance} = \frac{15,000}{\tan(\theta_1)}$$

The middle needs to be 25 °C and the north 0 °C.

Using kelvin to avoid 0 °C in math:

$$273 = \sin(\theta_1) \times C \times \left( \frac{11}{24} \right)$$

$$298 = \sin(\theta_2) \times C \times \left( \frac{12}{24} \right)$$

Solving for $C$ since its constant:

$$C = 273 / \sin(\theta_1) / 0.416$$

$$C = 298 / \sin(\theta_2) / 0.5$$

Note that using similar triangles:

$$\tan^{-1} \left( \frac{\text{Radius}}{\text{Distance}} \right) = \theta$$

So:

$$\theta_2 = \tan^{-1} ( 15,000 / ( (15,000 / \tan(\theta_1)) -15,000 ) )$$

Where $\theta_1$ is the angle from the North edge and $\theta_2$ is the angle at the Center.

To achieve room temp at the middle of the plane we need:

$$298 = \sin(\theta_2) \times C \times 0.5$$

To ensure a proper temperature in the North the value of $C$ must be:

$$C = 273 / \sin(\theta_1) / 0.416$$

Combining with the proper temperature for the center:

$$298 = \sin(tan^{-1}( 15,000 / ( (15,000/tan(\theta))-15,000) ) ) \times 273 / \sin(\theta) / 0.416 \times 0.5$$

Solving for $\theta$$:$$\theta = 0.785398°$$Solving for Sun distance using similar triangles:$$\text{Distance} = 15,000 / \tan(0.785398) = 1,094,200.5\text{ miles}$$Using similar triangles again to get the angles for the North, Center and South:$$\tan^{-1} \left( \frac{\text{Radius}}{\text{Distance}} \right) = \theta\tan^{-1} \left( \frac{15,000}{1,094,200.5} \right) = \text{North} = 0.785397979°\tan^{-1} \left( \frac{15,000}{1,094,200.5 - 15,000} \right) = \text{Center} = 0.79631297°\tan^{-1} \left( \frac{15,000}{1,094,200.5 - 30,000} \right) = \text{South} = 0.807535595°$$Solving for the appropriate \text{Solar Constant} to get a 25 °C Center:$$C = 298 / \sin(0.79631297) / 0.5 = 42,884$$Testing out our temperatures for the \text{North}, \text{Center}, and \text{South}:$$\sin(0.785397979) \times 42,884 \times 0.416 = 244 K\sin(0.79631297) \times 42,884 \times 0.5 = 298 K\sin(0.807535595) \times 42,884 \times 0.5 = 302 K$\$

So the extremely low angle is less than 1° high in the sky.

Note that the South will have increased heat due to the rain shadow and the North is freaking cold and actually colder than that because the ice will reflect more.

• How low is "extremely low"? – Brian S Oct 8 '14 at 13:23
• That depends on the size of the mountain relative to the size of the north, since the shadow needs to cover a sizable chunk of it often enough to keep it frozen. Edit: I posted the maths for the Exalted maps I've seen. I spent quite some time so hopefully I got it right. – Black Oct 9 '14 at 19:25
• chuckle About 10 minutes for the idea. About 7.5 hours for the maths. – Black Oct 9 '14 at 19:32
• @Black I thought I was the only one that does that :P – mechalynx Oct 9 '14 at 20:07
• @ivy_lynx Lol, you should have seen the size of the original before I posted on "The One" design. You'd probably think I was going for a thesis on the subject of planar planets. Although I can't help but imagine your usual answers taking much more time than mine, as most of them cover so much. – Black Oct 9 '14 at 21:21

I'm going to assume 'earth' for the point of atmosphere and what this mountain would generally be.

About 80% of the mass of the atmosphere is within the first 9-17 km (thicker at equator) of altitude. At 50km you enter the mesosphere which is the top end for clouds (and these are rare and a special type). Keep going up...low orbit satellites are found around 180 miles (300km) in the middle of the Thermosphere (thermosphere will hit temps of 1500 celcius, but it'll feel cold because it's near vacuum here)...which I guess means an advanced society should leave communication satellite wreckage less than 1/3 of the way up this mountain.

At 300 miles above earth where we find the ancient city (by your post, I went with the 300 miles is where the city is and not the top of the mountain), the pressure is low enough that the pressure within a human hand will start to expand the hand to several times it's natural size (there's a brutal online video for evidence of it...some poor guy jumping out of a balloon had his glove come off). The air will not support life at all (oxygen thins out and you're mostly in hydrogen and nitrogen at this point). And you should be relatively close to weightless at this point.

Several times during the day, an inhabitant of the ancient city of Meru should be able to look out the window downwards about 50 miles to see the international space station float by (ya, the ISS is around 250 miles up). Standing at the top of this 600 mile mountain should mean you've successfully broken out of the earth gravitational pull and you should be able to throw rocks into the sun. Weather would be fun as you're starting to hit the Van Allen radiation belt...would be nothing but electrical storms.

This of course means the mountain cannot really be explained without some form of magic...with the rotation of the planet, there's a good chance the top of this mountain should break off into space and start floating around as it's own stellar body. A volcanic eruption should be shooting lava into space.

In more practical terms...I think this is a mountain of myth and lore. Standard people would barely be able to survive (atmosphere limitations) even at the lowest base points of this mountain. It'd be a 'dark' area where no life is really capable of inhabitting and as such would likely be the source of much lore (creatures of the mountain?). Creatures that can live on this mountain have to do so nearly void of oxygen...might get some interesting near alien species of monsters cropping up. It would be a giant impassible black hole on most human maps.

• A mountain only 600 miles high isn't tall enough to cause the top to break away due to rotational speed. You only get that once you reach a height of 22,000 miles or so, where the rotational velocity is on the order of the orbital velocity (aka. geosynchronous orbit). – Mark Oct 8 '14 at 5:19
• Yes, it also wouldn't be at rotational velocity so a stone thrown from the top of the mountain would just fall... – Tim B Oct 8 '14 at 8:29
• Rotation is not an issue, as this is not a globe. (The sun literally flies from east to west overhead, then pops into what is effectively hammer space to begin the journey again the next day.) Interesting points, though. – Brian S Oct 8 '14 at 13:20
• A flat disk earth would not be stable under Newtonian Gravity, so this world must have something else. It would also have very little mass compared to a globe, Therefore air pressure and so on might not behave the same way as on earth. – Oldcat Nov 13 '14 at 1:02