Mathematical questions about the Imperial Mountain (Exalted)

[Duckie]

In the Role playing game Exalted (no, come back, it'll have math, I promise), there is a mountain at the center of the world called the Imperial Mountain. This mountain is 600 miles tall. That is not a typo. Also, the world is flat. Don't bother considering these parts with science.

Assuming the atmosphere has approximately the same composition as earth, how far away can you see thie mountain, and what does it look like at varying distances?

Some basic back-of-the-envelope calculations (actually just thinking about it without attempting to do math) I've done imply that even at a distance of 2,000 kilometers the mountain is fecking huge, but I am just vague enough on how to work angular size calculations that involve flat ground (consider a person looking at a light house, determine size of light house) rather than stellar objections.

Further, would not atmospheric diffraction and haziness get involved here? There's very little data I can find for how far an object can be seen on a clear day or a non-clear day, because distances of thousands of kilometers don't occur on earth without being very high up due to us having a horizon, nor do we have a 600 mile tall mountain to experiment with. I assume that at far distances it will get blurry, but I doubt that after just a few hundred kilometers it will stop being visible because it's so bloody enormous, although it could be my conception failing. Will it be just a huge black smudge on the horizon occluding a section of the sky? What sort of calculations can be done to determine how much of the sky is occluded at varying differences?

Since the earth is flat, the sun presumably travels overhead in lines of longitude to make the days vary for season-equivalents in Creation, if they do in fact vary for seasons. Regardless, the sun will eventually go behind this mountain, depending upon angles and distances involved. In either case, however, wouldn't this cause vast sheets of shadow, or basically early sunsets, depending upon the seasons? How significant would this effect be?

If the size of the mountain in more than height is important, just assume a slope angle of 45 degrees to make it a generic right cone if you'd like. The mountain is definitely not like Olympus Mons, it's more of an actual mountain looking thing that you would recognize as the actual iconic Δ shaped thing. More numbers can be provided if I've forgotten to specify something.

[Oni Koneko Damien]

A very quick and roughly done visual aid. Going by the map in the first edition Exalted Sourcebook, the entirety of the known world is about 8000 miles wide. The Blessed Isle, where the Imperial Mountain is located, is about three thousand miles wide. Below are a few quick rough sketches I did in paint. What a side view of the Exalted world would look like, with a six-hundred mile tall mountain in the middle, with a side view of the entirety of China plunked in an eight-thousand mile wide ocean:



Hope this helps a little with the visualization.

[Duckie]

So, even at the furthest the mountain is still going to take up a sizeable amount of the sky- IIRC I estimated it to be about 10 times the size of the moon in diameter for its height at the distance of lookshy or the imperial city (I forget which) before realising that I suck at math and I shouldn't be trying these things.

But really, I think atmospheric distortion and the like would prevent getting a clear image of it. For one, from 4,000 miles away, wouldn't all the reflected light coming from the mountain have already hit something, been bent by diffraction into a path that would get rid of it before it hits your eyes, or otherwise disposed of in some way in the same way that makes things blurrier and slightly bluer as they get further and further away with more air in between them?

Although I'm assuming creation works the same way as earth, which is never a good bet since the world is flat, there's a 600 mile tall mountain at the center of the world, everything is made of just 5 elements, and you can defeat the ocean with your fist. Quite possibly air wouldn't work that way, although that's getting into 'why even bother making that assumption territory' since when in doubt Exalted with the possible exception of electromagnetism (which appears, bizarrely, not to exist, leaving some odd gaps in physics which continues working blithely without caring) appears to work on a macro-scale in the same way.

[Gaidin]

re Atmosphere: It's hard to not assume it works the same. The general rule of thumb for Exalted has usually been 'Like normal, but with these differences." I don't remember if its said anywhere in a book, but most storytellers have the mountain visible to some extent from pretty much anywhere that isn't wyld. And we can tell the atmosphere is survivable at least up to 600 miles given Meru was built nearly to the very top in the First Age, and that was left bare only because they couldn't control the elemental forces. They left it as a game preserve(as opposed to unsurvivable due to lack of atmosphere).

[Junghalli]

Re atmospheric distortion: the moon is much farther away from us than this mountain, but we have no problems clearly seeings its shape when it's illuminated. At 600 km tall most of the mountain would project well above the atmosphere, and the light reflected off that part would mostly be subject to no more atmospheric interference than a celestial object. Although I wouldn't be too surprised if there was a "haze" effect at the base of the mountain from that part being washed out by atmospheric interference. During the daytime I think it might look something like this:



Assuming a set-up with a disc-shaped "planet" that is "tumbling" with respect to the sun or being orbited by the sun you'd get a brief period twice a day where the sun has disappeared behind the rim of the world from the perspective of the lowlands but can still be seen from the perspective of someone at the top or on the slopes of this very high mountain. During these periods the mountain would shine in the night sky with reflected sunlight, like our moon does, and the people on the "planet" could watch the darkness either climb the mountain and eventually consume it (at sunset) or descend down it and reveal more and more of it (sunrise). These events would probably be pretty short lived assuming an Earthlike day/night cycle, but spectacular nonetheless if you're close to the mountain, and an interesting sight from pretty much anywhere you could see it. Might look something like this from the same distance from the mountain as the first picture:



The rest of the night I think it would just be a mountain-shaped hole in the stars. Earthlight doesn't make the new moon glow substantially IIRC, so even on moonlit nights (assuming this world has a moon, of course) I'd guess it'd still be dark, but I wouldn't necessarily take that to the bank, especially if you were close to it, where it would fill a lot of the sky. I'm assuming, BTW, that this world does at least have stars. Without them I'd guess it would probably be invisible at night, although if there was a moon but no stars the lack of stars might enhance the visibility of whatever feeble light it reflects from the moon.

[Duckie]

There are indeed numerous stars and a moon on Creation. So, you think that the afternoon siesta type thing where the sun is blocked by the mountain (which, since the mountain is in the center, would be at just before or just after noon) wouldn't be too long, besides for the immediate vicinity of the mountain which will be shrouded in twilight for half the day? I'm not really sure how to model the shadows, assuming the sun takes a straight path over the equator of the disc, but I know for certain that only a very small stripe of the equator would have significantly long times in the shadow due to basic physics. But I have no idea how to tell how long it'd be.

[Gaidin]

Another thing to remember about the geography of the Blessed Isle, is that while all the surrounding mountains are certainly less prominent than the center mountain(which is the elemental poll of earth), they are still like our Himalayas. Not sure how much it affects the imperial mountain's visibility except at extreme close range to the surrounding mountains.

[Ariphaos]

Creation is actually about 15,000 miles wide (800 miles per inch, the map in the first edition books being about 17.5 inches wide and the White Wolf download I built my maps of Exalted off of being a bit wider than that.

I actually tried working this out. Given sufficient atmosphere, Mie an Rayleigh scattering will cloud and redshift any object out of view, but it doesn't seem like a 'mere' six-seven thousand miles is enough for that to happen each day. There will be days in the Threshold where it is hidden by haze, but other times - not so much at all.

[The Nomad]

The new Glories of the Most High contains a wealth of information about Creation's celestial makeup.

Apparently, the Sun is actually the Unconquered Sun's spaceship (big enough to warrant a monorail so as to operate on the outside hull. Yes, the UCS' mechanics are tough buggers): the Dirigible Engine Daystar. It disappears into Elswhere (Exalted's subspace) when it reaches the limits of its course, near the limit of the world. And reappears on the opposite side of Creation at Dawn after a night of cooling down in Yu-Shan.
Originally, Creation had no day/night cycle, it appeared only after Luna was created by the Primordials Cytherea and Oramus, "from everything that was not of Creation, brought into Creation" (to paraphrase GotMH).

Creation's sky has an actual ceiling, and contains numerous spacetime anomalies through which eldritch horrors from beyond can crawl inside the world. Creation's spatial void is not actually, well, a void, there is still a tenuous atmosphere even at thousands of miles above Creation.

The Moon (or rather, the Silver Chair) is an actual planetoid, on which Luna's palace (as well as towers for the Maiden of Fate) stands. Its surface has standard 1G gravity and a breathable atmosphere and even contains a sort of Garden of Eden in one of its craters. The Moon is linked to Creation's surface by a magical ladder that moves everyday somewhere in Creation, and allows anyone to cross the thousands of miles of distance in exactly one hour (with a gravitational inversion in the exact middle of the trip, in defiance of normal gravity), protected from interception or the environment.

Yep, Creation is weird.