# Hollow World Maths Question

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Ok, so let's say you're standing at sea level and looking at the horizon. It begins about 3 miles away as the Earth's curve becomes noticeable.

So, inside a hollow version of earth, let's say with an interior diameter of approximately 7,000 miles (assuming a 500 mile thick crust on either side), at what distance would the upward curve of the "horizon" begin? Let me just say for the record I'm no damned good with math beyond simple adding and subtraction. I could be bloody well wrong but I imagine the ground looking relatively flat for many, many miles before the upward curve noticeably begins.

The reason I ask is I'm going to be running some adventures in my homebrew that take place in its hollow interior. Think Burroughs' Pellucidar, but with magical beasts and aberrations instead of dinosaurs.

The circumference of the outside of your planet is 2*Pi*r=21,911.1486 miles. Going off of the assumption that in your world the curve becomes noticeable at 3 miles, or 3/21,911.1486=0.00013642 as a fraction of the circumference.

Now, your interior circumference is 2*Pi*r=18,849.559 miles.

18,849.559*0.00013642=2.57145642 miles.

Round as you see fit. I hope this helps.

Thanks, it does!

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With that thin a crust with a hollow interior and 'earth' level gravity wouldn't the whole thing implode? I would think you'd have to make the crust out of some ridiculously hard material just to resist such compression, densely packed earth or pelagic clay probably won't get the job done. Or is that going to be a wizard did it thing, yeah probably best that a wizard did it. Are we to assume earth-like flattening values or are we dealing with a perfect sphere? I mean that diameter is roughly earth sized, slightly smaller. 11250 kilometers vs 12600ish kilometers for earth, so for roughing it in should we be using earth values for all the variables?

The simpler answer is the upward curve of the horizon occurs at the speed of plot. Unless your entire gaming group are geologists, nasa engineers, or straight up math nerds I don't think they'll call you on it. And if they do... throw more mutant aberrations at them, or explain it as an ever shifting thing as a result of external pressures or whatever.

Regards,
DRS

I figure in a game where multi-ton lizards can fly, cast spells, and breathe fire I can have a world with a relatively thin crust.... lol

DRS3 wrote:

The simpler answer is the upward curve of the horizon occurs at the speed of plot. Unless your entire gaming group are geologists, nasa engineers, or straight up math nerds I don't think they'll call you on it. And if they do... throw more mutant aberrations at them, or explain it as an ever shifting thing as a result of external pressures or whatever.

Regards,
DRS

Throwing more aberrations at them is a great way to distract them from math... lol

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Do not scoff the roleplaying math nerds, for we will use out superior number crunching to destroy all that oppose us.

Considering that the crust is more than ten times the thickness of Earth's crust, indeed somewhere around a sixth of the entire radius of Earth, I think it should be fine.

Try to find some old Hollow World Mystara materials. It's been done before, so why reinvent the wheel?

My first RPG experience was Hollow World. East and west were backwards...17 years later, I still have to actively remind myself which way east REALLY is...

My solution: have the interior be under a constant Reverse Gravity effect. It provides a cool new environment for adventuring, and also stops the world from imploding.

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RumpinRufus wrote:
My solution: have the interior be under a constant Reverse Gravity effect. It provides a cool new environment for adventuring, and also stops the world from imploding.

I was under the assumption that it already was, unless the entire adventure is everyone piled together at the center fighting to see who gets to stand on top of everybody else.

CampinCarl9127 wrote:
RumpinRufus wrote:
My solution: have the interior be under a constant Reverse Gravity effect. It provides a cool new environment for adventuring, and also stops the world from imploding.
I was under the assumption that it already was, unless the entire adventure is everyone piled together at the center fighting to see who gets to stand on top of everybody else.

OK... maybe I should read the entire OP before posting. Carry on.

Nazard wrote:

Try to find some old Hollow World Mystara materials. It's been done before, so why reinvent the wheel?

My first RPG experience was Hollow World. East and west were backwards...17 years later, I still have to actively remind myself which way east REALLY is...

I like reinventing wheels. It's why I design my own settings. I sorta remember the Mystara stuff (never played in the setting) but it didn't really do much for me. It's also going to be the default psionic setting in my homebrew.

Pathfinder Starfinder Roleplaying Game Subscriber

Also keep in mind another factor... the attenuating visibility caused by the haze of an atmosphere. and that's not counting clouds.

I was actually thinking about these things last night.

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Nazard wrote:

Try to find some old Hollow World Mystara materials. It's been done before, so why reinvent the wheel?

My first RPG experience was Hollow World. East and west were backwards...17 years later, I still have to actively remind myself which way east REALLY is...

I've actually been converting some of the old Hollow World Mystara materials from 1st edition D&D over into Pathfinder materials for private use for quite some time now.

There's no material on how far you can see before the curve of the Hollow World becomes noticeable. However, as far as gravity... Magic did it. Specifically, Ka the Preserver's magic.

Y'see, Ka was this 45-foot long carnivorous dinosaur who started saving all of these cultures from extinction by kidnapping them and putting them in the Hollow World. You probably remember this, having played in the Hollow World setting. Anyway... Ka became a god and kept doing his thing.

Opened up a pinhole-sized gateway to the elemental plane of energy for use as the "sun". Set floating continents near to the gateway to help the people of the Hollow World tell time, only set the atmosphere to go up a certain distance above the surface of the Hollow World (not anywhere close to the floating continents), set entrances to the Hollow World at the poles, and all kinds of other wacky stuff.

But nothing math-nerdy.

Best wishes!

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Pathfinder Starfinder Roleplaying Game Subscriber

Since your players aren't going to have the equipment, the technology, nor even the grounding to ask those questions, I wouldn't worry about the answers.

If players insist, gently but firmly remind them that their characters did not grow up in Space or Internet Age America.

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My love for Edgar Rice Burroughs' "Pellucidar" series of pulp sci-fi from the early 20th century has had me wanting to run a hollow world game for years; decades, even. I could just never get the right ideas to gel. I don't want to use dinosaurs (imo they've been over used) so it finally hit me that this would be the perfect place to drop mutated creatures, aberrations, and magical beasts instead. So one night while just sitting and listening to music it all seemed to fall in place. And for over 20 years I've been monkeying with the place of origin for a race of psionic humans who once conquered most of my homebrew setting. I love it when an plan comes together. I'm not too worried about the science or the magic that makes the hollow world possible. It just "is".

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Pellucidar books were mind blowing for me because of this setting. There was a scene in (the 2nd book) where the protagonist was being chased in a canoe by a bunch of canoes on wide open sea water. He did have to look up to find them. Blew my mind.

Another thing to consider is that spell durations would be effective because it is High Noon ALL THE TIME in the hollow world.

But one particularly interesting thing is Golarion is hollow! See here:

http://pellucidarskartaris.blogspot.com/search/label/Pathfinder

quote:
"Incredible rumors suggest that the beasts that make the realm famous somehow emerged from an impossible underworld with its own false sun, a savage microcosm in which the dinosaurs never died and humans never emerged from their primitive origins. The Pathfinder Society has mounted five expeditions to this rumored inner world, but none of (sic) have ever returned from the country alive."

and

quote:
"Some are said to be so huge that they are themselves inverted worlds, that the denizens walk and live along the inner surface of the vault in defiance of gravity, and that their skies are lit by a glowing orb of brilliance akin to the sun itself floating at the immense cavern's center."

CampinCarl9127 wrote:

The circumference of the outside of your planet is 2*Pi*r=21,911.1486 miles. Going off of the assumption that in your world the curve becomes noticeable at 3 miles, or 3/21,911.1486=0.00013642 as a fraction of the circumference.

Now, your interior circumference is 2*Pi*r=18,849.559 miles.

18,849.559*0.00013642=2.57145642 miles.

Round as you see fit. I hope this helps.

This all sounds correct, except what is the reason for saying the curvature becomes noticeable at that point? I am not saying you are wrong, you certainly seem to know your stuff, just asking.

And on hollow worlds, they make most preposterous ideas sound sensible. OK, so gravity holds you to the inside. Why doesn't it cause the crust to all explode outwards due to this "gravity"?

And contrary to an earlier post from campincarl, with realistic physics your party would not fall to the center of the hollow earth. Unless the reason is it is all full of air, so you would fall towards the center of mass. But is that really hollow?

What is clear is the crust would have to be strong beyond belief not to collapse into... something shaped like a planet.

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Pathfinder Starfinder Roleplaying Game Subscriber
Joynt Jezebel wrote:
CampinCarl9127 wrote:

The circumference of the outside of your planet is 2*Pi*r=21,911.1486 miles. Going off of the assumption that in your world the curve becomes noticeable at 3 miles, or 3/21,911.1486=0.00013642 as a fraction of the circumference.

Now, your interior circumference is 2*Pi*r=18,849.559 miles.

18,849.559*0.00013642=2.57145642 miles.

Round as you see fit. I hope this helps.

This all sounds correct, except what is the reason for saying the curvature becomes noticeable at that point? I am not saying you are wrong, you certainly seem to know your stuff, just asking.

And on hollow worlds, they make most preposterous ideas sound sensible. OK, so gravity holds you to the inside. Why doesn't it cause the crust to all explode outwards due to this "gravity"?

And contrary to an earlier post from campincarl, with realistic physics your party would not fall to the center of the hollow earth. Unless the reason is it is all full of air, so you would fall towards the center of mass. But is that really hollow?

What is clear is the crust would have to be strong beyond belief not to collapse into... something shaped like a planet.

With realistic physics, giants would collapse under their own weight, dragons and pegasi can't fly, and you wouldn't be playing this game. In D20/Pathfinder, you're perfectly legitimate in having your world being a flat disk supported by 4 elephants, all balanced on the back of a turtle.

The moral of the story is .... stop overthinking the game and it's settings.

I actually have set a campaign on a world that rest on the back of a turtle, which rest on the back of an elephant. It was a very long time ago and a mistake. Its just too preposterous for suspension of disbelief.

And I am fully aware of the points you make LazarX and don't think I am overthinking things. This thread started with someone trying to think sensibly about a hollow world setting. What I was pointing out is in many ways you can't, hollow planets are just too unrealistic.

In a Pathfinder game set on a normal planet sure, many things work differently to the real world, most notably magic. But gravity works pretty much normally, except on dragons et al, which have magical advantages for sure. Things still fall down, and a player can make sensible deductions about how much damage it will do if you drop a boulder on someone or something.

In a hollow planet, situations can arise where its anyone's guess what will happen, especially with gravity. What happens if the players tunnel into the ground. Is the ground as hard as uh ground, or as tough as it would have to be not to collapse. And if you tunnel all the way through does the atmosphere escape into space.

Pathfinder is high fantasy and unrealistic as is. Hollow planets are cool and novel. But they ramp up the difficulty of any sort of suspension of belief massively and are so unrealistic situations can arise that are impossible to reason about.

Air isn't completely transparent. Even without weather or dust intervening far-off mountains tend to be tinted sky blue and I think eventually would fade into the sky if you could see far enough. On the other hand if air thins with (reverse) altitude in your hollow world you might be able to see really distant terrain more easily than that a few hundred miles off.

The angular width of the sun or the moon is about 2 degrees. I'm thinking something would need to be at least twice that distance off where the horizon would be for you to see the curve. Plugging values of 86 degrees, 86 degrees, and long side lengths of 4000 miles into a triangle calculator tells you that you're looking 550 miles away in the hollow world. I'm pretty sure that'd be a beautiful shade of sky blue.

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Sorry, the sun or moon is about half a degree across. Trying that again with correct details gives 140 miles. You should be able to make out the curve in good weather conditions.

CampinCarl9127 wrote:
I was under the assumption that it already was, unless the entire adventure is everyone piled together at the center fighting to see who gets to stand on top of everybody else.

Side note, but:

It's actually a curious property of hollow spheres and an inverse square law, that there would be no gravitational force at all inside a hollow sphere. i.e. people just float around, they don't fall toward the center or toward the shell. (it's something like: the math works out such that no matter where you are, the section of the crust to your left is pulling with equal force to the section on your right, so there is no net force.) (I guess if it were spinning, there would be a force pushing you to the shell, strongest on the equator.)

Joynt Jezebel wrote:

I actually have set a campaign on a world that rest on the back of a turtle, which rest on the back of an elephant. It was a very long time ago and a mistake. Its just too preposterous for suspension of disbelief.

And I am fully aware of the points you make LazarX and don't think I am overthinking things. This thread started with someone trying to think sensibly about a hollow world setting. What I was pointing out is in many ways you can't, hollow planets are just too unrealistic.

In a Pathfinder game set on a normal planet sure, many things work differently to the real world, most notably magic. But gravity works pretty much normally, except on dragons et al, which have magical advantages for sure. Things still fall down, and a player can make sensible deductions about how much damage it will do if you drop a boulder on someone or something.

In a hollow planet, situations can arise where its anyone's guess what will happen, especially with gravity. What happens if the players tunnel into the ground. Is the ground as hard as uh ground, or as tough as it would have to be not to collapse. And if you tunnel all the way through does the atmosphere escape into space.

Pathfinder is high fantasy and unrealistic as is. Hollow planets are cool and novel. But they ramp up the difficulty of any sort of suspension of belief massively and are so unrealistic situations can arise that are impossible to reason about.

I'm going to respectfully disagree with you, here. In an imaginary setting, you can reasonably suspend your disbelief to include beings from other planes of existence just as easily as you can reasonably suspend your disbelief that you're living inside a planet as opposed to living on the outside of its shell. The only significant difference is that you can't easily fly off into space, which requires an equivalent suspension of disbelief to accept that a wooden galleon carries an air bubble with it and survives journeys of millions or billions of miles to visit other worlds or have high-sea-like battles in zero gravity environments.

Accepting a hollow world is not more challenging to accept than living inside a spherical space station of incredible size. How does it work? Who cares? It's magic. Someone wished it into existence, or some god created it. Besides, I believe that different rational people are not limited to what beliefs they can suspend or not depending on how gravity or physics may or may not work in an imaginary magical setting.

For the religious players out there, the Abrahamic God created a world in seven days, and He could just have easily put life inside of it as on the outside because He's, y'know, omnipotent.

Best wishes!

jerrys wrote:
CampinCarl9127 wrote:
I was under the assumption that it already was, unless the entire adventure is everyone piled together at the center fighting to see who gets to stand on top of everybody else.

Side note, but:

It's actually a curious property of hollow spheres and an inverse square law, that there would be no gravitational force at all inside a hollow sphere. i.e. people just float around, they don't fall toward the center or toward the shell. (it's something like: the math works out such that no matter where you are, the section of the crust to your left is pulling with equal force to the section on your right, so there is no net force.) (I guess if it were spinning, there would be a force pushing you to the shell, strongest on the equator.)

Can we assume that Golarion spins on its own axis? If so, I find it perfectly reasonable to assume that a hollow world, whether inside Golarion or otherwise, might also spin on its own axis.

Additionally, you'd only float in either the complete absence of gravity or the existence of equal and consistent gravitational pull from all directions (i.e. the far side of the sphere, which is much further away from you than the near side, pulling on you with equal force as the near side, despite it being much further away). If the pull was stronger the closer you got to a certain side, which makes sense given that we're not equally pulled toward Venus as we are toward Earth, gravity would pull you "down" toward the nearest section of crust as opposed to having equivalent pull on your "left" as it does on your "right".

That is, of course, unless the sphere is so small or the gravitational pull is do weak that you'd float no matter what, or alternatively, that the gravitational pull is so strong that you're effectively glued to a certain portion of the inner shell.

Happy gaming!

Bodhizen wrote:
Nazard wrote:

Try to find some old Hollow World Mystara materials. It's been done before, so why reinvent the wheel?

My first RPG experience was Hollow World. East and west were backwards...17 years later, I still have to actively remind myself which way east REALLY is...

I've actually been converting some of the old Hollow World Mystara materials from 1st edition D&D over into Pathfinder materials for private use for quite some time now.

There's no material on how far you can see before the curve of the Hollow World becomes noticeable. However, as far as gravity... Magic did it. Specifically, Ka the Preserver's magic.

Y'see, Ka was this 45-foot long carnivorous dinosaur who started saving all of these cultures from extinction by kidnapping them and putting them in the Hollow World. You probably remember this, having played in the Hollow World setting. Anyway... Ka became a god and kept doing his thing.

Opened up a pinhole-sized gateway to the elemental plane of energy for use as the "sun". Set floating continents near to the gateway to help the people of the Hollow World tell time, only set the atmosphere to go up a certain distance above the surface of the Hollow World (not anywhere close to the floating continents), set entrances to the Hollow World at the poles, and all kinds of other wacky stuff.

But nothing math-nerdy.

Best wishes!

Well, damn. That explains why the Genesis game's called Warriors of the Eternal Sun.

Pathfinder Starfinder Roleplaying Game Subscriber
Joynt Jezebel wrote:

Pathfinder is high fantasy and unrealistic as is. Hollow planets are cool and novel. But they ramp up the difficulty of any sort of suspension of belief massively and are so unrealistic situations can arise that are impossible to reason about.

For you maybe. I majored in Physics at Rutgers. i enjoy reading Tarzan's adventures in Pellucidar as much today, as when I did as a child.

Take some advice from the late great Issac Asimov when he commented on the original release of Star Wars.

"Park your brain outside, and enjoy the movie."

Compartmentalisation of your outside real world knowledge and your character knowledge is an important roleplaying skill. Perhaps you should use the Hollow Worlds that are so problematic as an excercise in developing this skill.

Thinking seriously about a hollow world setting isn't about getting abstract numbers. It's thinking about what kind of ecology and civilisations you seal up in, in essence the story elements of hollow worlds, not their improbable physics.

Bodhizen wrote:
jerrys wrote:
CampinCarl9127 wrote:
I was under the assumption that it already was, unless the entire adventure is everyone piled together at the center fighting to see who gets to stand on top of everybody else.

Side note, but:

It's actually a curious property of hollow spheres and an inverse square law, that there would be no gravitational force at all inside a hollow sphere. i.e. people just float around, they don't fall toward the center or toward the shell. (it's something like: the math works out such that no matter where you are, the section of the crust to your left is pulling with equal force to the section on your right, so there is no net force.) (I guess if it were spinning, there would be a force pushing you to the shell, strongest on the equator.)

Can we assume that Golarion spins on its own axis? If so, I find it perfectly reasonable to assume that a hollow world, whether inside Golarion or otherwise, might also spin on its own axis.

Additionally, you'd only float in either the complete absence of gravity or the existence of equal and consistent gravitational pull from all directions (i.e. the far side of the sphere, which is much further away from you than the near side, pulling on you with equal force as the near side, despite it being much further away). If the pull was stronger the closer you got to a certain side, which makes sense given that we're not equally pulled toward Venus as we are toward Earth, gravity would pull you "down" toward the nearest section of crust as opposed to having equivalent pull on your "left" as it does on your "right".

That is, of course, unless the sphere is so small or the gravitational pull is do weak that you'd float no matter what, or alternatively, that the gravitational pull is so strong that you're effectively glued to a certain portion of the inner shell.

Happy gaming!

No. It really does work that way, though I've forgotten the math involved. Given the usual assumptions of "uniform spherical shell", gravity really does cancel out. Essentially the closer you are to one side, the less mass there is pulling you that way, but since it's closer it still pulls just as hard as the greater, but more distant mass pulling you the other way.

There would be some minor, probably not detectable variations since the shell of your Hollow Earth probably isn't of uniform thickness or density nor exactly spherical.

But that's the wrong approach to take in my opinion. As is worrying about spin - which might provide pseudo gravity, but it would vary from max at the equator to nil at the poles. Unless you really want to play around with gravity and other weird effects, in which case go wild.

Probably better to just assume it's roughly earth-normal gravity and get on with the pulp adventure. The gods made it that way. Don't worry about trying to apply real world physics to it.

thejeff wrote:
Don't worry about trying to apply real world physics to it.

It can be fun to try to figure our some plausible-sounding unreal world physics. Maybe the sun floating in the middle emanates some kind of repulsion force that keeps people stuck to the sides.

Or maybe the world does spin, creating a band of normal gravity where humanoids dominate in the temperate zones. There are whole realms of low or zero gravity near the poles, where dragon-like creatures can fly under their own weight. At the equator is a heavy gravity zone - humanoids can barely survive there, but small dense things can thrive.
Crossing from one normal-gravity band to the other requires a journey of incredible hardship, so there are two entirely separate cultures that know virtually nothing about one another.
However, they can see each other, stretched out across the 'sky' of land and ocean. With a powerful telescope you can make out distant cities above you - perhaps even flash messages across the divide with bright lights.
(An alternative way to cross the equator is to fly directly from one pole to the other using some kind of glider - close to the sun there won't be any pseudo-gravity either, so you just have to be able to withstand the heat.)

Now, does the sun pulse from light to darkness to create nights? Is it dark on one side and light on the other and spins on an axis? Or is it constant so there no night? If so, what effect would that have on society, where you have minimal need for lighting and can sleep when you feel like it? Would people work in shifts? Would they snack and take short naps and have no concept of 'breakfast'?

If you had good engineering skills, you could have cable cars running hundreds of miles between cities - with no terrain in the way a single strong taut cable wouldn't have much trouble supporting the weight of a passenger.

(That last one probably isn't really true, but it sounds like it might be, which is the important thing.)

Matthew Downie wrote:
thejeff wrote:
Don't worry about trying to apply real world physics to it.

It can be fun to try to figure our some plausible-sounding unreal world physics. Maybe the sun floating in the middle emanates some kind of repulsion force that keeps people stuck to the sides.

Or maybe the world does spin, creating a band of normal gravity where humanoids dominate in the temperate zones. There are whole realms of low or zero gravity near the poles, where dragon-like creatures can fly under their own weight. At the equator is a heavy gravity zone - humanoids can barely survive there, but small dense things can thrive.
Crossing from one normal-gravity band to the other requires a journey of incredible hardship, so there are two entirely separate cultures that know virtually nothing about one another.
However, they can see each other, stretched out across the 'sky' of land and ocean. With a powerful telescope you can make out distant cities above you - perhaps even flash messages across the divide with bright lights.
(An alternative way to cross the equator is to fly directly from one pole to the other using some kind of glider - close to the sun there won't be any pseudo-gravity either, so you just have to be able to withstand the heat.)

Now, does the sun pulse from light to darkness to create nights? Is it dark on one side and light on the other and spins on an axis? Or is it constant so there no night? If so, what effect would that have on society, where you have minimal need for lighting and can sleep when you feel like it? Would people work in shifts? Would they snack and take short naps and have no concept of 'breakfast'?

If you had good engineering skills, you could have cable cars running hundreds of miles between cities - with no terrain in the way a single strong taut cable wouldn't have much trouble supporting the weight of a passenger.

(That last one probably isn't really true, but it sounds like it might be, which is the important thing.)

It can be fun, but it's also likely to lead to contradictions and exploits, quite possibly game-breaking ones.

Spinning a planet for pseudo gravity will need to be much faster than a normal planet spins and will require a much stronger crust, which won't be inhabitable, since it's spinning fast enough to throw everyone off - not to mention the atmosphere.

Huh...This sound somewhat familiar...Ah! You need to have some Lizardfolk in Medium Armor, some Goblins in Medium/Heavy Armor, some Tengu archers,and a bunch of Ogrillons on one side; humans in medium armor, and humans in heavy armor on the other; and the third force should be aberration zombies.

Spoiler:
Halo

Why bother with a crust at all? Your hollow world could be a pocket in an infinitely vast plane. This could be taking place on the elemental plane of earth.

I like Matthew Downie Idea about the two separate cultures separated by the gravitational "ocean." It makes the fact that you are in a hollow world relevant to the plot. Maybe one of the cultures has discovered that it's Chosen One was born in the other gravity band. So the PCs must travel through the vast wilderness that is known as The Lands of Weight to retrieve the Chosen One. Those lands are filled with all manner of bizarre organisms, and the pcs must always contend with the extreme gravity.

Once they arrive on the other side, they find a world that is more alien for how similar it is to their own. The customs are strange and their values clash. The supposed Chosen One is unsympathetic to the PC's plight and uninterested in coming with them. Now they must find some leverage or proceed to kidnap him.

Bodhizen wrote:
I'm going to respectfully disagree with you, here. In an imaginary setting, you can reasonably suspend your disbelief to include beings from other planes of existence just as easily as you can reasonably suspend your disbelief that you're living inside a planet as opposed to living on the outside of its shell. The only significant difference is that you can't easily fly off into space, which requires an equivalent suspension of disbelief to accept that a wooden galleon carries an air bubble with it and survives journeys of millions or billions of miles...

Well, my view about the unbelievability of the setting was mostly a result of my flat world on a turtle campaign, which incidentally predated all the discworld novels.

But I have set a campaign on a world with impossible 4 dimensional geometry which worked OK, and confused the hell out of my players, always a merit.

But if everyone is having fun all is well.

Joynt Jezebel wrote:

But if everyone is having fun all is well

And in the end, this is all that matters. I didn't mean to spark a mathematical, scientific debate regarding the physics of such a world, but it's been an interesting read. My players won't have any trouble suspending their disbelief over a hollow world anymore than they will for spellcasting or dragons. I did ask the question about the distance to the horizon because I do have a math nerd in my group and it's something he would probably ask... lol

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Joynt Jezebel wrote:
CampinCarl9127 wrote:

The circumference of the outside of your planet is 2*Pi*r=21,911.1486 miles. Going off of the assumption that in your world the curve becomes noticeable at 3 miles, or 3/21,911.1486=0.00013642 as a fraction of the circumference.

Now, your interior circumference is 2*Pi*r=18,849.559 miles.

18,849.559*0.00013642=2.57145642 miles.

Round as you see fit. I hope this helps.

This all sounds correct, except what is the reason for saying the curvature becomes noticeable at that point? I am not saying you are wrong, you certainly seem to know your stuff, just asking.

And on hollow worlds, they make most preposterous ideas sound sensible. OK, so gravity holds you to the inside. Why doesn't it cause the crust to all explode outwards due to this "gravity"?

And contrary to an earlier post from campincarl, with realistic physics your party would not fall to the center of the hollow earth. Unless the reason is it is all full of air, so you would fall towards the center of mass. But is that really hollow?

What is clear is the crust would have to be strong beyond belief not to collapse into... something shaped like a planet.

Because the OP said it was. I took the number as a given.

As for the rest...magic.

DRS3 wrote:
With that thin a crust with a hollow interior and 'earth' level gravity wouldn't the whole thing implode? I would think you'd have to make the crust out of some ridiculously hard material just to resist such compression, densely packed earth or pelagic clay probably won't get the job done. {. . .}

Paizo Superscriber; Pathfinder Starfinder Society Subscriber

The Dyson Sphere (see Wikipedia) is a hypothetical structure that advanced cultures might build around a star in order to harness all the energy output of that star.

See also Larry Niven's novel Ringworld, which posits a ring-shaped structure (with the star at the center), with the civilization built on the inner surface, which is concave (high-walled) so that centrifugal force can keep the air "in" the inner surface. Kind of cool because he answers the question of "always high noon" (a ring of vast metal-looking plates and cables rotates much closer to the sun, alternately casting shadow or letting the light through cable-linked gaps have no solid plates, creating zones of light and dark to create day and night). Because the ring is the circumference of a planetary orbit, rather than of a single planet, the view of the "ring" up above is extremely different from what you might see inside a hollow world.

Continuing with Ringworld - I recall there are also meteor-impact sites viewed from "outside" (under) the ring that punch through the surface; when the characters in the novel view the inner surface, they see the ring material deformed to create "mountains" taller than the ring wall (some open at the top like volcanoes) where the meteor punched in (or through), so that no breach would let all the air bleed out.

I realize a lot of that doesn't apply to a hollow world, but it might be helpful for ideas as you think through:
1) Is there a functioning day/night cycle? How does it operate?
2) Does air fill the entire space inside the sphere, or only up to a certain height? If it's all air and you fly all the way "up" to the "sun" at the center, what is its environment like? (Air to the center, and a gate to the plane of fire?)
3) Are there seasons? How do they function? (Spring/Summer/Autumn/Winter? Dry/Monsoon/...)
4) Speaking of weather, does it rain? What other weather patterns might be unique to the interior of a hollow sphere?
5) What form does the passage (if any) between interior and exterior worlds take? (Volcano-like mountains on the inside, the openings of which lead to the passage between surface world? Are the openings only at the north and south poles (a la Hollow World)? Does the world have a Darklands/Underdark equivalent and only passage through it lets you traverse between surface and hollow world?)

A lot of the questions you pose I've not given much thought to, because they won't really be relevant to the adventure. So let's see what I have here:

There is no day/night cycle. Consequentially there are no nocturnal species, though some creatures that live in the shaded gloom of the giant tropical forests have low-light vision. The eternal noon day sun has also caused some creatures to evolve into subterranean versions of their species so they will have darkvision, but are virtually blind outside.

I don't recall if the Pellucidar novels made it clear how high the atmosphere extended above the surface. I'm going to have it thin out at great heights, though will probably extended higher than the surface world's.

There really isn't much seasonal change. The world is nearly one entire jungle, though I will have regions where the forests are made up of giant fungus or very primitive tree-like plants similar to those in Earth's ancient past. There are grassland regions, or at least large spaces where the trees thin out to wooded savannah.

It does rain, oftentimes in disastrous flash floods.

For the purposes of the adventure, there will be a magical portal that leads them to the Inner World (which I've not named yet, btw. I spend a lot of time coming up with names until I find one that I like). In the past, the psionic race that dwells there did conquer a huge portion of my homebrew's largest continent, so a few magical portals were probably not enough to allow massive armies through. Therefore there is probably a different means of of passage, possibly at the poles as described in the Hollow Earth theories.

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Spotting distance will matter more in world like this instead of less.

We do not need to worry about elevation since you see everything from everywhere. You just need enough to see over local terrain.
What is important is how far away you can see a boat or an army.

The rule I came up with is perception check DC 15+1/quarter mile. One can take 20 in 120 degree arch in 2 min or 6 min for everything. Apply size stealth modifiers to this. A telescope halves the distance penalties but take 10 times as long to scan.

-10 for a light rain -20 for heavy rain or light fog -30 for heavy fog.

This allows a lookout with a +20 to perception to see person 12.5 miles away and ship at 20.5 miles.

Navigating should not be all that hard since even a small town should visible at more the 50 miles and mountains can be seen hundreds if not thousands of miles away.

Mathius wrote:

Spotting distance will matter more in world like this instead of less.

We do not need to worry about elevation since you see everything from everywhere. You just need enough to see over local terrain.
What is important is how far away you can see a boat or an army.

The rule I came up with is perception check DC 15+1/quarter mile. One can take 20 in 120 degree arch in 2 min or 6 min for everything. Apply size stealth modifiers to this. A telescope halves the distance penalties but take 10 times as long to scan.

-10 for a light rain -20 for heavy rain or light fog -30 for heavy fog.

This allows a lookout with a +20 to perception to see person 12.5 miles away and ship at 20.5 miles.

Navigating should not be all that hard since even a small town should visible at more the 50 miles and mountains can be seen hundreds if not thousands of miles away.

Great ideas! Thanks!

Well trees will still reduce spotting distance to the standard "In a sparse forest, the maximum distance at which a Perception check for detecting the nearby presence of others can succeed is 3d6 × 10 feet. In a medium forest, this distance is 2d8 × 10 feet, and in a dense forest it is 2d6 × 10 feet."

If one gets above the trees it will be very easy to features more then 10 miles away since you can look down on them instead of across to them.

thejeff wrote:
Bodhizen wrote:
jerrys wrote:
CampinCarl9127 wrote:
I was under the assumption that it already was, unless the entire adventure is everyone piled together at the center fighting to see who gets to stand on top of everybody else.

Side note, but:

It's actually a curious property of hollow spheres and an inverse square law, that there would be no gravitational force at all inside a hollow sphere. i.e. people just float around, they don't fall toward the center or toward the shell. (it's something like: the math works out such that no matter where you are, the section of the crust to your left is pulling with equal force to the section on your right, so there is no net force.) (I guess if it were spinning, there would be a force pushing you to the shell, strongest on the equator.)

Can we assume that Golarion spins on its own axis? If so, I find it perfectly reasonable to assume that a hollow world, whether inside Golarion or otherwise, might also spin on its own axis.

Additionally, you'd only float in either the complete absence of gravity or the existence of equal and consistent gravitational pull from all directions (i.e. the far side of the sphere, which is much further away from you than the near side, pulling on you with equal force as the near side, despite it being much further away). If the pull was stronger the closer you got to a certain side, which makes sense given that we're not equally pulled toward Venus as we are toward Earth, gravity would pull you "down" toward the nearest section of crust as opposed to having equivalent pull on your "left" as it does on your "right".

That is, of course, unless the sphere is so small or the gravitational pull is do weak that you'd float no matter what, or alternatively, that the gravitational pull is so strong that you're effectively glued to a certain portion of the inner shell.

Happy gaming!

No. It really does work that way, though I've forgotten the math involved. Given the usual assumptions of "uniform spherical...

You're correct, assuming a uniform spherical shell: Shell theorem.

Of course, whether a hollow shell world is sufficiently close to uniform is something to think about. As for spinning, that would work at the equator, but get weaker and weaker as you approach the poles.

I don't remember how much detail Elven Star goes into on the subject of Pryan's curvature and gravity, but I rather liked its immense size and the four suns at its center. I don't recall any particularly deep physics involved, but given the nature of the Wave in the Death Gate Cycle it's assumed that physics does not follow the same rules as in our world. So can it be in Pathfinder, and it really doesn't require any more suspension of disbelief than it does to accept that completely nonmagical giants can exist without crushing themselves to death. And don't even get me started on Pathfinder optics....

The world is big. If you want to be 'looking down' at something by even one degree from the horizontal that something needs to be well over a hundred miles away, as I pointed out earlier.

Unless you're on the high seas, or establishing a network of heliograph towers, or flying high above the ground, or maybe - if the atmosphere is transparent enough - checking for large armies mobilizing in another country, spotting distance will not change significantly.

Another thing that gets overlooked for hollow worlds: air conditioning. Heat from the pseudo-star is going to build up fast (too much even for a jungle) unless you also provide something like Shadow Squares with a connection to the Negative Material Plane.

UnArcaneElection wrote:
Another thing that gets overlooked for hollow worlds: air conditioning. Heat from the pseudo-star is going to build up fast (too much even for a jungle) unless you also provide something like Shadow Squares with a connection to the Negative Material Plane.

This is true, but like a lot of "actual science" is something I'll probably overlook in favor of just pure fantasy.

UnArcaneElection wrote:

Another thing that gets overlooked for hollow worlds: air conditioning. Heat from the pseudo-star is going to build up fast (too much even for a jungle) unless you also provide something like Shadow Squares with a connection to the Negative Material Plane.

Unless the sun rotates on the outside of the earth. Then it heats up the inside section that the sun on the outside is at. With the hallow earth being large enough there shouldn't be a "buildup" of heat as cold and hot air rotates.

Cool effect that you could add is that the sun that rotates around shines on the deep roots on the outside of the earth that burrow all through the earth and the trees, plants, etc give off light as they are powered by the sun and shine as regular bright light. Maybe some trees or plants have bulb sacs that are similar to lamp posts. Maybe the grass gives off light. When the sun rotates to the other side of the earth the trees, plants, etc still give off a violet purple glow as it creates a dark and spooky setting as players can somewhat see but only in a 30-60ft distance only.

Maybe the roots that burrow all through the earth bind the earth crust and keep it from imploding or exploding. Who knows, who cares. Maybe the crust is all magnetic plates, maybe gravity originates and is dispersed across the earth's crust as it's charge (or not) by the rotating sun outside. Maybe the trees and roots transfer air, heat, cold, or whatever through themselves to their roots and out to the outside of the earth and vice-versa.

avr wrote:
maybe - if the atmosphere is transparent enough - checking for large armies mobilizing in another country, spotting distance will not change significantly.

Now that is a really cool idea.

You could also see things like tsunami's and cyclones approaching.

Kysune wrote:
UnArcaneElection wrote:

Another thing that gets overlooked for hollow worlds: air conditioning. Heat from the pseudo-star is going to build up fast (too much even for a jungle) unless you also provide something like Shadow Squares with a connection to the Negative Material Plane.

Unless the sun rotates on the outside of the earth. Then it heats up the inside section that the sun on the outside is at. With the hallow earth being large enough there shouldn't be a "buildup" of heat as cold and hot air rotates.

I suspect you may be wrong there kysune.

If there is enough absorption of heat through the crust to make days significantly warmer than nights, ie superficially like the real world, then I am not sure anything like that amount of heat will escape during the night. So it will just keep warming up overall. Air rotating isn't the point, its the accumulation of heat inside.

And with a pseudo sun inside the sphere, sure it will heat up alarmingly, but you will also get some very large discrepancies between air temperatures near and far away from the pseudo sun. This could lead to some really, really intense storms and winds.

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