Hollow Planet Mathematics

[MarkB]

One alternative to having a magical gravitational field in the crust would be for there to be an anti-gravity field emanating from whatever light source you put in the centre of the world - so rather than being pulled down by the shell, you're being pushed out from the centre.

That would allow for a more uniform gravitational effect inside the world, and could be tied into its mythology - perhaps, when the gods placed the energy source in the world's centre, they knew that the power it represented would be a temptation to its inhabitants, so they gave it a physical repulsion effect as a form of protection. The simulated gravity is merely a side effect.

 

[Kaodi]

One alternative to having a magical gravitational field in the crust would be for there to be an anti-gravity field emanating from whatever light source you put in the centre of the world - so rather than being pulled down by the shell, you're being pushed out from the centre.

That would allow for a more uniform gravitational effect inside the world, and could be tied into its mythology - perhaps, when the gods placed the energy source in the world's centre, they knew that the power it represented would be a temptation to its inhabitants, so they gave it a physical repulsion effect as a form of protection. The simulated gravity is merely a side effect.

I do not know. Personally I was not going to have a visible light source or worry about how gravity works the way it does. Because if you start messing around by making gravity a push, you might start having weird physical implications which also now have to be explained away. Falling damage, for instance, would either be negligible or things would become "heavier" the higher they rose up in the air... All structures would have to be more pyramid shaped I think in the latter case. And this because the repulsion field must either get stronger the closer you get to it, or anything that can fly could reach it. I think hand-waving gravity so as to work properly would be much easier...

 

[Janx]

I do not know. Personally I was not going to have a visible light source or worry about how gravity works the way it does. Because if you start messing around by making gravity a push, you might start having weird physical implications which also now have to be explained away. Falling damage, for instance, would either be negligible or things would become "heavier" the higher they rose up in the air... All structures would have to be more pyramid shaped I think in the latter case. And this because the repulsion field must either get stronger the closer you get to it, or anything that can fly could reach it. I think hand-waving gravity so as to work properly would be much easier...

I think you're being overly picky, especially when dealing with a fictional construct for the purposes of playing a fantasy game.

it's trivial to rule that the anti-gravity/reverse gravity field pushes in all directions from a center point with equal force. Just like real gravity pulls all objects toward the center point. it's the exact same thing in reverse.

For jumping, the force affecting you pushes in a straightline from the center through you to the ground in the shortest path (assuming a smooth sphere surface). The same as the gravity, pulls you down in a straight line to the center of the earth.

I do get what your concern about pyramid shaped buildings. I would think though, that this would olny be an issue for very tall and wide buildings. Otherwise, the angle from the center to the ground crossing the edge of the building is likely to not be significant to cause torque on the edge of the building. and this effect is comparable to what ancient builders had to overcome, which is why for a long time, buildings had a limit on the height man could build. It's why walls were thicker on the bottom than on top.

Using eye-ball guesstimation, it doesn't have to be a problem. I suppose if you pull out your slide-rule, the math won't work out in some niggling way.

The point is, the anti/reverse gravity sun is a pretty clever solution, and it's more plausible than using centrifugal force which causes the poles to have 0G (though a case could be made that Giants live closer to the poles, and the regular races live near the optimal 1G zone).

A problem I'd be curious to hear, is how to make the sun set/rise.


I once did a campaign based on the world being like Order of the Stick. All stick figures. The would was truly flat, yet wrap-around. The sun traveled acros the center (well, a designated center) in a line (thus forming the equator). I also deemed that the sun existed at all places along that line such that there were no time zones. Regardless of where you were, if it was noon, the sun was directly overhead. If it was sunset, it was in the west (of the observer's position).

 

[Kaodi]

The point is, the anti/reverse gravity sun is a pretty clever solution, and it's more plausible than using centrifugal force which causes the poles to have 0G (though a case could be made that Giants live closer to the poles, and the regular races live near the optimal 1G zone).

A problem I'd be curious to hear, is how to make the sun set/rise.

Like I said, personally I would do a lot of handwaiving. For instance, if the campaign world is a demi-plane, it is trivial to determine that gravity works however the plane's creators wanted it to. I would make it so that at the centre gravity would equally pull in every direction. Of course, since the centre is really just a point, and surrounded by air, it would probably be impossible to place something at the exact centre and have it stay there for very long.

The light problem would also just be solved by magic... The world arbitrarily becomes light and dark. Either light would seem like it comes from the direction from the centre, so that shadows can still appear below things, or it actually lights up the entire world, including inside and underground. Shadows would still be cast by alternate light sources normally.

 

[Aloïsius]

I think it's easiest to solve the problem by making the hollow earth a giant cavern similar to a "void" onion layer inside the earth rather than making the whole planet hollow. This way, you have no problem with up and down, as they are still in the same direction than at the surface. The surface crust would be supported by huge pillars, and would be a very thin one. Just fill the cavern with a lot of water vapors (volcanism...) so that no one can see the "ceiling" from the ground. Add some kind of light source if you need one.

 

[Beginning of the End]

This is more like what I was talking about, though big enough it is more like, " the ground looks reasonably flat to me, " such that at least if you shot an arrow the surface distance that could be covered would be neglibily affected by the curvature.

My understanding is that in an O'Neill colony you'd get weird arrow flights and the like because the "gravity" is actually a centrifugal spin. But if you're handwaving the gravity so that it works normally, then hollow spheres as small as an O'Neill colony would give you the effect you're looking for.

So, basically: If you're looking at anything even remotely planet-size, you won't have problems.