Hollow Earth Physics
August 17, 2013 4:41 PM   Subscribe

Until last night I was unaware that the hollow earth conspiracy was a thing. Since then, I've been driven crazy by trying to imagine the physics of it. What would gravity be like on a shell planet? Details about the exact setup within.

Consider if you had a shell object made of very dense unobtainium, such that it had the same mass as a solid planet of the same size, but the shell was only a few Km thick.

Would gravity effects on the surface be equivalent between the two?

If you drilled a hole into the shell would objects dropped in go all the way to come to rest in the middle of the shell, or would they just hang out somewhere in the empty void?

Bonus points for physics details about multiple shells, like those in Iain Banks' Matter.
posted by odinsdream to Science & Nature (25 answers total) 4 users marked this as a favorite
I suggest you check out the theories behind the Dyson sphere while waiting for other Mefites who know more math than I do for the rest of it. :)
posted by SMPA at 4:56 PM on August 17, 2013 [1 favorite]

The physics of this is quite simple. On/in a (uniform) sphere, you only feel net gravitational effects from matter at a smaller radius than you. So, for a shell, you are totally weightless once you get inside the surface. Inside the shell, it would be just like being in deep space far away from any matter.
posted by Betelgeuse at 4:57 PM on August 17, 2013 [4 favorites]

Oh. And just to add: the gravity effects of a uniform sphere and uniform shell are totally equivalent - both exert a force as if all the mass was concentrated in a point at the center.
posted by Betelgeuse at 5:01 PM on August 17, 2013 [3 favorites]

Imagine yourself inside the sphere somewhere, and you're a mathematical point. Now project a square onto one side of the sphere. Draw lines from the corners of the square to your point, and then extend them to the other side, forming another square.

If it's further away, it's also larger. If the composition of the sphere is unform, then it turns out that the gravitional effect of one of those squares on you exactly balances the gravitational effect of the other one. Since every part of the sphere is balanced by the part opposite it, you are not subjected to any unbalanced gravitational force -- and you are in freefall.

That's true no matter what the sphere is made of, as long as all of it is made of the same stuff.
posted by Chocolate Pickle at 5:04 PM on August 17, 2013 [2 favorites]

The gravitational coefficient of acceleration on earth (g) is derived roughly from Newton's law of gravitational attraction; g = G*m1*m2/r^2, where G is the gravitational constant, m1 is the mass of the earth, m2 is the mass of the moon, and r is the distance between the centers of mass of the earth and the moon. If the earth was hollow with the same density characteristics as in reality, then the value of the scalar m1 would be much smaller, and thus g would also be much smaller. Recall that density = mass/volume.
posted by oceanjesse at 5:13 PM on August 17, 2013

As others have mentioned, the gravitational force due to a shell inside that shell is zero. so the occupants inside would feel that the gravitational pull due to earth is zero.

Here is the proof.

They however would feel the pull of Moon etc and so there would be an ever changing direction for gravitational pull. water globules inside would constantly be sticking to the side of surface closest to moon. and thus would become an ever-rolling tide on the surface.
posted by TheLittlePrince at 5:19 PM on August 17, 2013 [11 favorites]

To add an extra layer of fun, it seems to be a common belief that the actual interior of the hollow earth is somehow extra-dimensional or supernatural in nature. Of course, this explains why all of the observational evidence speaks against the idea. It works sort of like Portal in my imagination.
posted by feloniousmonk at 5:36 PM on August 17, 2013 [1 favorite]

For historical background the hollow earth theory originated with John Cleves Symmes, Jr. in his No. 1 Circular.
posted by plastic_animals at 6:00 PM on August 17, 2013

If memory serves, some of the earlier hollow-earthers - Cyrus Teed was one, if I'm not mistaken - believed that there isn't really such a thing as gravity and that we are held onto the surface of the Earth by centrifugal force.
posted by FAMOUS MONSTER at 6:55 PM on August 17, 2013 [1 favorite]

Would gravity effects on the surface be equivalent between the two?

To answer this question specifically, the gravity effects on the surface would indeed be exactly the same.

For anything that is spherically symmetrical, the gravity acts the same as though the entire mass is concentrated at a point in the center of the sphere.
posted by flug at 7:42 PM on August 17, 2013 [1 favorite]

Bonus points for physics details about multiple shells

As others have pointed out, above, if you're inside a hollow sphere--anywhere inside the sphere, it doesn't really matter where--the gravitational forces of the mass in the sphere's shell cancel out. You get no net gravity at all--'weightlessness' so to speak.

And as I pointed out above, for any hollow sphere that you are outside of, the mass of that sphere acts, for gravitational purposes, exactly as though it is concentrated at the center of that sphere (or, equivalently, exactly as a spherical planet of the same diameter and mass).

So for the 'multiple shell' system, just put those two ideas together:

- Any shell that is outside of you has no gravitational effect at all

- Any shell that you're on the outside of has gravitational effect of of a planet of that radius and mass

So in short, to calculate gravitational effects, ignore all shells outside of you. Sum the mass of all the shells inside of you and use that total mass plus your distance from center of mass to figure the force of gravity using the usual formula (which you can find here, if curious).
posted by flug at 7:56 PM on August 17, 2013 [1 favorite]

I love Hollow Earther's. They have so much pluck!

Way at the bottom, I'm going to speak to the gravitational question you posed. Stay with me...

Regarding Hollow Earth, you could read Jules Verne's Journey to the Center of the Earth, but hot damn if the 1959 movie isn't AWESOME!!

It really got me going as a kid, but like you, I did not know until recently that this was A Thing.

I'm going to stop here and add a bunch of varied resources for you to explore + add one giant rabbit hole for you to jump into. Are you with me? Good.

Star Trek Next Generation has an episode where they encounter a Dyson Sphere and discuss the physics. In fact, it's the episode where Scotty (James Doohan,) the original Enterprise engineer, makes a guest appearance. It's called Relics.

Now. iTunes Podcasts have become infinitely more searchable - so if you google names of Hollow Earth Theory promoters, individual interviews across various shows will be available to listen to.

Similarly, if you go to a website called RedIceCreations.com and search their site using the term, "hollow earth theory," I'm sure you'll come up with a bunch of podcasts to listen to, just to get you started. In fact, I'll do that for you now.

Hope that link works out like I planned, with the search answers to relevant podcast discussions about Hollow Earth Theory.

Here is the rabbit hole!

Recently, I heard a podcast with someone talking about the politics of Math and Science. They specifically stated that current Science does not actually know what Gravity *IS*.

The complaint was that although Gravity was observable and measurable, current science doesn't really know how it is created, and that any mathematical formula related to its calculation is theory, not fact or law.

This person was not concerned with Hollow Earth Theory, only the toxic politics of Science and Math. Being keen on your question, I immediately related this statement to the curiosity that is Hollow Earth Theory. Maybe the proponents of Hollow Earth are on to something?

I'm off to search out this statement. The problem is that this Gravity thing was a small example in a larger thesis. I'll update as I research exactly who said scientists only have a theory about gravity, but no idea what it really is.

I immediately related their statement to the Hollow Earth Thing, even though I'm pretty sure they didn't.

OK. I'm off to hunt down this link for you.

posted by jbenben at 11:41 PM on August 17, 2013

The bigger problem is the gravitational effect between the Hollow Earth and the sun. Any Hollow Earth theory (that doesn't reject gravity) has to preserve the Earth-sun gravitational attraction from conventional astronomy, so that Earth's orbit doesn't change. That means either the Earth has the same mass as now, but all smushed into some unbelievably dense shell. Or the Earth is less massive, and the sun must therefore be more massive to compensate, and then all the planets must be less massive to compensate for that, etc.
posted by vasi at 11:53 PM on August 17, 2013 [1 favorite]

If you google, "Gravity Not Proven," you'll come up with heaps of links.

Follow the first link, and you'll find a video of Stephan Hawking and Michio Kaku admitting Science can't pinpoint yet what Gravity is.

Gravity is a Theory. So, no, we can't REALLY tell yet via Science if Hollow Earther's are right or wrong.

How fun!
posted by jbenben at 12:27 AM on August 18, 2013

A theory is not the same as a hypothesis, as a theory is a 'proven' hypothesis, that, in other words, has never been disproved through experiment, and has a basis in fact.
posted by oceanjesse at 12:35 AM on August 18, 2013 [5 favorites]

Also, I love that this red ice creations site considers the possibility of a hollow earth while a side widget tracks anomalies in the earth's magnetic field. It's funny because the earth has a magnetic field because of its iron core. Woo-tastic! Ok, I'll stop now.
posted by oceanjesse at 12:41 AM on August 18, 2013 [1 favorite]

the gravity effects on the surface would indeed be exactly the same.

I'm not so sure of this. Yes, at a great distance, (like the distance to the moon) the gravity would be the same. But this unobtainium must be pretty dense stuff, and it's concentrated right at the surface, some of it right at your feet. I wonder if that might cause gravity right at the surface to be greater than normal earth gravity, which would then decrease faster than normal gravity does as you traveled away from that surface. You know, that g1g2/d2 stuff.
posted by DarkForest at 1:14 PM on August 18, 2013

No, the shell theorem is not an approximation, so it applies at any distance outside the shell.

Shell theorem bonus: we also wouldn't be able to gather gravitational evidence of crystal spheres around the earth by observing its effects on the planets inside it.
posted by jepler at 3:47 PM on August 18, 2013 [2 favorites]

Just to be totally clear, I am not a hollow-earth-theorist or really interested in the conspiracy angles beyond the physics. I'm more interested in it from the Big Dumb Object perspective and how realistic physics would apply to such an object.

So I think I understand that if we're really talking about a perfect sphere, gravity would be the same on or above the surface. But, if you took the shape of the actual earth, which isn't perfect, wouldn't you have gravitational hotspots? It seems like their significance would be related to the thickness of the shell.
posted by odinsdream at 5:49 AM on August 19, 2013

Don't try to understand it. It will only drive you crazy, because it's a crazy theory believed in by crazy people. It's got nothing whatever to do with the real world, or physics or any other science.

Giving a logical argument will produce only angry denial.

Just walk (or preferably run) away.
posted by KRS at 6:34 AM on August 19, 2013

KRS, maybe I'm not being clear. I don't believe there is such a conspiracy or that the earth is actually hollow. I'm asking about how such an object, if it did exist, would behave. This is the same kind of speculative question as figuring out how fast Larry Niven's Ringworld would need to spin, or how tall the sidewalls on a Banks Orbital would need to be to keep in atmosphere, for example.

I'm not asking how people justify the insane belief that we actually live on a hollow planet.
posted by odinsdream at 8:19 AM on August 19, 2013 [1 favorite]

But, if you took the shape of the actual earth, which isn't perfect, wouldn't you have gravitational hotspots? It seems like their significance would be related to the thickness of the shell.

In real life, the real earth has various irregularities (not perfectly spherical in various ways, various masses that are not distributed symmetrically) and these can be detected, and in fact are detected, by various experiments that map the Earth's gravity field in detail.

But, given any particular configuration of a gravitational field created by a near-spherical object (like the Earth) you could quite certainly duplicate that exact gravitational field by a near-spherical thin-shell type object. You just manipulate the thin shell to have various asymmetries and so on. It's thicker in some places, thinner in others, it has various components with greater or lesser mass, etc. Designing a thin-shell very-close-to-a-sphere-shape that has a geoid identical to the geoid of a close-to-filled-in-sphere shape is the sort of problem that is always going to be solvable, as long as you are allowed to use materials with any needed density.

So in terms of gravitational field alone, I'm 100% confident it could be done, given the right sort of unobtanium of necessary density.

Where the hollow earthers run into trouble, though, is gravity isn't our only source of info about the Earth. Once you're trying to duplicate every characteristic of the actual Earth with a hollow shell, it gets much harder. How are you going to model continental drift, the planetary magnetic field, various thermodynamic-related facts about the Earth (heat of the interior, etc), the exact characteristics of seismic waves passing through the Earth's interior, and all the other physical details the actual Earth has?

The answer is, of course you can't model all those things with just the 'hollow shell' model of the Earth, and that's why scientists don't use that type of model. But I suppose it's fun to try . . .

this unobtainium must be pretty dense stuff, and it's concentrated right at the surface, some of it right at your feet. I wonder if that might cause gravity right at the surface to be greater than normal earth gravity

Don't want to get into a debate here--and really only answering this because the response might be enlightening to the OP--but nope! The Shell Theorem is pretty surprising to most people, so I'm not surprised that your disbelieving if this is the first time you've heard of it. But it's very well established. And you don't have to be miles or millions of miles outside the shell for it to work--an inch or a millimeter will do. Really you just need to be outside the sphere, even standing right on it will do.

In (very) simplified terms, the fact that in the shell you have a whole lot of very concentrated mass very close to you, right under your feet, is exactly compensated for by the fact that there is then nothing but empty, mass-less space for thousands of miles, all the way to the other side of the shell. Whereas in the actual Earth all those thousands of miles between you and the opposite side of the earth are filled up with very massive stuff, all of which exerts a gravitational force on you.

With gravity it is a combination of mass and distance that creates the total effect, and it just so happens that those two effects just cancel each other in the cases of the filled sphere and hollow shell sphere.

It's quite amazing and, indeed, unexpected that these two situations are identical, but they are. It's like when you start out with a really complicated algebra problem and it magically turns out that you can cancel a few terms, then a few more, then a few more, and after a few pages of complicated calculations you come up with the result, "=1". That just doesn't happen in real life--but here's a case where it does! Everything cancels out and the filled sphere really is identical to the hollow shell, in gravitational terms.

posted by flug at 4:26 PM on August 19, 2013 [1 favorite]

flug; your "aside" is exactly why I asked this question. Thank you.
posted by odinsdream at 5:12 PM on August 19, 2013

What about rotation? Centrifugal force! If present, it'd cause maximal interior 'gravity' at the equator and zero 'gravity' at the poles, which, since the earth is not like that, would be enough to disprove the whole idea that the earth is inside-out. But then again, the poles are magnetic...
posted by Sys Rq at 1:06 PM on September 11, 2013

odinsdream: "If you drilled a hole into the shell would objects dropped in go all the way to come to rest in the middle of the shell, or would they just hang out somewhere in the empty void?"

I'm curious about this part of the question. I'm assuming the object would fall and gradually experience less gravity as it got closer to the inside, then zero as it passed the inner edge? Since it had momentum, it'd just keep going at the speed it had as it passed the inner edge (atmospheric friction notwithstanding), eventually bouncing off the opposite side of the sphere?
posted by Joakim Ziegler at 9:51 PM on September 13, 2013

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