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I've been wondering, would it be possible to achieve levitation of an object in the center of mass of a planet?

I ask this because the gravity is the attraction between bodies and theoretically the planet would pull the object to every side at the same time with the same force in its center of mass, making it in theory, levitate.

Am I missing any physics law in my theory?

As I said I'm only interested in the theory

DGaspar
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  • Welcome to WorldBuilding! If you have a moment please take the [tour] and visit the [help] to learn more about the site. Have fun! – Secespitus Jul 04 '17 at 09:09
  • I think the more interesting question is where that point would be. Certainly not at the exact (mass weighted, geometric?) centre of earth, you would still feel the sun, moon and centrifugal forces. Also how does one even construct such a pocket deep within the earth? If you want your story believable, you should ask that last question first. If you are new to physics or forces in general, check out https://en.wikipedia.org/wiki/Electrostatic_levitation and understand how this is exactly the same – Raditz_35 Jul 04 '17 at 09:33
  • @Raditz_35 I was not asking how such a hole would be made for that there is this https://worldbuilding.stackexchange.com/questions/84875/is-planetary-drill-possible?noredirect=1&lq=1 – DGaspar Jul 04 '17 at 10:15
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    Your understanding of physics is basically correct, but, naturally, you need a hollow space filled with air at the centre of mass. It will float because it's effectively weightless, or in microgravity, if you want to be exact, levitation implies something is lifting the object up. So it's not levitation. – a4android Jul 04 '17 at 10:59
  • @DércioGaspar You mean the thread where everyone says that you cannot "drill" through the earth offers a solution to your problem of having a pocket of air at the core? I want to know how to do this as well, could you do me a real favor and include a statement in your question how you would do that so that I learn something? – Raditz_35 Jul 04 '17 at 11:16
  • See also this question and answer with mention of toroid planet. – user11153 Jul 04 '17 at 12:06
  • Good theoretical question. It's one of those questions you ponder about but then forget. Probably impossible in practice though. – n00dles Jul 04 '17 at 14:35
  • Yes, I know it is impossible to achieve with current technology, but that was not the question. I was asking if my logic was correct, not if it was possible – DGaspar Jul 04 '17 at 14:42
  • It sounds as if most or all of these answers, and probably the original question, assume that this "planet" is at least mostly spherically symmetrical. It's easy to come up with a shape where there is a significant gravitational pull at the center of gravity (e.g. a sphere with a large protuberance). – Daniel Griscom Jul 04 '17 at 21:17
  • @Raditz_35 how is that at all relevant? Why do you presume one is making a story? What if this person is simply curious about whether that could occur believably. I've seen many questions ask things that were actually prompted by seeing the event in some other story and just wanting plausibility or deniability due to them doubting its realistic result. – user64742 Jul 04 '17 at 23:39
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    @Typhon "Why do you presume one is making a story?" Uhm, because this is the worldbuilding.SE? – Fl.pf. Jul 05 '17 at 08:06
  • Btw, the possibility was raised in Hal Clement’s novel Still River – JDługosz Jul 05 '17 at 08:33
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    Why all the people reading "Earth" when OP just said "planet"? – dmcontador Jul 05 '17 at 10:08
  • If it's at the center of a planet, it's not going to be air... – R.. GitHub STOP HELPING ICE Jul 05 '17 at 15:49
  • Perhaps relevant: The Algebraist by Iain M Banks. – Sobrique Jul 05 '17 at 16:49
  • Dupe? : https://worldbuilding.stackexchange.com/questions/1137/hollow-planet-with-another-planet-inside-it/

    Also on Physics: https://physics.stackexchange.com/questions/139144/stability-of-planet-enclosing-shell-supported-by-atmosphere/139208#139208

     – Rick Jul 05 '17 at 19:26
  • The Briefly, the answer is yes. But it is not appropriate to speak of levitation, which is commonly used to speak of somehow opposing the force of gravity so that an object does not fall. In this case there is no force of gravity to oppose, the net gravitational force at the centre of mass being zero. Other answers dealing with air, the difficulty of digging holes, influences of sun and moon, anisotropic distribution of mass and other things are all irrelevant to the question as posed and may be disregarded. – Anton Jul 05 '17 at 23:21

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By the shell theorem any body inside an hollow spheric shell would not feel the gravitational attraction of the shell, for the very reason you mention. And that not only in the center of the sphere, but anywhere in the hollow space comprised by the shell.

So, provided you can drill till the center of the planet and make an hollow space, any body placed there would experience (in the approximation of the theorem, from which a real planet is quite far) no gravitational pull from the planet surrounding it.

L.Dutch
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Both theoretically and practically: no.

Earnshaw's theorem (which was initially developed for electrostatic forces, but is valid for gravitational forces as well) states that no static configuration of attractive (or repellent) forces can result in a in a stable stationary equilibrium.

The object might float for substantial time (depending on how precise you position it in the gravitational center), but any misalignment or disturbance, no matter how tiny, will eventually cause it to drift off-center, with increasing speed. This is very different from an object circling a planet, which might will continue to circle the planet even when its orbit is significantly being disturbed.

Anyway: a civilization which is capable of hollowing out a planet can easily provide means for active stabilization of such an object. I suspect that this civilization uses the center of their planet for recreational purposes. "The Menace from Earth" by Heinlein comes to my mind (even though the story deals with Moon's reduced gravity, not zero gravity). Note that the air pressure at the center of the planet might be substantial, if not kept under control by airlocks or other mechanisms.

Klaws
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    +1 for pointing out that, even if such an impossible feat would be accomplished, retaining such an object perfectly balanced would prove equally impossible. The whole universe as we see it formed due to such tiny disturbances. – r41n Jul 04 '17 at 14:03
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    By the shell theorem (see link in another answer), the object would float anywhere inside. However, the shell theorem's premises include a perfectly symmetrical homogenous sphere. So if Jules Verne's hollow earth were achievable, there would be some net gravity vector everywhere, but it wouldn't be much and it wouldn't always be "down." – WGroleau Jul 04 '17 at 14:43
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    No planet can be perfectly symmetrical unless it is intentionally built that way, *and* it would also require zero moving things on the surface, *and* it cannot be orbiting a star (which causes tidal differential gravity, solar tides on Earth), etc. Anything in the center will drift. Heck, quantum fission of elements in the floating object will impart microscopic thrust, so will the random motion of air molecules and other molecular vibrations. Earnshaw wins, the shell model is purely theoretical and IRL impossible to achieve. – Amadeus Jul 04 '17 at 15:46
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    Earnshaw's theorem is about a collection of point charges. The arrangement described by the OP, specifically being inside a hollow world, cannot be described using only points, so this answer is actually null and void. – Octopus Jul 04 '17 at 16:33
  • @Amadeus *and* nothing can be orbiting the planet, either, right? – Dan Henderson Jul 04 '17 at 17:10
  • @DanHenderson I should think that orbiting object (call it a moon) would also gravitationally drag the object around, making its center of mass misaligned with the planet's center of mass, thus increasing the planet's pull of gravity on the same side as the moon and decreasing it on the side opposite the moon. I haven't done the math but, with no resistance (it was floating to start), I suspect the object at the center will spiral out to hits the inner-wall of the hollow center. The moon induces a tiny offset, then much amplified by having >1/2 the planet on one side and <1/2 on the other. – Amadeus Jul 04 '17 at 17:57
  • @Octopus Why not? Each atom (or smaller) is a gravitational point charge. There's a very large but finite number of atoms in a planet. – user253751 Jul 05 '17 at 02:26
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    @immibis Earnshaw's theorem only applies if all of the particles are free to move independently. The planet would naturally have some amount of structural strength to it and so Earnshaw's theorem doesn't apply. – AJMansfield Jul 05 '17 at 02:46
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    "with increasing speed"? According to https://en.wikipedia.org/wiki/Shell_theorem "no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell". – Nicolas Raoul Jul 05 '17 at 10:17
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    That the equilibrium cannot be stable does not mean it must be unstable - it could be indifferent – Hagen von Eitzen Jul 05 '17 at 14:42
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    The comment by Klaws is entirely flawed. If the object is stationary at the centre of mass of the planet, there is no force on it. It follows that it will not move. Nor is there any way that work can be done on the object to increase its kinetic energy. Klaws is entirely wrong therefore to talk of "increasing speed". Earnshaw's theorem is irrelevant. – Anton Jul 05 '17 at 23:18
  • I don't think it is applicable here. The bottom of the wheel of gravitational potential will be such fixed point. In theory an object - or dark matter particle - would just work as pendulum across the center (as Earth does around Sun) if they were misalligned however in practice a friction will put it to stop until the amplitude is equivalent to Brownian motion. For sure it won't "drift off-center, with increasing speed" as it would violate conservation of energy - such object would gain both potential and kinetic energy. – Maja Piechotka Jul 06 '17 at 06:24
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    If you add an atmosphere the gravity of the atmosphere would likely dominate any deviations from the shell model. Thereby stabilizing objects in the center. – Rick Jul 06 '17 at 14:43
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Theoretically - yes.

Practically - no.

If you are at a point in space and you are surrounded by a homogeneous shell of matter, the gravitational gradient would be 0, you would float. (Newton, Gauss and other proved that, it is mathematically fairly easy to prove).

Practically, the earth is not really homogeneous, and making a hollow sphere at the center of the earth would be practically impossible due to the gravity at the core. Also, the deepest hole man has ever drilled is 12 km, and with an earth radius of 6.000 km that is nowhere near the center. Problem is pressure, heat and torque (the longer the rod, the more "twisted" it gets when drilling). Everything melts, there is no material known which can withstand the pressure and heat combined with the heat of friction from drilling.

Also, if you didn't experience gravitational pull from the earth anymore, you would still feel it from the moon and sun.

Fl.pf.
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    Some SF story describes an approach by an alien race to hoolow out the Earth by drilling a hole as far as they get, then blasting though the remainder of the crust and then, somehow, allow the liquid core to drain from the Earth. I don't remember the exact details. The drill hole was, most probably, in Great Britain, as, whenever the Daleks or Doctor Who pick a random landing spot or do a crash landing, they land somewhere in GB. Possibly near London. Or a quarry in Wales: http://tvtropes.org/pmwiki/pmwiki.php/Main/BBCQuarry – Klaws Jul 04 '17 at 12:53
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    Although you would feel the pull from the Sun, you wouldn't fall towards it, for the same reason the Earth doesn't, right? – Mark Jul 04 '17 at 13:39
  • @Mark you're right, you would maintain the orbital momentum. The moon would pull you around though ;) – Fl.pf. Jul 04 '17 at 13:42
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    As this is a question on worldbuilding, and not on how to actually drill a hole in our Earth. So practical complications that prevent us humans to do this to our own planet are out of the scope of the question. –  Jul 04 '17 at 14:52
  • @Geliormth not really true. Even aliens have to obey the laws of physics. And I answered the question, I just added more information – Fl.pf. Jul 04 '17 at 14:53
  • But the gravitational force from the moon and sun should move the earth just as much, so in relation to your position within the hollow earth that would not affekt you right? – Alex Jul 05 '17 at 06:48
  • @Klaws The notion of "hollow planet" is also present in SF/fantasy without having to "dig out". The Brentford Triangle series of books by Robert Rankin feature the idea (albeit mostly in the mind of one individual) of an earlier race living "in the centre of the planet" (and IIRC in one book this place is visited). To some extent Magrathea (of Douglas Adams' Hitchhiker's Guide to the Galaxy), although an artificial creation, also qualifies. – TripeHound Jul 05 '17 at 06:51
  • The gravitational pull of the Sun and Moon would be the same for the inner object and for the outer shell, so that would not affect "levitation", in the same way that an astronaut in a spaceship in orbit can "levitate" despite being affected by the gravitational pull of Sun, Moon and Earth – SJuan76 Jul 05 '17 at 07:40
  • @SJuan76 that's can't be entirely the case, since then we wouldn't have tides, right? – Fl.pf. Jul 05 '17 at 08:04
  • Uhhh.. we have tides because Earth (and specially water) is not a completely rigid solid, which makes for the portions of Earth more affected by the external body gravity to be displaced. With a solid body a) you do not have tides and b) the gravitational force by any object is the same as if you applied that force to the center of mass of the object. – SJuan76 Jul 05 '17 at 08:08
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    You could probably compensate somewhat for the non-homogeneous nature of the planet by making your hollowing out area irregular to match, but the end result is a space in which you feel weightless, and will carry on until you bump into a wall, not somewhere where you will be attracted towards the centre of the sphere. – rjmunro Jul 05 '17 at 08:42
  • @rjmunro uhm no sorry, that's not how things work – Fl.pf. Jul 05 '17 at 08:47
  • @Fl.pf. What isn't how things work? The OP seems to be asking for a state where you would be attracted to the centre of the sphere. That's impossible. If the sphere was perfect, you would feel perfectly weightless inside, and would travel until you hit a side (not attracted to the centre). If the sphere was imperfect, there would be some amount of gravity inside it, drawing you towards the edge somewhere. I stated that you could attempt to reduce this by hollowing out more on the side you were drawn to, but only "somewhat", not completely unless the sphere was perfect. – rjmunro Jul 05 '17 at 12:51
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The main issue should be the stability of the balance. The center of a shell isn't a stable balance point, so even if you need a lot less energy to keep the object at a specific point, every little moves will take it away from the center.

Alexis Le Gal
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    Welcome to WorldBuilding Alexis! If you have a moment please take the [tour] and visit the [help] to learn more about the site. Have fun! – Secespitus Jul 04 '17 at 12:03
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Assume for a moment that the situation exists. How it comes about is beyond the scope of the question.

Assume also that the outer body is thick enough to generate the gravity to keep the outer biosphere from floating away, while thin enough to leave sufficient space between the outer and inner bodies. Both bodies rotate and have centers of gravity. Theoretically, as long as the centers of gravity coincide, the system will remain stable.

The main problem is, interesting systems are dynamic, not static. A habitable world will have tides, magma, tectonic activity, and other disturbances to the equilibrium. It's possible the system could have a strange attractor (see chaos theory) that it tends to return to, in other words a self-correcting wobble.

In geologic time, though, it's inherently unstable. Rotation rates change, things shift, outside forces interfere. A moon, for instance, would unbalance everything. Several moons, on the other hand, could make it more stable. If you could adjust the trajectory of one or more moons, with some furious hand waving, it could work.

Ralph Crown
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  • By "(un)stable," do you mean the OP's idea that a net gravitational vector would be zero, resulting in a stable position, or that the gravitational changes would over a long enough time cause the planet to deform or break up? – WGroleau Jul 04 '17 at 14:47
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Yep, as gravity acts on all sides, so if you had a planet with an empty space or a space full of gas at the center for some reason, the gravity on whatever object is at the dead center would make a net force of 0, so it will float at the center of mass.

TysonDennis
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I am no physicist but I know that gravity exists where dense matter bends the space. Denser the matter - greater the gravity pull.

Every planets core should be the densest place on(in) it, it is being perceived as a gravity pull towards its surface, towards the planet's center. However, if we hollowed the core it would no longer be dense so no gravity there. Also the planet would disintegrate without the gravity holding it together.

The only solution would be this:

  • the floating core is incredibly dense so it would have its own gravity field that could hold the rest of the planet around it.
  • the hollowed out core should have a spherical shape and its walls should withstand extreme pressure from outside and not collapse
  • planet should be a perfectly symmetrical sphere

As I said - I am no physicist but would it work?

The gravity core would float inside the hollow spherical center that wouldn't allow the planets matter to collapse towards the core. If the planet would be a perfect sphere and the core would be precisely in the middle, the gravitational pull in every direction would attract the same amount of matter which would be held in bay by the hollowed core inside walls. Therefore the core would be always in the center of the planet, it would actually float.

In reality this structure (planet) would be highly unstable and couldn't exist naturally. Even to artificially construct such an object would be incredibly hard

Mārtiņš Radiņš
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    Can you rewrite your argument? I find quite hard to understand what you state. – L.Dutch Jul 05 '17 at 08:31
  • Welcome to WorldBuilding! If you have a moment please take the [tour] and visit the [help] to learn more about the site. Have fun! – Secespitus Jul 05 '17 at 08:33
  • I'm quite sure you mix the cause and effect. Planets are denser in center because this is state with least gravitational energy, however it is not a strict requirements. It is possible to have a 'balloon' planet - assuming crust would have sufficient compress strength - with air inside. However it is certainly unlikely for such planet to arose naturally and it is unstable configuration. If anything would disturb the dome it would collapse to center and air would form atmosphere. – Maja Piechotka Jul 06 '17 at 06:30
  • Please don't downvote my answer just because you don't understand physics... – Mārtiņš Radiņš Jul 06 '17 at 09:13
  • @MaciejPiechotka I described how such a planet would even exist, I don't quite understand what did you mean with "cause and effect". Also, as I said - I am not a physicist, but the denser the matter, the greater the gravitational pull, so "Planets are denser in center because this is state with least gravitational energy" is completely false. – Mārtiņš Radiņš Jul 06 '17 at 09:18
  • @MārtiņšRadiņš (I haven't downvoted your answer) - sorry now I misunderstood your comment. – Maja Piechotka Jul 06 '17 at 16:13
  • @MaciejPiechotka That wasn't meant for you :) – Mārtiņš Radiņš Jul 10 '17 at 07:00