# Would an object float in mid air at the center of mass of a planet

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

• Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! Commented Jul 4, 2017 at 9:09
• 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 en.wikipedia.org/wiki/Electrostatic_levitation and understand how this is exactly the same Commented Jul 4, 2017 at 9:33
• 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. Commented Jul 4, 2017 at 10:59
• @Typhon "Why do you presume one is making a story?" Uhm, because this is the worldbuilding.SE? Commented Jul 5, 2017 at 8:06
• Why all the people reading "Earth" when OP just said "planet"? Commented Jul 5, 2017 at 10:08

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.

• Comments are not for extended discussion; this conversation has been moved to chat. Commented Jul 7, 2017 at 2:10

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.

• +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
Commented Jul 4, 2017 at 14:03
• 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. Commented Jul 4, 2017 at 16:33
• @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. Commented Jul 5, 2017 at 2:46
• "with increasing speed"? According to 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". Commented Jul 5, 2017 at 10:17
• That the equilibrium cannot be stable does not mean it must be unstable - it could be indifferent Commented Jul 5, 2017 at 14:42

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.

• 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: tvtropes.org/pmwiki/pmwiki.php/Main/BBCQuarry Commented Jul 4, 2017 at 12:53
• 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
Commented Jul 4, 2017 at 13:39
• @Mark you're right, you would maintain the orbital momentum. The moon would pull you around though ;) Commented Jul 4, 2017 at 13:42
• 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.
– user26494
Commented Jul 4, 2017 at 14:52
• 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. Commented Jul 5, 2017 at 8:42

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.

• Welcome to WorldBuilding Alexis! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! Commented Jul 4, 2017 at 12:03

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.

• 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? Commented Jul 4, 2017 at 14:47

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.

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

• Can you rewrite your argument? I find quite hard to understand what you state.
– L.Dutch
Commented Jul 5, 2017 at 8:31
• Welcome to WorldBuilding! If you have a moment please take the tour and visit the help center to learn more about the site. Have fun! Commented Jul 5, 2017 at 8:33
• 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. Commented Jul 6, 2017 at 6:30
• Please don't downvote my answer just because you don't understand physics... Commented Jul 6, 2017 at 9:13
• @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. Commented Jul 6, 2017 at 9:18