What would happen to the Earth if Gravity disappeared?

Question

This is a multi-tiered question. I have seen these larger questions before, but if I need to separate them out into their own questions let me know.

In my story I have a machine that can manipulate gravity, either increasing it or decreasing it. The how is not important, I want to know what would happen after it was turned on at different levels.

What would happen to the earth if a zero-g environment were created on the earth that is:

• 1 cubic foot
• 10 cubic feet
• 100 cubic feet
• 1 cubic mile
• 10 cubic miles
• 100 cubic miles
• Encompassing the entire surface of the earth and atmosphere, but not penetrating into the surface
• Encompassing the entire earth, from the top of the atmosphere right down to the core.

These events will be localized to the Earth, meaning that the Earths gravity still exists outside of the area of effect.

Area outside of the zero-g environment experience normal gravity, including directly above it. Time frame is indefinitely (or until the machine is turned off).

I assume that when you get into the larger areas that it will have extremely detrimental effects on the Earth, what would these be? On what kind of time scale would the atmosphere leave and make the planet uninhabitable? Would the planet break apart? Would it happen within minutes, hours, days, years?

Answer 1

I'm assuming all but the final two situations are with the effect epicenter on the surface of the Earth in an open area.

1 cubic foot, 10 cubic feet, 100 cubic feet

Gravity is gone inside a relatively small area. The air pressure inside the volume might be a little wonky, causing a perpetual updraft. The air at the edges of the volume, especially the bottom, would be under more pressure than the air just inside and it would pour in and flow upward to the slightly lower pressure air on top.

1 cubic mile

The ground half a mile down is under a fair amount of pressure from the ground above it (about 200 atmospheres). As the device turns on the pressure is immediately relieved and the ground will pop up rather violently. There is no gravity to stop the upward motion and the ground will reach the top of the volume and then oscillate at the edge. Moving past the edge and falling down to collide with ground moving upward. Eventually any floating ground material will pile up at the edges outside the volume of effect. This would be a great way to do some strip mining.

10 cubic miles

At 1.3 miles down the ground has 645 atmospheres of pressure from the ground above it. When the device is enable this pressure is immediately released and the ground violently explodes upward, likely killing anyone on the surface. The ground will rapidly reach the upper edge of the volume and be flung in all directions. Air rushes into the sides of the volume and blows out the top into the low pressure atmosphere above. The heavier than air materials will eventually settle around the edges of the volume.

100 cubic miles

Similarly to the 10 cubic mile case, except the pressure released is over 1,400 atmospheres at 2.98 miles down. The explosion is more violent and spreads material even further away. The volume cycles huge amounts of air through it and significantly disrupts the local weather.

encompassing the entire surface of the earth and atmosphere, but not penetrating into the surface

We all die. We lose significant air pressure and people would asphyxiate immediately. Everything not bolted down is now airborne as it's no longer tethered to the Earth by gravity it continues along its path. You would observe this as the the Earth and everything bolted down as pulling away from you and everything not bolted down. Everything gets a turn at exiting where the edge of the atmosphere used to be then being pulled back down to collide with the surface of the Earth again. Masses of vehicles, boats, and bodies will begin to form into huge hurricane spirals due to the coriolis effect. The floating debris begins to move at different speeds than the surface of the Earth as it spins. Eventually everything gets dumped into an ocean (assuming the effect hugs the surface of that too, otherwise it's flying around with our bodies).

encompassing the entire earth, from the top of the atmosphere right down to the core.

The Earth explodes. The core is under immense pressure from the weight of the ground above it. Suddenly that weight is gone and that pressure is going to equalize. The mass of the Earth ejects from the edge of the anti-gravity volume but there is no Earth to maintain the gravity outside of it. It continues outward but is eventually pulled into an oscillating dance at the edges of the sphere while pieces on the far side pull on pieces on the opposite side. As they fall into the anti-gravity sphere they continue through where the Earth once was at constant velocity (unless they hit other pieces doing the same) and emerge to be pulled somewhere else. Oh, and obviously, everyone is dead.

Answer 2

Pressure release and earthquake

Let's say the earth is flat. Someone standing at the center would feel weightless. The closer he gets to the edges the more matter he will have behind him and the stronger gravitational pull will be. He will literary feel like he is climbing a steeper and steeper mountain. It's the same for the matter which composes the Earth. Think of it as a sponge. As soon as you release it it will expand and take more place. It the same for matter: at the center it weights nothing but it is squeezed between the matter which stands at the edges, willing to collapse. This squeezing (pressure) compresses matter which consequently will to expand as soon as possible. The moment you suppress gravity you allow matter to expand and release its potential energy as a sound wave travelling through Earth.

In my opinion if you target a block which is inside the crust this would look very much like an earthquake and would have similar impacts on the environment. If you activate this on a volume that contains crust and air I think that everything described by @Samuel is correct.

No centripetal force anymore

According to Newton's laws of motion, any object to which is applied a force $F$ will move through empty space in straight line forever. It's linear motion and no force is required to actually move. Force is required to change the momentum (direction and speed). Objects on Earth's surface are not moving in straight line because of a centripetal force which keeps changing their momentum. They want to move in linear motion but they can't. They are like a rotating ball attached by a string. This force is Gravity.

The Earth is spinning very fast. The angular speed of Earth's rotation in inertial space is about $7.2921150\times 10^{-5}\ \text{rad/s}$ (solar second). When you multiply this by equatorial radius of $6\,378\,137\ \text{m}$ it gives you a tangential speed of $465.1\ \text{m/s}$. If you were able to remove gravity from a block of matter, nothing (as far as I know) would stop it from moving in straight line at $465.1\ \text{m/s}$ into space except for the frictional forces and the effect area. Friction might be quickly overwhelmed as your block increases in size.

Scratching the surface

I meant to have the area of effects not penetrate the surface on any of the scenarios except the last one

If your machine does not target Earth's crust at all things tend to be gentler. Imagine everything @Samuel talked about without any violent explosions. On a large scale however, air displacements would significantly affect the weather, producing exceedingly violent winds travelling at huge speed and destroying almost everything on its passage.

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The speed of light

If your matter losses its mass it must become something massless and there is not many options here: it should turn into energy (otherwise your Universe has energy leaks which is very weird and question all modern physics). According to the mass-energy equivalence equation $E=mc^2$ this is completely devastating and equivalent to an anti-matter bomb. Since I suppose this is not really interesting for your story, you have to take this into account, either to ignore it of find a way to avoid it.

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How do you do this?

The how is not important, I want to know what would happen after it was turned on at different levels.

I disagree and how is certainly a question you should ask to yourself and be clear about in your question: how does your machine remove gravity from the block of matter? Does it modify space-time curvature? Does it make you matter massless so almost unaffected by gravity (turning it into electromagnetic waves and therefore making it travelling at light speed)? It might impacts the answers you obtain here.

Answer 3

For the one that encompasses the surface and atmosphere, you don't mention whether the anti-gravity goes with the atmosphere as it leaves Earth, but let's assume it doesn't.

The first thing that's going to happen is that anything not stuck to the ground will get flung into space by centripetal force. However, as soon as it hits a 100km altitude (the traditional "beginning" of space and outer limit of the atmosphere), it's going to be captured by gravity again, albeit slightly less of it.

This means that all the survivors will live at 100 km on a sort of invisible bubble - almost as if they were in a low orbit (though not the same thing). They'll have to be able learn to swim, though, as all the water will go with them, and form a giant floating ocean around the earth.

Things will tend towards the equator but this movement will be limited by the masses of water.

Saltwater and fresh water will mix so there'll be nothing to drink up there, and I imagine food production will be impossible too.

For people who stayed indoors, and are still on Earth's ceilings, their water is now all gone except what was left in their attic tanks, and they will most probably not be able to breathe because if there's any air left it's only courtesy of the pressure of the air from 100 km above them, which is likely to be tiny (since most of the atmosphere is above the new ocean, and anyway, the Earth's spin is trying to push it away) Besides it's going to get very cold because of the shield of water blocking the sun.