Low gravity cavern. Countering Earth's gravity.

[Cosmologist]

I create a large mountain out of an extremely dense material and hollow out a cavern beneath it. What kind of material would be best and how tall would the mountain need to be for its gravity to counter earths gravity? I want to create a low gravity chamber.

Neutronium would be nice but thats hard to come by. How about lead or spent uranium? Maybe not uranium. Even spent radioisotopes have some residual radiation don't they? Something dense anyway. Gold would be nice but I doubt there is enough on earth. Maybe after Planetary Resources freights a few asteroids of the stuff back to Earth it will be more affordable. Anyway, what would work and what would be financially feasible?

[Jens]

I suppose you could use a mixture of heavy metals. Uranium isn't necessarily bad, because it is radioactive (regardless of whether it's spent or not), but it decays through alpha decay, and alpha particles are stopped by even a few centimeters of air, so there isn't any danger unless the roof collapses (in which case the radiation is the least of your problems!)

Which brings up the big issue. How exactly do you propose to support this structure? It would have to be huge, and the earth's gravity flattens things out (which is why we don't have mountains that are 100 kilometers high, for example. You'd probably be talking about something that is a significant portion of the earth's weight (remember that the core of the earth is made of heavy things like iron and nickel). And the earth's mass is more than a sextillion tons, so you'd need to support maybe quadrillions of tons of material I guess.

[cjameshuff]

I create a large mountain out of an extremely dense material and hollow out a cavern beneath it. What kind of material would be best and how tall would the mountain need to be for its gravity to counter earths gravity? I want to create a low gravity chamber.

Neutronium would be nice but thats hard to come by. How about lead or spent uranium? Maybe not uranium. Even spent radioisotopes have some residual radiation don't they? Something dense anyway. Gold would be nice but I doubt there is enough on earth. Maybe after Planetary Resources freights a few asteroids of the stuff back to Earth it will be more affordable. Anyway, what would work and what would be financially feasible?

Uranium is "only" 19.1 g/cm^3, a couple times the density of iron at normal pressure and not much denser than the core. You're going to need a lump the size of a small planet. The critical mass of even depleted uranium would be a bigger issue than the radiation.

To cancel out Earth's gravity, you'd need an object with a surface gravity close to Earth's. Nothing made of normal matter is going to be smaller than a planet (it may be smaller than Earth, but still planet-sized). And such an object made of something like neutronium (assuming you find such a substance that can exist under Earthly conditions) will just sink through Earth's crust and make its way to the core. If you want low gravity, you have to get off the planet.

[grapes]

Uranium is "only" 19.1 g/cm^3, a couple times the density of iron at normal pressure and not much denser than the core. You're going to need a lump the size of a small planet.

And the average earth density is a little more than a fourth of that, so your small planet would have to be a bit more than a fourth the radius of the earth--about the size of the moon. Pretty big.

[Cosmologist]

Curses. Foiled again. Is there any noticable lessening of gravity in the worlds deepest places? I realise thats only a few kilometres. Caves in china or deep mining shafts. What about the bottom of the marianas trench? The water density is pretty intense for a few kliks over that. Did James Cameron lose any weight on the trip down?

[cjameshuff]

Curses. Foiled again. Is there any noticable lessening of gravity in the worlds deepest places? I realise thats only a few kilometres. Caves in china or deep mining shafts. What about the bottom of the marianas trench? The water density is pretty intense for a few kliks over that. Did James Cameron lose any weight on the trip down?

It's probably measurable with sensitive instruments (variations in gravity being used to detect things like ore bodies and oil deposits), but nowhere near noticeable. Our deepest mines have barely scratched the surface of the planet.

[grapes]

Curses. Foiled again. Is there any noticable lessening of gravity in the worlds deepest places? I realise thats only a few kilometres. Caves in china or deep mining shafts. What about the bottom of the marianas trench? The water density is pretty intense for a few kliks over that. Did James Cameron lose any weight on the trip down?

Not appreciably.

In fact, the earth's density profile results in the interesting situation that the force of gravity is close to constant all the way down to the core-mantle boundary (CMB). The CMB is about halfway to the center of the earth.

The reason for that is, the (symmetric) layers above you do not contribute to the force, so in a constant density earth, the force would be proportional to (g * r), which decreases linearly from g at the surface (r=1) to zero at the center (r=0). That's because the mass is proportional to r^3, but the effect is proportional to 1/r^2. The result is simply proportional to r. So, even if the earth were of constant density, gravity wouldn't decrease substantially over the "short" distances available to us at the surface.

Wolframalpha.com
Plot r, 0 < r < 1

For the real earth, a better (but still over-simplified) model is one where the core is twice the density of the rest of the earth. Then, the plot looks more like this:

Wolframalpha.com
Plot [{x + 1/(8*x^2),2*x},{x,0,1},{y,0,1}]

[neilzero]

Unless you want 0.999g your only hope is Earth orbit or solar orbit where you can tether two space craft to each other and spin. The least massive craft will have the most artificial gravity, so 1/6th g and 0.38 g are likely practical. Neil

[Ivan Viehoff]

Let's actually do an order of magnitude calculation.

Apparently your big advantage in putting a counteracting mass on top of your chamber is that it is much closer to the chamber than the centre of the earth, where the earth's gravity acts, and gravity goes with r^(-2). The earth has a radius of 6371km. Suppose we put our counteracting mass an average of just 0.1km above the chamber. Now (6371/0.1)^(-2) is about 1/(4 billion), so to counteract the earth's gravity you'd only need about that fraction of the earth's mass in a concentrated lump above you at an average of 100m distance. Unfortunately the earth weighs 6E24 kg, so you'd need 1.5E15kg. If we choose some heavy rocks like with a density of 3000 kg/m3, that would have a volume of 5E11 m3, or only 500 km3. Nevertheless the problem of concentrating a mass equivalent to 500km3 of rock at an average of 0.1 above you is impractical. Using lead wouldn't help much, we'd still need about 130km3 of that. Even if we try to use that r^(-2) factor and try to concentrate the counteracting mass just 10m above the chamber, we still need a mass equivalent to 5km3 of rock, and that can't practically be put just 10m away.

If instead we mine to the roots of mount Everest, and suppose that the counteracting mass is an average of 3km above us, now we would need Mt Everest to contain a mass equivalent to about 500,000 km3 of rock, which is rather larger than reality, at least that which is an average of 3km away. So yes, indeed, a mine at the root of mount Everest would have a detectably lower gravity than the surface of the earth, but we are talking something like 0.1%.

[utesfan100]

Why not look for a cave (or dig a tunnel) under a large granite mountain?

Or take a ship to the Indian ocean and enjoy natural variations in gravity.

http://en.wikipedia.org/wiki/Gravity...ate_Experiment