Standing On The Surface Of A Gas Giant

[Pontiuth Pilate]

Let's say you're standing on the outer surface of a gas-giant planet made of hydrogen gas (like Jupiter).

Of course, since you are denser than the gas, you will fall down "into" Jupiter.

Now at some point you would slow down and then stop falling altogether as the hydrogen is so dense.

So, some questions:

1) how far below the surface would you be?
2) what atmospheric pressure would you be experiencing?
3) would you be able to "walk" on this subsurface, or would you just float like an object caught between two layers of liquid of different densities?
4) what force of gravity would you feel?

This is a mindbending thought experiment

 

[ainwood]

I would imaging that Archimedes principle applies. You will fall until your weight matches the weight of the fluid you are displacing.

 

[Pontiuth Pilate]

Right.

But wouldn't that mean the atmospheric density is the same as the density of your own body? That would be.... a LOT of Pascals.

 

[ainwood]

Pascals is strictly a measure of pressure, not density, although they are related. Density would not be that high - people are roughly buoyant in water, so the relative density wouldn't be much different.

At a guess, I'd think that the pressure / gravity would compress your body somewhat, meaning that your density would be somewhat higher.

Note that the pressure would probably crush your chest, considering that you couldn't breathe the atmosphere. This is akin to trying to breath uncompressed air through a hose when your 3 metres under the surface of water - can't be done (your chest muscles aren't strong enough).

 

[The Last Conformist]

I can't be bothered to look stuff up ATM, but here's some commnets:

1) how far below the surface would you be?
No idea. In fact, I'm not sure there is a such point - it might be that the atmospheric density remains below human body density (~1) all the way down to the liquid "ocean" covering the core of the planet.
2) what atmospheric pressure would you be experiencing?
Enough to kill you.
3) would you be able to "walk" on this subsurface, or would you just float like an object caught between two layers of liquid of different densities?
You'd float, assuming there is a such surface - walking requires a rigid substrate.
4) what force of gravity would you feel?
None. Think of astronauts exercising "zero g" in a water tank.

 

[ainwood]

2) what atmospheric pressure would you be experiencing?
Enough to kill you.

Only if the atmosphere was not breatheable. It is not the pressure that would kill you; it would be the pressure differential between the atmosphere and your internals. If you could 'breathe' the atmosphere, then the pressure would equalise, and it is possible that you could survive (although whether biological processes worked at the higher absolute pressure could then be limiting).

 

[Bill3000]

Assuming an ideal gas, I think a possible attack of the problem would be the following:

1) Take a particular pressure value of Jupiter at a particular height as a reference point.

2) Use the fact that the pressure of a gas would be directly proportional to e^(-U/kT), where U is the change in the potential - be sure to normalize it. Gravitational potential would be used. (-GMm/r at a particular height)

3) Using Archimedes' principle, equate the weight of the displaced volume with that of the buoyant force. Use this to find both the height and thus pressure and density of the gas at the particular height.

4. Gravity is then easily calculated as -GMm/r^2.

I'm too lazy to do the calculations at the moment. Anyway, the cheating way is that you'll burn in the atmosphere far before the height reached - if not burned, crushed. And such a point might not exist at all in the first place.

Pascals is strictly a measure of pressure, not density, although they are related. Density would not be that high - people are roughly buoyant in water, so the relative density wouldn't be much different.

At a guess, I'd think that the pressure / gravity would compress your body somewhat, meaning that your density would be somewhat higher.

We'd be talking about atmospheric density, not the density of your own body. Though yeah, you'd measure atmospheric pressure, not density - you can get density through a proper equation of state - easiest one being that of an ideal gas. But I don't know if it would work for Hydrogen at the pressures required.

 

[The Last Conformist]

Pontiuth specified a hydrogen atmosphere, which isn't breathable.

 

[skadistic]

I don't understand why you'd stop falling. If there is gravity You'd go to the center untill you hit solid right?

 

[Mirc]

At some point, Archimedes' principle will stop you.

 

[ainwood]

We'd be talking about atmospheric density, not the density of your own body.

But they'd be approximately equal when you'd reached an equilibrium.

Though yeah, you'd measure atmospheric pressure, not density - you can get density through a proper equation of state - easiest one being that of an ideal gas. But I don't know if it would work for Hydrogen at the pressures required.

Hydrogen is roughly ideal up to reasonably high pressures (and over a wide range of temperatures). But it really comes down to how accurate you want your answer to be.

 

[The Last Conformist]

Though yeah, you'd measure atmospheric pressure, not density - you can get density through a proper equation of state - easiest one being that of an ideal gas. But I don't know if it would work for Hydrogen at the pressures required.

Using the ideal gas law, molecular hydrogen at a randomly chosen temperature of 290K and a density of 1kg/dm^3 works out at about 1.2GPa, or about 12,000 atmospheres. Deviations from ideality would, I suppose, make the actual pressure higher.

 

[The Last Conformist]

I don't understand why you'd stop falling. If there is gravity You'd go to the center untill you hit solid right?

You'd stop falling for the same reason a helium baloon doesn't fall to the ground at some point lift beats gravity.

 

[skadistic]

You'd stop falling for the same reason a helium baloon doesn't fall to the ground at some point lift beats gravity.

So what would be the lift?

 

[The Last Conformist]

So what would be the lift?

Acquaint yourself with Archimedes' principle.

 

[Pontiuth Pilate]

Pascals is strictly a measure of pressure, not density, although they are related.

Yes; I mean the atmospheric pressure would have to be very high for the density to be sufficient.

Another point is: in reality, you would never stop falling, right? I mean that you would fall until the theoretical equilibrium point, but at that point the pressure would be enough to compress your body to a higher density. And so on. So you'd keep falling until you hit the core I think.

If your body was strong enough to resist compression, then you'd float.

 

[ainwood]

Another point is: in reality, you would never stop falling, right? I mean that you would fall until the theoretical equilibrium point, but at that point the pressure would be enough to compress your body to a higher density. And so on. So you'd keep falling until you hit the core I think.

If your body was strong enough to resist compression, then you'd float.

As an analogy, if you jump in a pool, you don't just keep sinking, and in a gas giant, it would be largely the same. As the external pressure increased, you would be compressed until the inter-molecular repulsive forces within your body balanced against the external pressure, at which point, you wouldn't be compressed any more. It would reach a state of equilibrium.

 

[The Last Conformist]

Yes; I mean the atmospheric pressure would have to be very high for the density to be sufficient.

Another point is: in reality, you would never stop falling, right? I mean that you would fall until the theoretical equilibrium point, but at that point the pressure would be enough to compress your body to a higher density. And so on. So you'd keep falling until you hit the core I think.

Nope. Lift rises with pressure much faster than what your body would be compacted, so you'd stop only a little below the eq. point for the incompressible case.

Plus, you've got a gigantic ocean of liquid metal hydrogen between the atmosphere and the core.

Edit: Hm. From some googling, there appears to be no clear boundary between the atmosphere proper and the liquid "mantle" around the Jovian core.

 

[Gogf]

Only if the atmosphere was not breatheable. It is not the pressure that would kill you; it would be the pressure differential between the atmosphere and your internals. If you could 'breathe' the atmosphere, then the pressure would equalise, and it is possible that you could survive (although whether biological processes worked at the higher absolute pressure could then be limiting).

Couldn't parts of you other than your longs be crushed? It would take a lot of atmospheres of pressure to make gaseous hydrogen be the same density as the human body. The much pressure might beyond the critical point whereby hydrogen can no longer be a gas, in which case you DEFINITELY couldn't breath it .

 

[Gogf]

Another point is: in reality, you would never stop falling, right? I mean that you would fall until the theoretical equilibrium point, but at that point the pressure would be enough to compress your body to a higher density. And so on. So you'd keep falling until you hit the core I think.

Your body resists compression much better than hydrogen gas does, so I suspect your would continue to fall until a certain point, with the amount of the fall becoming ever smaller. Sort of like an asymptote.