My question is: if we could throw a steel bar into an ocean with a depth equal to the radius of the sun, and with the same gravity on the surface as the earth, would the bar keep fallin until it reaches the center of the water/planet? If not, what is the requiered depth for the bar to stop falling? and if it would, what if the planet was even bigger (like the size of a red giant?)?
(theres only water in this planet)
Salt water or fresh water?
And what sort of steel, too.
a plain-carbon steel and fresh water
I’m not a physicist, but my WAG is that the density of the water would increase as you got deeper due to the weight of the water above. At some point the density of the water would equal the density of the steel bar and it would float at that level.
Well, according to this phase chart:
http://www.lsbu.ac.uk/water/phase.html
water becomes solid at around 10^10 Pa no matter what the temperature.
So if the pressure towards the center of the hypothetical ocean hit 10^10, one can imagine that a steel bar would stop falling, since it would basically hit something solid.
The next question is how deep a collumn of water would it take to give you 10^10 Pa.
Here’s a chart I found that shows temperature versus pressure of ocean water. (Yes, it’s salt water. Also, at more extreme depths, the line ought to start curving to the right since the water is denser. But this ought to give an upper bound.)
According to the graph, you get 1 dBar of pressure for each meter of depth. So 1000 meters of depth ought to give you at least 100 bars. That’s about 10^7 Pa, according to a pressure converter I found online.
So at no more than 1000km down, the water ought to get solid. That’s about 600 miles.
So my back-of-the-envelope-guess is that the bar sinks about 500 miles and stops.
My quick calculation using a constant bulk modulus for water of 2.2 GPa yields a pressure of 19000 bar to reduce the volume such that the density of the water would be equal to steel.
That’s a terrible assumption, since compressibility chages with pressure, and I neglected the (much lower) compressibility of the steel itself. But it’s a ballpark idea.
brazil84 doesn’t that pressure water density basically depend on a mass equal to that of the earth to hold true? On a mass of say 4 times that of earth wouldn’t the chart be way off? I’m asking not telling here.
I think the problem is broken: On a celestial body made entirely of water and comparable in size to the sun, how do you have earth gravity?
(I can’t figure out if the OP means radius or diameter when talking about the “depth” of the water, but either way I don’t think it makes sense)
ok dont spoil all the fun for me.
Hmmm… This sounds like the Jelly Tots solar system. Would that much water become a Red Giant or a Nova?
Another variable that hasn’t been mentioned is that the gravity is not linear as the bar approaches the center of the mass.
The problem is, there’s a simple answer and a complicated answer to this question. The simple answer ignores things like the compressibility of water and other physical changes due to high pressure, and changes in gravity, and all the like. If you ignore all those details, then the answer is just that the bar keeps sinking forever, because it’s always denser than the water. But this is boring.
If you want any answer other than that, though, you have to start considering all of those factors we neglected in the simple case. And they’re all interrelated, so you can’t really pick and choose which ones to consider. That gives you the kind of answers that you said were spoiling your fun.
And don’t worry about trying to make things easier on us. We like questions like this to be complicated.
Yeah I think you are right. The question asks us to assume that the gravity is the same for that of the Earth though.
I checked out the link. I can’t question the data of people who know a lot more about this shit than I do but it’s counterintuitive. Can anyone provide an explanation to a layman about how you can have ice at high pressure and high temperature? It seems like the mechanisms for crystallization under those conditions must be totally different than the Earth’s-surface phenomenon of freezing.
I can’t give you an explanation, but there is apparently a difference between Ice-1 and Ice-7.
And especially Ice-9!