Internal pressure in planets and stars

[Boerseun]

The popular understanding of pressure in the cores of planets and stars is that it's enormous. But - shouldn't it be zero? 'Cause at the centre of a sphere such as a star, gravitational pull is equal in all directions. So, the way I see it, and I'm probably wrong, is that if you could somehow float in the center of a star, you should be inherently weightless. The highest pressures should be roughly halfway between the core and the surface, somewhere in the 'mantle', not so?

[tolworthy]

Yes, the gravitational force from the central rocks is zero. But you still have the force transmitted from the higher levels where gravity is much stronger. I am a great fan of Journey To The Center of the Earth, so I've spent some time on this problem. ;) Even if the earth's core had zero weight, the heavy rocks at the surface are pushing inwards. It's Newton's basic laws. Those forces have to be balanced, or else the earth would collapse in on itself. The enormous forces at the crust are balanced by enormous pressures further down.

From a Jules Verne point of view, the bottom line is that you COULD have cracks and fissures in the top few miles of crust. But after that, even a mere hundred miles down, the weight of the rocks above your head is just unbelievable. It is still POSSIBLE to have tunnels and gaps right down to the core, but they would have to be carefully designed by an advanced race.

[Boerseun]

But explain this to me:

 

If there was a hypothetical elevator shaft running all the way to the Earth's core, built by an extremely advanced race of aliens ;) , and you should hitch a ride on this elevator, would this describe your journey:

 

At the top of the shaft, as you wait for the doors to close, you weigh your normal 80kg's. I'm not referring to your mass, that won't change, but to your weight.

As you go down, you should start weighing less, seeing as there's a gravitational pull from the layers of rock above you.

Eventually, you reach the core, and you're floating in your elevator, 'cause you're being pulled in all directions at once.

Now, if you were inbedded in the nickel/iron mass that make up the core, you'd also be weightless, all pressure should be concentrated in a spherical zone about halfway the distance from the surface to the core.

Such a zone of increased pressure might just look on a seismic analysis like the border phase between the mantle and the core, no?

[tolworthy]

Yes. you would be heavy at the surface and weightless at the middle. But until you get to the middle, there is always more mass below you than above you. So you will always be pulled downwards.

 

I remember reading a calculation somewhere that, if you drilled a hole through the earth, and slide through it in a perfectly frictionless vehicle, it would take two hours to get ANYWHERE. Meaning, for example, if the hole went through the earth's core, you would fall faster and faster for one hour. (Acceleration is greatest at the earth's surface, and zero at the center. Your speed is zero at the earth's surface, and maximum at the earth's core.) Then for the second hour you slow down, and finally come to a stop at opposite side of the earth. Of course, if you didn't grab onto something, you would start to fall toward the core again. In this imaginary frictionless vehicle, you could oscillate back and forth forever. The ULTIMATE bungee jump!

 

The really interesting thing was that the same calculations work even if you don't go straight down. You could go in a straight line from any part of the earth's surface to any other part, and it would take two hours. Of course, the real problem is getting the frictionless vehicle...

[karlfreak]

could u prhaps find these calculations for me

[tolworthy]

could u prhaps find these calculations for me

After a little searching, it seems I got the time wrong, and Douglas Adams got it right. The actual time is 42 minutes. (I think I got the 2 hour thing by getting confused over space planes - they typically claim the slower, two hour time)

 

Yes, The Hitchiker's Guide to the Galaxy was right. 42 is the answer to a lot of very interesting problems.

 

As for the original question, it is a very old one. It was the inspiration for the famous rabbit hole fall in "Alice in Wonderland." Here is the best summary I could find:

 

"Carroll's interest in the matter is indicated by the fact that in Chapter 7 of his Sylvie and Bruno Concluded, there is described (in addition to a Mšbius strip, a projective plane, and other whimsical scientific and mathematical devices) a remarkable method of running trains with gravity as the sole power source. The track runs through a perfectly straight tunnel from one town to another. Since the middle of the tunnel is necessarily nearer the earth's center than its ends, the train runs downhill to the center, acquiring enough momentum to carry it up the other half of the tunnel. Curiously, such a train would make the trip (ignoring air resistance and friction of the wheels) in exactly the same time that it would take an object to fall through the center of the earth — a little more than forty-two minutes. This time is constant regardless of the tunnel's length."

[Boerseun]

Very interesting. Makes sense! Provided you have a frictionless environment, and I suppose the train will have to be assisted somehow for the last couple of meters at the other end, otherwise you'll end up with perpetual motion... ;)