Tuesday, September 18, 2012

Falling through the planet - geek edition.

Marco September 17, 2012 at 12:15 am
Hope they don’t fall into one of those bottomless pit traps!

ToaSoul September 17, 2012 at 5:50 am
those make no sense its pretty much impossible to make

a “bottomless pit” there has to be an end sometime!!

Argent Stonecutter September 17, 2012 at 7:03 am
If your pit’s deep enough there’s no bottom, just another top!

Raska September 17, 2012 at 10:56 am
that would get /weird/. You fall and fall and fall and then are spit out at the edge of the pit. *shudders* portal physics are mindbending

Argent Stonecutter September 17, 2012 at 11:19 am
Well, actually, you’d get cooked by the heat of the molten core of the earth long before you get anywhere near the opposite top.

Argent Stonecutter September 17, 2012 at 11:26 am
Ignoring thermal effects and air resistance, it would take 42 minutes.

It turns out that *any* trip along any straight line (chord) through the earth under gravity, and ignoring friction, would take 42 minutes. That’s also half the orbital period for a sea-level satellite (though it would have to be a black hole or something to avoid being slowed down by air resistance).

So if you had an evacuated maglev line from San Francisco to New York, it would take 42 minutes. San Francisco to Bombay? 42 minutes. San Francisco to Los Angeles? 42 minutes. The science is easy. Engineering it, now that’s a charming young woman.

Keldor September 17, 2012 at 2:22 pm
Of course, once you add just a tiny bit of friction, you’d fall until you stopped just short of the other side, at which point you’d fall back the other way, stopping just short of where you started. You’d continue falling back and forth for quite some time before eventually settling in the center of the earth, at which point you’d face a climb of nearly 4000 miles to return to the surface…

Argent Stonecutter September 17, 2012 at 4:10 pm
Oh, you want *realistic* calculations?

Let’s see, in a vacuum the maximum velocity would be almost 8 kilometers per second. Terminal velocity for a human at 1 atmosphere is more like 50 meters per second. So under ideal conditions you’d have less than 1% of the speed to get back to the surface on the first pass. Air pressure would get higher as you dropped, and acceleration due to gravity would be reduced, so your actual velocity as you passed through the center would be much less than 50 meters per second.

Also, the walls of the tunnel at that depth would be several thousand degrees, so the terminal velocity of the charred remnants of your body would be even lower.

Keldor September 18, 2012 at 12:22 am
To be fair, if you just let air fill the shaft, the pressure would be such that somewhere around 1/3rd (napkin calculations FTW!) of the way down, the pressure would be such that air would become a solid, so you wouldn’t even make it to the core. Engineering-wise, proper climate control (including a vacuum for you to fall through in your spacesuit) would be the least of your concerns, given that the strongest materials known to science would collapse like a wet sponge under an 18-ton hydraulic press. 50 million PSI is a *lot*.

Keldor September 18, 2012 at 12:34 am
Come to think of it, air would be solid well before that. I was basing my calculations on the theoretical depth in Jupiter where hydrogen becomes solid, and multiplying my 10 to account for the different gravity, but hydrogen is much lighter than air, about 15-fold, so, assuming a similar amount of pressure turns mostly nitrogen into a solid (ideal gas laws state that the number of particles determine the pressure/volume, so the relative density of the gasses is completely determined by their relative atomic weights (and temperature, but we’re assuming that’s the same)), the depth for solid air would only be around perhaps 75 miles, which is well away from the center.

Keldor September 18, 2012 at 12:36 am
Actually, 40 miles.

Marco September 18, 2012 at 2:08 am
Oh I love how you guys incorporate real science within the fantasy realm! I think Tarot would approve greatly if she was there!

Argent Stonecutter September 18, 2012 at 8:11 am
The partial pressure of oxygen would be toxic only 6 km down. I don’t think you can extrapolate so linearly from Jupiter, though, not just because Earth’s gravity is less but also because it falls off much faster with depth.

The walls of the tube would be under significantly higher pressure than that from the molten rock (average density 5 grams/cc, versus 0.0012 g/cc for air). Like I said, the engineering challenges are a real charming young woman.

Raska September 18, 2012 at 10:55 am

C-Shock September 17, 2012 at 8:38 pm
Argent Stonecutter, your science is now the “About Me” info on my skype. and i’m putting it on facebook, if it’s not a problem…just to increase general knowledge. you is smart!

Argent Stonecutter September 18, 2012 at 9:59 am
Heh, maybe I should preserve this thread in my blog.

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I'm just this shapeshifting simulation of a critter originally from a little planet in the Slow Zone that you've probably never heard of.