Although he is now 36, and a mathematician for Sylvania, Paul Cooper has never lost his boyhood enthusiasm for the fanciful science-fiction stories of Jules Verne. While musing about Journey to...
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While an interesting theoretical concept, the physics behind it would much such a thing impossible without the technology that would make it unnecessary.
First the raw physics, with the center of the earth at 10,000 degrees F, we would need materials better than tungsten that melts at 6,000 degrees F, would boil at 10,000 degrees F. But this could be overcome by using layers of insulation and exotic materials to build a pipe capable of withstanding the temperature.
The next point, withstanding the pressure of 3.6 million atmospheres. Again in theory a pipe with an effective wall thickness equivalent to 30 feet of high strength steel would be required. So an insulated layered pipe might be around 300 feet in diameter at the earths center, and just inches at the surface. Of course the technology to drill such a pipe stack would be the next challenge, solved by something similar to a tunnel boring machine in order to install pipe segments to line the hole as it's drilled.
Even if the technology could be invented, the logistics of the amount of time it would take is still huge. A tunnel boring machine can do around 35 feet per day under the easy conditions hear the earths surface. So drilling down to the core would take close to 2,000 years
And the final obstacle isn't one of building it, but using it. The idea is to use the earths gravity to accelerate to the earths core, and then use that speed as a slingshot to return to the surface on the other side. But the 42 minute trip is calculated "without air resistance", which is the final obstacle. The obvious solution is actually impossible to achieve. That is to simply vacuum out the air, thus eliminating the air resistance, and make the tunnel a conduit to the other side. People would simply be in a capsule, or wear space suits to survive the trip, but one hitch.
There is no way to draw a vacuum that deep. Think about it. Two hundreds miles above the earth, is the vacuum of space, and it can't draw a vacuum to the earths surface only 200 miles from it, because of gravity. So the same would be true trying to draw a vacuum on the earth tunnel. Without a vacuum, the air pressure approaching the core would be above 500 atmospheres, so even at the temperature inside the tunnel, it would be a liquid.
So the final question is how long would it take a series of stacked pumps to pump the air from the bottom of the tunnel to the surface. Which alone would require over 20,000 pump stages, and decades or centuries until a vacuum could be achieved.
Even ignoring the cost, the amount of energy, and the engineering, the time to drill it out, and make it operational would be thousands of years.
By then warp drive and transporters would make it obsolete.