If I fell to the center of the Earth

[Triskadecamus]

@jackdavinci

What facts are those? Sure the Earth is filled with magma but that’s not a law of physics, that’s an arbitrary geological situation. Let’s posit the same question on an Earth size body whose core has cooled (and hasn’t been destroyed by an expanding sun).

Yep, it’s a coincidence that the Earth is made of rock, and iron, with a core of molten material.

So, we have to conduct your experiment on another solid object of the same size, which is solid clear through. Solid what? Tungsten might be strong enough to resist flowing back into a tunnel bored eight thousand miles through it. I don’t think so, but hey, I don’t have a cite to prove it isn’t. (Hint: Did you ever wonder why there is so much round stuff in the universe?) Oh, wait, tungsten is too dense, the gravity would be too high.

But hey, like I said, we are picking and choosing our physics here, and requiring strict mathematics at the same time, once we make our choice. So, we make it out of a special alloy with the same proportional density as the earth at every level, but an incredible tensile and compressive strength. (Hey, it worked for Larry Niven, why not us?)

The outer walls of our tube are frictionless. I don’t think anyone has finally decided about air. If there is air, you get slowed down to zero, probably a couple of hundred feet either before or after the center. (I don’t know if you would float in air at the center, maybe, maybe not, depending on the physics chosen for that one.) If there is not air, well, imagine a physics that keeps it out.

The shape of the tube has to be different for falling through, and falling back. Unless you want to imagine a physics that lets it be straight. Once you imagine that, you can fall straight through, and straight back. In fact, you can fall out the other end, and have Australians offer you shrimp on the barbie.

Without the magic, it cannot be there at all. With magic, all things are possible, and you can do the math any way you want. So, how do you want to do the math?

Tris

[flight]

@Triskadecamus

Let me get this straight.

We are going to ignore the facts of physics that make it impossible for the hole to exist at all. We are going to ignore the facts of physics that make it impossible for the hole to stay open. We are going to ignore the facts of physics that make it impossible for our path to be a straight line.

And then we are going to selectively rely on an arbitrary subset of those physical facts to ascertain the time it takes us to fall through the imaginary hole.

Have you ever taken a physics course, because the above is an excellent description of just about every physics problem I have ever seen. Unless, of course, you keep a bunch of massless, frictionless pulleys in your garage. To be fair, the coriolis effects are not as easily ignored and it is better to have this thought experiment take place at the poles.

@sciguy

For the drag constants, I used the default values provided in the calculator here, converted into metric.

Unfortunately these will not work. Drag coefficients are Reynolds Number dependent. Your Reynolds number will be all over the place during the fall, particularly when the density starts getting really high. Also, you need to assume that the hole is of a very large diameter relative to you or there will be very bad blockage effects that will shoot your drag very high.

Lastly, I think your calculation assumes a constant density throughout the Earth. The core is, in fact, much more dense than the crust or mantle and therefore g will not decrease as quickly as expected.

[flight]

@Triskadecamus

Yep, it’s a coincidence that the Earth is made of rock, and iron, with a core of molten material.

So, we have to conduct your experiment on another solid object of the same size, which is solid clear through. Solid what? Tungsten might be strong enough to resist flowing back into a tunnel bored eight thousand miles through it. I don’t think so, but hey, I don’t have a cite to prove it isn’t. (Hint: Did you ever wonder why there is so much round stuff in the universe?) Oh, wait, tungsten is too dense, the gravity would be too high.

But hey, like I said, we are picking and choosing our physics here, and requiring strict mathematics at the same time, once we make our choice. So, we make it out of a special alloy with the same proportional density as the earth at every level, but an incredible tensile and compressive strength. (Hey, it worked for Larry Niven, why not us?)

The outer walls of our tube are frictionless. I don’t think anyone has finally decided about air. If there is air, you get slowed down to zero, probably a couple of hundred feet either before or after the center. (I don’t know if you would float in air at the center, maybe, maybe not, depending on the physics chosen for that one.) If there is not air, well, imagine a physics that keeps it out.

The shape of the tube has to be different for falling through, and falling back. Unless you want to imagine a physics that lets it be straight. Once you imagine that, you can fall straight through, and straight back. In fact, you can fall out the other end, and have Australians offer you shrimp on the barbie.

Without the magic, it cannot be there at all. With magic, all things are possible, and you can do the math any way you want. So, how do you want to do the math?

Tris

How about this: you have a large diameter hollow tube made of unobtainium that has very little mass but near infinite tensile and compressive strength and is as long as the diameter of the Earth (hardly any more unbelievable than a massless, frictionless pulley). It is capped at both ends and has an interior vacuum. You ram it through the center of the Earth from pole to (rotational) pole. Our intrepid adventurer (with pressure suit, he wouldn’t splat in a vacuum, but he wouldn’t live either) then steps through an airlock at one end, cimbs across the ceiling to center himself, and swan dives into oblivion.

A while later he catches hold of a capture net at the far end and rests for a bit in another airlock while the ends of the tube are removed and hurricane winds fill the tube with air. While the surrounding area tries to recover from the inevitable natural disaster, our adventurer once more climbs out over the void and with one last sigh releases his grip and falls deep into a thought experiment.

[Triskadecamus]

@flight

You ram it through the center of the Earth from pole to (rotational) pole.

You realize, of course, this means no shrimp. Penguin stew, maybe.

Tris