A hole through the Earth

[Butters]

Hypothetically. If a hole was drilled, with some super super strong mterial to line the walls and hold it open, right through the planet, at the precise centre, and out through the other end. Would there be any downward pull within the shaft?

If you were suspended over the hole by a rope, would the absence of any solid matter between you and the antipodean sky at the other side make you weightless? Or would you be pulled in to sides and down?

 

[Christopher]

Hypothetically. If a hole was drilled, with some super super strong mterial to line the walls and hold it open, right through the planet, at the precise centre, and out through the other end. Would there be any downward pull within the shaft?

If you were suspended over the hole by a rope, would the absence of any solid matter between you and the antipodean sky at the other side make you weightless? Or would you be pulled in to sides and down?

This is a classic physics problem. The answer is, yes, you would feel a gravitational pull toward the center, because you'd be affected by all the mass of the Earth, not just that directly below you. Every particle of mass on the planet is always pulling on you at the same time; it's just that all their vectors pulling in different directions cancel out to make a single vector pulling you toward the exact center of mass. So every particle pulling you down and to the left is cancelled out by a particle pulling you down and to the right, so they add up to straight down. Thus, even if there's no mass directly below you, you're still getting pulled downward.

However, if you're inside a uniform, hollow spherical shell of mass, then there are particles pulling up on you as well as down, and in that case, all the pulls cancel out completely and you're weightless. Of course, the Earth is not a hollow shell, but the upshot is that as you descend toward the center of the Earth, you still feel a downward pull by the mass that's closer to the center than you are, but all the mass that's farther from the center acts is effectively like that hollow shell, with its gravity cancelling out so that you don't feel it. (Allowing for the Earth's lack of perfect sphericity -- this is just an approximation, a thought experiment like the impossible shaft itself.)

So at the top of the shaft, you'd feel the Earth's full gravity, but as you descended deeper and deeper, you'd be pulled on only by the mass below you, so you'd feel less and less weight the deeper you got, until you'd be weightless at the center (because you'd then be getting pulled equally in all directions by the mass of the Earth surrounding you).

Bonus factoid: If you jumped into the shaft without a rope, you'd accelerate as you fell toward the center and then decelerate once you passed it. If the interior of the shaft were a frictionless vacuum, you'd come to a stop right at the surface on the other side of the shaft, then fall back again and oscillate back and forth through the shaft indefinitely. And the time it would take to complete an entire back-and-forth cycle would be 84 minutes, which is exactly equal to the time it would take for a satellite to orbit the Earth at its surface altitude (if the Earth were a perfect sphere with nothing for the satellite to hit and no atmosphere to slow it).

 

[Asbo Zaprudder]

Here's the Mathematics:
http://www.askamathematician.com/20...n-jumped-down-this-tunnel-how-would-you-fall/
Coriolis force also comes into play.

 

[Haggis and tatties]

^^^Mathematics and facts,you don't need all those, you only need some old wooden planks in your 4000 mile deep hole, we won't bother too much about heat issues either, but here is a small video that should explain all your questions, unless of course you are one of these unreasonable people that requires actual facts over what i just said.

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[YellowSubmarine]

And the time it would take to complete an entire back-and-forth cycle would be 84 minutes, which is exactly equal to the time it would take for a satellite to orbit the Earth at its surface altitude

Huh. It never occurred to me that the orbital period depends solely on the perihelion, and doesn't care about the eccentricity of the orbit. And I've heard Kepler's third law. My mind was just blown.

 

[Asbo Zaprudder]

Huh. It never occurred to me that the orbital period depends solely on the perihelion, and doesn't care about the eccentricity of the orbit. And I've heard Kepler's third law. My mind was just blown.

That's not correct - sorry. The period depends on the size of the semi-major axis of the orbit, not the periapsis distance. (Also, perihelion is the appropriate term for a solar orbit; periapsis refers to an orbit about an unspecified body). The orbital period is not a constant for the same periapsis and different eccentricities. Otherwise, long-period comets would take the same time to orbit as inner planets. The semi-major axis is equal to the mean of the apoapsis and periapsis.

 

[Asbo Zaprudder]

Just for completeness - the periapsis distance is the semi-major axis distance times (1 - e), where the eccentricity e of an orbit is defined by the semi-minor axis b and semi-major axis a as e = sqrt(1-(b/a)^2). The period is proportional to the semi-major axis to the power 1.5, irrespective of the eccentricity, so it must also be proportional to the periapsis divided by (1 - e), all to the power 1.5. Thus, the more eccentric the orbit (e tending to 1) for the same periapsis, the period must increase as (1 - e) to the power -1.5. So, for an eccentricity of 0.5, the period would be 2 sqrt(2) times longer (about 2.828) than a circular orbit (e = 0) with an identical periapsis.

 

[publiusr]

A tunnel through the moon might be easier
https://www.reddit.com/r/space/comments/2bt1sm/is_the_moons_core_hot_could_we_dig_a_moon_base/
https://www.physicsforums.com/threads/tunneling-through-the-moon.487478/

 

[Asbo Zaprudder]

If by easier, you mean not quite as impossible. As the first link suggests, Vesta or other asteroids are a possibility - but tunnelling all the way through would still be an expensive operation for almost no benefit.

 

[Christopher]

As the first link suggests, Vesta or other asteroids are a possibility - but tunnelling all the way through would still be an expensive operation for almost no benefit.

That depends. One proposed method for creating an artificial space habitat is to drill a hole through the axis of an asteroid, fill it with a sort of heavy-duty balloon, melt it with solar mirrors, then spin and inflate it until it cools into a hollow cylindrical shape whose interior you can pressurize and terraform. Although it would probably be done with a much smaller asteroid than Vesta.

 

[Asbo Zaprudder]

Yeah, tunnelling all the way through an asteroid as large as Vesta, Ceres and so on would be pointless was indeed what I meant. Not sure I'd trust the structural integrity of smaller asteroids. It might be better to mine them to obtain the materials for space habitats. However, given the current state of human space exploration and investment, any serious asteroid exploitation will probably be way beyond my lifetime.

 

[Christopher]

Not sure I'd trust the structural integrity of smaller asteroids.

You wouldn't have to. That's the point of melting, spinning, and inflating them. The molten material hardens into a uniform, thin shell around the cylindrical space. And it's probably more for radiation/meteoroid shielding than basic structural integrity, which would probably come from what you build inside the rocky shell.

However, given the current state of human space exploration and investment, any serious asteroid exploitation will probably be way beyond my lifetime.

There are already businesses developing plans for asteroid mining, with target dates in the 2020s-30s. Once a new frontier becomes profitable, expansion and exploitation tend to accelerate rapidly. And the profit potential of asteroid mining is immense, since the asteroids contain far more mineral wealth than the Earth's crust, and once you get over the hump of getting out of Earth's gravity well, it's far easier to extract that mineral wealth from the asteroids since it's closer to the surface.

 

[Asbo Zaprudder]

I'm sceptical, given the ropey performance of some Earth-based mining companies, but if they can meet those time scales, it'll be interesting to watch what happens in the next decade or two. I suspect some of the proposals might not be economically viable except for the rarest of mineral resources - rare earths*, gold, silver, copper, some transition metals, platinum, palladium, rhenium, rhodium, ruthenium, osmium, tungsten, and maybe lithium and iridium. As you say, once any extraction and refining systems are in space, it's just a matter of dropping the products back down the gravity well for recovery. I suspect the necessary investment is likely to run to many tens of billions of dollars but again that's a guess and economy of scale should kick in at some point. Not done much reading lately on such topics so many of my guesses are likely well off the mark.

*Rare earths aren't actually that rare in most cases but perhaps they'll be easier to extract from asteroids. They have important industrial applications so are worth considering, particularly if one wanted to decouple from the Chinese, who produce 95% of the world's supply.

 

[Gary7]

Would never ever work. The pressure would be too great and will crush the shaft at some point towards the core... that's if somehow the walls were capable of resisting the magma heat. But I think the pressure would be an even greater challenge.

 

[David cgc]

Bonus factoid: If you jumped into the shaft without a rope, you'd accelerate as you fell toward the center and then decelerate once you passed it. If the interior of the shaft were a frictionless vacuum, you'd come to a stop right at the surface on the other side of the shaft, then fall back again and oscillate back and forth through the shaft indefinitely. And the time it would take to complete an entire back-and-forth cycle would be 84 minutes, which is exactly equal to the time it would take for a satellite to orbit the Earth at its surface altitude (if the Earth were a perfect sphere with nothing for the satellite to hit and no atmosphere to slow it).

In Jasper Fforde's Thursday Next series, as part of their premise of taking place in a reality similar to, but somewhat wackier than, our own, a technological left turn meant that rather than the jet aircraft, long-distance high-speed travel was accomplished through a network of underground tunnels directly connecting various cities around the Earth called the Gravitube, with transit cars falling halfway and decelerating halfway, as you describe. The reason it comes to mind was that it was noted that, because of the way the direction of gravity and direction of travel balanced out, every trip through this system takes 42 minutes, whether from London to New York or London to Tokyo.

Funny that Elon Musk hasn't realized this is just combining his tunnel thing and his hyperloop thing yet.

 

[Kerock]

If you dropped a golf ball sized piece of a neutron star it would be so heavy it would punch a hole right through the earth and out the other side. Somewhere in orbit on the other side gravity would slow it and it would fall back through the earth again, but since the earth had turned it would make a new hole through the earth. The process would continue until the earth was a piece of swiss cheese. Ultimate planet buster.
Dr. Farrell Edwards - Physics 212 USU 1986

 

[CorporalCaptain]

a golf ball sized piece of a neutron star

How stable would such a system of matter be? What would keep it golf ball sized?

 

[Santaman]

^^Magic!

 

[Christopher]

If you dropped a golf ball sized piece of a neutron star it would be so heavy it would punch a hole right through the earth and out the other side. Somewhere in orbit on the other side gravity would slow it and it would fall back through the earth again

If it were simply dropped rather than given any initial thrust, then it couldn't rise any higher on the far end than the altitude it was initially dropped from, for the same reason a bouncing ball can't bounce any higher than its starting height. Not only would gravity be slowing it from the moment it passed the center and started rising again, but friction would be slowing it too.

David Brin's 1990 novel Earth involves the Earth being endangered by an artificial mini-black hole that accidentally gets free and is eating the Earth slowly from within as it bounces around in this way.

 

[CorporalCaptain]

If it were simply dropped rather than given any initial thrust, then it couldn't rise any higher on the far end than the altitude it was initially dropped from, for the same reason a bouncing ball can't bounce any higher than its starting height. Not only would gravity be slowing it from the moment it passed the center and started rising again, but friction would be slowing it too.

David Brin's 1990 novel Earth involves the Earth being endangered by an artificial mini-black hole that accidentally gets free and is eating the Earth slowly from within as it bounces around in this way.

Larry Niven had the idea of a mini-black hole dropped from surface level eating Mars in "The Hole Man" back in 1973.