Exploring the Earth's Pole-to-Pole Hole: A Trench Digger's Tale

[Pocketwatch]

Suppose a hole was drilled from the north pole to the south pole all the way through the earth. The hole is five feet in diameter. Assume it is not freezing cold and you are standing next to the hole and curious about what would happen to you if you jumped in. While you are standing there trying to decide if you should jump into the hole, you decide to lie down on the ground and you take a long nap. When you wake up, you discover that the hole has changed. Then a girl walks up holding a glass of water...

Meanwhile a man is living at the equater and he likes to dig trenches. One day he begins digging a trench. The trench is five feet wide and the man keeps the bottom level as he digs. The trench is running north and south. After digging the trench ten feet deep and whatever length it took to keep the bottom level, the man hears his wife calling him from the south end of the trench. So he walks out the south end of the trench and his wife gives him some food. His wife tells him that his daughter is at the other end of the trench with something to drink. So he walks back through the trench and out the north end and his daughter gives him something to drink. The man goes back to work and digs the trench 100 feet deeper. He hears his wife calling again from the south end so he walks out the south end, eats, then walks out the north end of the trench and gets a drink from from his daughter. The man keeps digging the trench deeper and deeper and and to keep the trench level it becomes longer and longer. The man knows that his wife and daughter are afraid to come into the trench so whenever he gets hungry he walks out the south end and his wife feeds him and whenever he gets thirsty he walks out the north end and his daughter gives him something to drink.

(For the purpose of this story, let us assume that the man does not run into any water to fill his trench, and the walls of his trench do not collapse and the temperature stays comfortable and he has no problem with air to breathe.)

The man keeps making the trench deeper and deeper and longer and longer until finally he reaches the hole that is drilled through the Earth from the north to south pole. His trench also is from pole to pole. The man is an expert trench digger and his trench matches perfectly with the hole.

The man is feeling thirsty, so he decides to walk to the north end of his trench to get a drink from his daughter. As he nears the north end of his trench he sees his daughter standing outside the trench with a glass of water. He also sees you standing next to his daughter. Feeling tired, the man calls to you and asks you to get the glass of water from his daughter and bring it to him. Without thinking you get the glass of water and you walk in and give it to him...

Please give me your comments on whether this seems logical or not.

 

[HallsofIvy]

I don't think the concepts "logical" or "illogical" apply. It just doesn't SAY anything. What is the point of the story?

 

[Einstein]

hmmmm...i c wat ur getting at...is it that..?...are u..?..actually I am not!

 

[LURCH]

I think the point is that you have just stepped into the hole you dug, and were pondering whether or not to jump into.

Is this not the crux of your question, pocketwatch?

 

[Janus]

Okay, the problem here is when you say that in order to keep the Trench "level" it must get longer as it gets deeper. This depends on what you Mean by "level" . if you mean as by measured by a plum bob, then no, the trench does not get longer as the bottom of the trench follows the curve of the Earth and actually gets shorter as you go deeper.

If you mean "Flat" as along a sight line, then the floor of the trench will not seem Level at all points as the man walks form end to end . As he walks from the center of the trench to the ends, it will seem to be increasing "uphill" , the deeper the trench ther more prounouced the effect. by the time he reachs, the hole you drilled, he will have to climb up a vertical well.

Hope this helps.

 

[ShadowKnight]

Almost sounds like something from a David Lynch film...
I think I understand your analogy - are you attempting to say that the ditch digger has dug a 5 foot wide trench where the bottom is always level with the long central axis of the earth? Almost like a very thin slice of an apple being removed? If I have your analogy right let me know but I still don't understand the question or the point you are trying to make.

 

[HallsofIvy]

[QU0TE]Okay, the problem here is when you say that in order to keep the Trench "level" it must get longer as it gets deeper. This depends on what you Mean by "level" . if you mean as by measured by a plum bob, then no, the trench does not get longer as the bottom of the trench follows the curve of the Earth and actually gets shorter as you go deeper. [/QUOTE]

I understood that. My question is still "what is the point"? What exactly do you want people to comment on?

 

[Pocketwatch]

Maybe it will help to visualize the trench another way. To make things easier let's assume that the Earth is a perfectly round sphere with a diameter of 8000 miles. Then we drill a hole through the Earth from pole to pole 5 feet in diameter. We then thread a cable with the same diameter through the hole. We then take both ends of the cable and pull so that we remove a slice of the Earth 5 feet wide forming the trench. In the middle of the trench the sides will be 4000 miles. We will then be 4000 miles from each of the poles. So, if we start at the north pole and go 2000 miles into the trench. the sides will be 2000 miles high. If we go 1000 miles the sides will be 1000 miles high. Now if we are standing at the start of the trench and we step i foot (12 inches) into the trench the sides would be 1 foot high. If you walk 10 feet. the sides would be 10 feet high. At the start of the trench if you placed a level on the ground it would show to be level and at any other point in the trench it will be level.

 

[Pocketwatch]

I know there is a flaw in my line of reasoning about gravitational forces. My line of reasoning is that gravity pulls in straght lines only. In the hole through the the earth, If I jumped in the hole, I would not encounter any mass that is directly beneath me pulling me down. Obviously, if you jumped into the hole you would fall somewhere.

I feel foolish now for expressing my misunderstanding about gravity but when I was imagining the man digging the trench it all seemed feasable. At some point in his trench digging the man would have to fall one way or the other.

 

[ShadowKnight]

So my analogy of the apple slice was close to the mark then.
I imagine your trench digger would still be 'pulled' toward the center of the earth, like the rest of us on the surface are. I can't imagine what the missing slice (and missing mass) would actually do to the Earth's gravity except possibly reduce the overall gravity since there is now mass missing. In my mind it MIGHT change the position of the center of the Earth (and accordingly the center of the gravitational pull) since the mass has now been greatly redistributed by the missing 'slice'. If this line of reasoning is correct than your digger could keep digging and the gravitational force would remain under his feet.

 

[Pocketwatch]

I agree with you ShadowKnight. It would seem to work that way, but still I am not sure. I am sorry that I did not pose my origional question so that everyone could understand it.

 

[Integral]

I am not even going to try to figure out what your "trenches" are all about. Let us first consider the problem of the simple hole through the earth. First assume the Earth is perfectly stationary, so it would indeed be possible to fall "straight" through the hole.

The gravitational force felt by a body is proportional to the distance to the center of the earth, as you approach the center your acceleration due to gravity reduces, finally to zero at the center.

So if you jumped into the hole, you would accelerate attaining a maximum speed at the center of the earth, then slow down until you reached the other end of the hole. At that point your speed would be zero, so you would fall back into the hole, repeating the process.

Essentially you would become a human yo-yo bouncing back and forth though the hole.

Of course if the Earth had ANY other motions you would hit the side of the walls at some point, this would finally result in your (bloody pulp of a body) coming to rest, suspended in the center of the earth.

Now if you were to dig a tunnel, or trench if you will, on shortest path from say NY city to South Africa, your weight would vary as you walked the distance, depending on you actual distance to the center of the earth.

 

[kokain]

I see what you are doing (I think). The "hole" that you are pondering over becomes the "floor" while you napped. I agree that the center of gravity would change as the mass was shifted. A cool question remains. If you did not sleep, but instead stood still and focused on the horizon (not where the trench is coming from, but at a right angle to the trench, say the trench on your right) would you begin to lean toward the trench as the center of gravity was shifted to your left? That would be cool. That is saying that the dirt from the trench was gone as it was dug. But where would the center of gravity be if the dirt were piled on the sides of the trench. Would the center of gravity be inside the void of the trench? Very MC Esher.

 

[Ring]

This is similar to the thought experiment, “what if the Earth were a cube"?

All the water and atmosphere would be in an areas near the center of the faces and getting to the edges would feel like you were climbing a vertical cliff. Starting from the edges you’d have the longest steepest perfectly flat ski run in the history of the universe.

 

[Marzright]

A little off topic

All this talk about gravity and mass, how gravity is due to distance from mass. made me think of somthing, perhaps known to someone out there.
How could of the Earth became bigger. If the Earth needed a start mass to obtain mass.
Perhaps I am asking to much... or not enuff.. I'm not sure how to make this clearer. Talk to yas soon.

 

[Pocketwatch]

The road that the man is building is parallel with the hole that is drilled through the center of the earth.

His road would always be downhill towards the midpoint and uphill to the other end.

To keep his road level, the man has to build it in a circular pattern instead of straight lines.

To build the road with the midpoint at the center of the earth, his road would follow a circle with a diameter the same as the radius of the earth.

 

[Alkatran]

If anything this is an excellent mind-trick. I didn't even think about the fact that he stepped into a hole...