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Thread: Drilling completely through the earth and jumping down the hole.

  1. #1 Drilling completely through the earth and jumping down the hole. 
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    So I have thought about this for a long time and i decided to post it here to see what you guys think.

    Say that the earth has no hot core (impossible I know) but you drill completely through the earth top to bottom (again impossible) and in an Alice In Adventure Land-esque fashion you jump down the hole. Now we all know that gravity holds people on top the earth down and people on the bottom up so when you reach the center of the earth gravity should be pushing on you and pulling you from every direction which should make you stop right in the center of the earth right? PROVE ME WRONG I HAVE THOUGHT ABOUT THIS ABOUT 3 YEARS. Of course remember the no hot core with magma and all that.


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    Moderator Moderator Janus's Avatar
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    Sorry, but wrong. As you fall towards the center of the Earth, you speed up, in addition, The net gravity pull on you will dcrease so that when you reach the center, it will be zero.

    The force due to gravity is found by:



    Where M and m are the masses of the two objects and d is the distance between their centers.

    In this case we will make M the mass of the earth pulling on you.

    Now, at first glance, it seems like as you get closer to the center of the Earth, and d gets smaller, F would get larger. The reason it doesn't is due to Newton's Shell theorem.
    Isaac Newton was able to prove mathematically that is you had a hollow sphere, and you were inside of it, the force of gravity inside would be zero everywhere in the sphere. No matter where you were in the sphere, all the different gravity pulls on you from the outer shell would cancel out.

    Now as you fall in towards the center of the Earth, it is like you are falling through a series of concentric hollow shells. The effect is that all that part of the Earth that is furhter from the center than you are exerts no net force on you. So the only part of the Earth's mass that still pulls on you is that part that is closer to the center than you are. So while d is getting smaller, M is getting smaller even faster. The end result is that the gravity pulling you towards the center of the Earth gets weaker the farther you fall.

    Once you reach the center, you will be mooving very fast and will fly right by it and start climbing up again towards the opposite side of the Earth. As you climb, the gravity pulling you back to the center will get stronger and begin to slow you. By the time you reach the other side of the Earth, it will finally stop you (assuming no friction), and then you will start to fall back to the center. You will repeat the same trip in the opposite direction, returning to where you started. If nothing stops you , you will just keep doing this.

    If there is friction, say from air in the hole, you won't be traveling as fast when passing the center and won't climb all the way back up to the surface before falling back. With each trip, you lose a little more speed and height. Eventually, you will settle at the center, But not until you oscillated back and forth a number of times.


    John Galt and Implicate Order like this.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    Forum Cosmic Wizard
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    Quote Originally Posted by Schrodinger's "Dead" Cat? View Post
    Now we all know that gravity holds people on top the earth down and people on the bottom up so when you reach the center of the earth gravity should be pushing on you and pulling you from every direction which should make you stop right in the center of the earth right?
    If there was air in the hole, you would quickly be incinerated/killed by the increasing temperatures and pressures as you descended. (NOT due to the heat of the core, but due to the standard adiabatic lapse rate.)

    If there was no air in the hole, and it was straight, you would hit the wall as your tangential speed drove you into the "forward" wall of the tube.

    If there was no air in the hole and you drilled it straight from pole to pole, you would fall through the center and out the other side. You'd then oscillate between the two ends forever.
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    Forum Professor pyoko's Avatar
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    You also have to take into account terminal velocity for a body at particular gravity and particular air pressure.
    It is by will alone I set my mind in motion.
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    Thanks Janus I wanted an answer to this for a while that was my first thought that you would go up and down repeatedly but then I thought you would just stop in the center after thinking it through. Thanks for clearing it up! And you don't happen to be a god suffering from a multi-personality disorder, right?
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    Moderator Moderator Janus's Avatar
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    Quote Originally Posted by Schrodinger's "Dead" Cat? View Post
    And you don't happen to be a god suffering from a multi-personality disorder, right?
    No, but I can be a two-faced SOB (no, not really)
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    Quagma SpeedFreek's Avatar
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    And interestingly, if you were to free-fall towards the Earth from a satellite in a circular orbit, and you fell straight down that hole (assuming no air resistance) through the centre of the Earth, you would continue to fall past the centre, out the other side and slow to a halt just in time to meet the same satellite again on the other side of its orbit before you fell back down again!



    http://hyperphysics.phy-astr.gsu.edu.../earthole.html
    "Ok, brain let's get things straight. You don't like me, and I don't like you, so let's do this so I can go back to killing you with beer." - Homer
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    Moderator Moderator Janus's Avatar
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    Quote Originally Posted by SpeedFreek View Post
    And interestingly, if you were to free-fall towards the Earth from a satellite in a circular orbit, and you fell straight down that hole (assuming no air resistance) through the centre of the Earth, you would continue to fall past the centre, out the other side and slow to a halt just in time to meet the same satellite again on the other side of its orbit before you fell back down again!



    Hole Through the Earth Example
    In addition, if you dig your shaft at an angle other than straight down, no matter what angle you dug at and where it came out, assuming no friction, the time it takes for you to traverse the shaft comes out to be the same time.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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