Random gravity question.


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This a problem we did back at school. As Relativity_17 and others have said, the gravitiational pull would be from every direction, and thus would cancel out. Ie it would be zero gravity

If you solve this rigorously you find that as you dig deeper into the earth the gravitional field you feel will just be from all the mass beneath you (so if you are 10km from the centre of the earth, you'd feel a gravitational pull from an object 10km in radius and the rest of the earth above you will have no effec ton you).

While the Gravitational force F is proportional to 1/r^2 if you are out in space away from the earth's surface, once you are inside the earth, the Force is proportional to r (specifically F = (GmMr)/R^3 , where M is mass of earth, R is radius of earth, r is distance you are from centre and m is the mass of you) So you can see that at r=0, F=0.

One thing that's quite interesting is that if you dug a tunnel from one side of the earth to the other, because the force is greatest at the surface and zero at the centre, if you dropped an object down this tunnel, it would simply oscillate from one side of the earth to the other. In fact it would take 40 minutes to do (that's 40 minutes to get from london to australia). In fact if you dug any tunnel to any location on earth, assuming zero friction, it should still take 40 minutes. So if you had a straight tunnel from London to New York and you "dropped down" it, you would take 40 minutes to get there.... theoretically that is. In reality there'd be too much friction to do so

Bravo! Mathematically, this concept is illustrated by using the Shell Theorem.

One caveat is that the model assumes constant density while in reality, the density of the Earth is not uniform everywhere so there might be unexpected differences as you drill towards the core, and of course, the model does not take into account the astronomical temperature as you move closer to the centre.

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thank u :p

:p You're welcomed.

Have you got the answer you're after? :) Point me to the thread if you can even though my Physics is more or less beginner quantum mechanics and special relativity. General relativity is beyond me.

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well my physics is at the basics.. but i still like to read anything PHYSICS :p

so i went through all the recent topics and all the catagories :p

and the most impressive was about the magnatism..

and the other one was about these particles who pass through mass as its not even there..

as in the whole world is invisible to it.. or unreal.. or not SOLID..

it was the best thing ..!!!.. glad i know about it :D

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well my physics is at the basics.. but i still like to read anything PHYSICS :p

so i went through all the recent topics and all the catagories :p

and the most impressive was about the magnatism..

and the other one was about these particles who pass through mass as its not even there..

as in the whole world is invisible to it.. or unreal.. or not SOLID..

it was the best thing ..!!!.. glad i know about it :D

Electromagnetism sure is fun but it can be described by a larger theory which also includes the strong force and the weak force.

I can't imagine your reaction if you were in my Subatomic Physics lectures. You wouldn't see the physical world the same way ever again. lol

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Electromagnetism sure is fun but it can be described by a larger theory which also includes the strong force and the weak force.

I can't imagine your reaction if you were in my Subatomic Physics lectures. You wouldn't see the physical world the same way ever again. lol

well

can u make me see it that way?

i really want to..

just tell me some points u learnt that would make me see the world differently..

it would be really nice of u

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For example, the electron is surrounded by clouds of photons which decay into a virtual electron and a virtual positron which in turn annihilate into another photon and so the cycle goes. That implies that the charge of the electron which is quoted as 1.6E-19 coulombs is only the charge measured at large distance. The true charge of the electron is infinite and is shielded by the dipolar coulds mentioned earlier. If you try to go closer and closer to the naked electron to measure its charge, you're going back in time.

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Remember that the Earth's gravity is not from the center of the Earth, but from the body as a whole. In physics problems, we often assume large objects to be a single point in space, but this is a false assumption since the Earth is very large. Every atom has mass and therefore exerts gravitational force. At the center of the Earth, you would be experiencing gravitational force from all the Earth's matter around you. If the Earth was spherical (it's not, but it's pretty close), you would experience zero gravity due to the vector cancellation of all gravitational forces by the Earth.

However, there is also the moon, which exerts gravitational force on the Earth and you (remember the ocean tides). So I suspect that in your hypothetical scenario, you would experience near-zero gravity but the net gravitational force vector would pull you toward the moon.

As an aside, your question is far from random.

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gravity would still pull you towards you center of the earth - even if you are at it. you'd still need to travel at more than 9.8 m/s^2 to escape earth's gravity.
Yikes. Way wrong, in lots of ways. As we've already discussed, the net gravitational force at the center of Earth is approximately zero due to the cancellation of graviational forces from all angles. 9.8 m/s^2 is the acceleration due to gravity when standing on Earth's surface. It is not a speed nor a velocity. Big difference, and you'd fail every physics class taken without knowing the difference. Furthermore, as you travel away from Earth, the acceleration due to Earth's gravity would be less than 9.8 m/s^2, so the net force required to "escape" Earth would decrease as you made it further into space.
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