If an object were to fall into a 2-sided hole through the center of the earth, where would it end up?

Question

The hypothetical hole is dug straight down, through the center of the earth, and out the other side. My theory is that the object will fall into the hole, and its momemtum will take it somewhat past the center of the earth. It will then fall in the opposite direction somewhat less past the center than previously. This will continue somewhat like a pendulum coming to rest until the object eventually is suspended in the hole at the center of the earth. If anyone can offer the scientific principles that either prove or disprove my theory, it would be greatly appreciated. Thank you.

Answer 1

You are correct. With no friction the object would oscillate forever between the surface where you dropped and the surface on the other side. Each time it would rise just to the surface and fall back again. With friction slowing it, it would not rise all the way to the surface and would rise a little less on each trip past the center, eventually coming to rest at the center of the Earth.

Answer 2

If you ignore friction -- suppose the hole is a sealed vacuum tube, then I think that the object -- a ball -- will oscillate from one side of the earth to the other ad infinitum.

It will accelerate all the way to the center, attaining maximum momentum and velocity there, and that "initial velocity" will be exactly sufficient to propel it (decelerating, of course) all the way to the other side, at which time and place the whole operation repeats itself in reverse.

The only thing (except friction) that could mess this up is the rotation of the earth. That might have an effect, and I think that's a tougher problem to figure out.

Answer 3

eliminating the overwhelming problem of heating at the center of the core ( for s&g's of course) the hollow tube would act as a "railgun" or Mass Driver . especially considering the laws of thermodynamics where in an object in motion would tend to stay in motion untill another force acted upon the object. In this highly untestable and seriously hypthetical situation the gravitational field would accelerate the objecttoward the center of the earth at which point all gravitational forces would be nulled and no longer act upon the object now travelling at terminal velocity. your assumption is that the forces would immediatly act on the object in the same strength as they did at the surface, which would not be the case because those forces would slowly start to act on the object. at which point the centrifigal forces of the rotation of the sphere would act on the the object with much greater force. causing the object to accelerate to an least an gravity escaping vector of over 17,000 miles per hour. Doesn't really disprove your theory just another peice for thought

Answer 4

You're absolutely right! Once the object is released gravity will accelerate it towards the center of Earth. The closer the object gets to the center, the stronger will be the gravitational force and its rate of acceleration will increase. The object will reach the center where gravity is null but continue on "upward" due to its momentum. As it pulls farther and farther away from the center, gravity will strengthen while the object's momentum decreases and it will slow down, stop, start back towards the center...and so on and so on.

Answer 5

You are describing what is known in classical mechanics as "the gravity train". If we can ignore friction (which of course we can't) and if we can ignore the engineering issues with the intense heat (which of course we can't), a "tube" that goes straight between any two points on the Earth can be used to transport anything from one point to the other in 45 minutes... no matter if you are going from the US to China or from New York City to Washington D.C.

Answer 6

According to theory, if you calculate, using Newton's universal formula of
g = GMm/(r squared)

You will obtain the result that the acceleration due to gravity becomes zero AT HALF THE DISTANCE TO THE CENTER OF THE EARTH. This is due to the change in M, that is mass of the earth to be considered is only that which is below the object.

So, this answer, is raising more questions instead of clarifying your doubt, isn't it?? Two points to me!!

Answer 7

You are somewhat right. The force of gravity on both sides of the earth will hold it in the center.

Answer 8

Without going back to my Physics books and re-calculating gravity as the the diameter of the Earth (and mass) shrinks, I believe your hypothesis is correct. Especially when friction is thrown in

Thanks,
Buster

Answer 9

that sounds rite... but the object would burn up/ compact itself before it gets there