Time to come back of stone through earths' centre.

[nimesh.joshi]

I want to find out a generlized answer of below mentioned question or just provide the concept or link to solve this problem:
Q: Considering earth as a spere, is tunnel is created passing through earths' centre. Now if a stone is just thrown from one end of the tunnel with zero m/s velocity. Will it come back? If yes, what will be the time to come back?
If another tunnel is created making angle x radian (Both ends of the create this angle with centre of the earth) will the stone come back again if it is thrown with zero velocity? If yes, then the answer in the form of angle x (angle radian).

 

[the_penetrator]

in principle it will oscillate. From end to end and back.

but variations in the gravity field (Earth is not a singular point as in exercises!) will affect this result.

the_penetrator©

PS: Are you interested in creating a hole in the Earth. Please let us so we can try get transported somewhere else. :wink:

 

[echo47]

Well sure, we can work out the acceleration equation, but we engineers like to pick on the practical issues. The earth rotates, so the stone will drag on the side of the hole, unless you drill along the axis. Air resistance will slow it down too. And it'll be a big nusiance keeping that pesky magma from filling up the hole. But the biggest headaches will probably be getting an environmental impact report and zoning permit prior to drilling.

 

[snake]

the earth are in rotation but the stone are too it will not affect the tragetory off the stone.

these idea to make a hole in the earth is the same in the cartoon dragonball-z when goku and friza are fighting in the namekuzen planet.

 

[nimesh.joshi]

I know its not possible to create the tunnel through earths' center. But if another tunnel is created making angle x radian (Both ends of the create this angle with centre of the earth) will the stone come back again if it is thrown with zero velocity? If yes, then the answer in the form of angle x (angle radian).
Then what will be the case its some how possible with angle x will be very less. Will the centrifugal force come into picture or it will be cancelled with equal and opposite force as is the case with rope and stone.

 

[guybrush]

I think that the direction of the tunnel respect to the rotational axis of the earth has to be taken in account.
If the tunnel is coincident with the earth rotational axis, the ball will oscillate up and down because of the Energy conservation principle.
Let's suppose now that the tunnel lay on equatorial plane. The ball on the surface has an angular velocity w equal to earth angular velocity but while falling down because of the gravity, the ball has to preserve the angular momentum, so decreasing the radius the angular velocity has to increase. Maybe its not impossible to write the trajectory with some math
Bye

 

[echo47]

Conservation of angular momentum. Stone has high angular momentum at surface, zero angular momentum at center. Assuming zero friction, the stone will quickly drift to the side of the hole (Coreolis force) and slide against it all the way to the center. The stone's angular momentum is transferring to Earth. The reverse occurs as the stone rises up the other side.

Some of the math:
http://www.madsci.org/posts/archives/jan2002/1011285522.Ph.r.html

Earth's orbit around the Sun further complicates the dynamics.