# A hole in earth

1. Jun 3, 2009

### jontyjashan

Hey
i m a newbie
suppose i drill a hole that passes through the centre of earth and reaches the
other point on earth
now i drop a ball in this hole
where wud it land???????????

2. Jun 3, 2009

### benk99nenm312

The ball would first go all the way to the center, and because of its momentum, it would keep moving through. It would get to a certain point on the other side (still in the hole) but its momentum would be counteracted by gravity, where then upon it would fall again to the center. It's sort of like a pendulum. This would continue to happen unitl the ball ended up at the center of the earth, where it would remain stationary.

3. Jun 3, 2009

### DaleSwanson

I agree with benk99nenm312, but I'd like to add some points. First if there were no friction or other forces other than gravity working on the ball then it would reach exactly the other side of the Earth, then fall back through. It would never stop going back and forth. Any friction though and it would never make it to the other side, it would stop short, and eventually would settle in the center.

Secondly I'd like to mention that no matter where the two exits for the hole are it would always take about 42 minutes for it to fall through. The formula for figuring out how long it will take is:
T = $$\pi * \sqrt{r / g}$$

Where T is time taken, r is radius, and g is acceration due to gravity. For Earth r = 6,378,100 m, and g = 9.81 m/s.

4. Jun 3, 2009

### Chronos

Correct, about 42 minutes. Unless the hole was from pole to pole, the ride would be bumpy.

5. Jun 7, 2009

### maze

If you drilled at a random place, how likely is it that you would hit land on the other side, as opposed to ocean?

6. Jun 7, 2009

### protonchain

75% of the Earth is water..... so 25%? :tongue:

7. Jun 7, 2009

### benk99nenm312

Ahh.. but the probability also depends on where you first start drilling. It's easy to hit China from where I am, but its hard to hit New Zealand from Greenland.

8. Jun 8, 2009

### Integral

Staff Emeritus
Benk,
You need to pull up Goggle Earth, China is in the Northern hemisphere,think about it.

9. Jun 8, 2009

### benk99nenm312

I wasn't necessarily saying it with the intention of having great accuracy, I was just jokingly stating a point. (China is popularly referred to being America's opposite position on the globe.)

10. Jun 8, 2009

Hence the title of the film "the China syndrome"

11. Jun 8, 2009

### LURCH

This is a fairly important point. It highlites the fact that the ball is essentially entering into a very elliptical orbit. In a vacuum it will continue to go back and forth through the center o fthe Earth. But, if the hole were not at the poles, then it is on a part of the Earth's surface that is moving (Eastward). As the ball falls down the hole, it is desending to a lower orbit, which means a faster orbit, which means ti bumps into the Eastern wall of the hole.

12. Jun 8, 2009

### fluidistic

I'd like to know how did you derive this formula.

13. Jun 8, 2009

### jontyjashan

how to derive this formula

14. Jun 8, 2009

If it is assumed that the earth has uniform density the object will move with S.H.M.
Maximum acceleration=g
g=-w^2.r (w= angular velocity)
T=2pi/w (T= time period i.e. time to go there and back again)
It is the same time period as for a satellite in close orbit.

15. Jun 8, 2009

Hey the orbit would be the least of your problems, the second your drill reaches molten rock, and metal under its enormous presure you'd have global warming the likes of Venus.

16. Jun 8, 2009

### maze

I don't think so. For example, you could imagine a world where one hemisphere is all land and the other is all water, in which case the answer would be zero.

17. Jun 9, 2009

### Dragonfall

Seriously? 42 minutes? Awesome. I'm gonna stop here before the numerologists creep in.

18. Jun 9, 2009

### fluidistic

Yes, but as Dadface pointed out this is only true if we suppose the density of Earth as a constant, which strongly differs from reality.

19. Jun 9, 2009

### benk99nenm312

yah, I was wondering about that. The only way I see to really calculate the time it would take is to split the earth up into sections according to density. Then, you would have to do some calculations for each section and add them up... maybe?

20. Jun 9, 2009

### Nabeshin

Welcome to the Wonderful World of Integration.