what happens if you drill a hole all the way through the earth and then dropped a tennis ball down the shaft?

Question

txs green for a detailed reply.

imagine the shaft is theoretically smooth from uk to australia for example and the heat of the earths magma is not an issue; what will the ball do when dropped????

Answer 1

This question comes up pretty regularly here, so I'll paste in my previous answer to it. We're assuming that it's a nice walled hole all the way through the center to the other side that protects you from the pressure and temperature, right? -

There are 2 interesting conditions. First, assume it was a hole only, not sealed at either end. If you jumped in, you would reach terminal velocity of about 120mph within a moment or so, and continue downward. Within about 10 minutes, you would start slowing down. The reason is that for every 10 miles down, the density of air would increase by a factor of 10 (it's the same in reverse going upward until you reach low outer space about 60 mile up, by the way); after about 45 miles, the density of the air would equal that of water - and you would float at that point as if you were in water, and would have trouble trying to swim either up or down, since, unlike water, the density and therefore the bouyant force of air is not constant with depth. You'll need help to get back out from reaching only about 1/100 of the way to the center.

As a second interesting condition and to solve this problem, you could seal both ends of the tunnel and apply a vacuum. Go through the airlock in a spacesuit and step down. If the vacuum was perfect, you would accelerate to thousands of miles per hour within a couple of minutes. You would accelerate at 32ft/sec^2 until a significant portion of Earth's mass was above you, and the rate of acceration would begin to decrease, though you still would be travelling thousands of miles per hour. This link

http://hyperphysics.phy-astr.gsu.edu/hba...

calculates that your speed when you reached center would be 7.9km/sec (17,700miles per hour). Acceleration at Earth's center would be zero. Gradually as you passed center Earth, gravity in the reverse direction will increase. If the vacuum were perfect, you would slow to zero speed just as you popped out the other end. The same link as above calculates the one-way trip as taking 42 minutes. If you don't grab ahold of something, the cycle will repeat and you will start falling back toward where you started. If the vacuum was very much less than perfect, you wouldn't quite make it all the way through, and would oscillate back and forth until air friction had robbed you of all your kinetic energy and left you stuck in the center, waiting for someone to drop you a 4000-mile-long rope.

Cripes, I wish people wouldn't guess at answers... No, no liquid air, and yes, the change in air pressure will be VERY dramatic.

Answer 2

The shaft would immediately close under pressure and the tennis ball would just hit dirt a few meters down and stop.

Provided you can keep the shaft open, the tennis ball would go on falling until it hit a hot enough area, where it would start on fire and quickly burn up.

Provided you can keep the shaft open and cooled down, the tennis ball would accelerate to terminal velocity very quickly, then decelerate due to decreasing gravity and increasing air resistance until it hits the point where the pressure is high enough that the air in the shaft becomes a liquid. If the tennis ball is not sealed on the inside, it will fill up partway with liquid air, and if it is sealed it will already have been squeezed into a tennis pancake on the way down, and either way its buoyancy depends on the density of its other materials as compared with the density of air; if it does sink, it will reach the center of the Earth, go a short distance past, slow down, come back through the center, and so on until a few oscillations later it would have come to rest at the center of the Earth.

Provided you can keep the shaft open, cooled, and somehow at a constant pressure throughout, the ball would accelerate to terminal velocity very quickly, then decelerate due to decreasing gravity through the center of the Earth, a short distance up the other side, then back down and so on for a few oscillations before it came to rest at the center of the Earth.

The one other scenario is if you made the entire shaft a vacuum. According to newtonian mechanics, the ball would continue to oscillate back and form from one side of the Earth to the other pretty much forever (assuming the shaft is frictionless, because the ball will be bouncing from side to side off the shaft due to the Earth's rotation, unless the shaft goes directly through the poles). In the real world, friction with the shaft and various energy exchanges by radiation would eventually cause the ball to come to rest at the center of the Earth, although it would probably take longer in this scenario than in the other scenarios.

So the only case where the ball does NOT come to rest at the center of the Earth is if it can float on liquid air. Otherwise it eventually reaches the center of the Earth. I hope this answers your question.

Answer 3

You wouldn't have liquid air. According to the shell theorem, the gravitational force diminishes as you descend, reaching zero at the center. The air pressure will increase somewhat, but not dramatically. The value of terminal velocity will decrease as air pressure increases and as the gravitational force decreases. The ball will slowly pass the center, then proceed with slow damped oscillations about the center.

Answer 4

remember when at the earths surface things drop 10m/s/s, if you drill hole no atmosphere, so what do you think will happen?