[net.physics] Hole through the Earth

jim (04/08/83)

Now that the "ice in water" question has been settled, here is another
one for you.

Suppose I drill a hole straight down, through the center of the earth,
and out the other side.  Suppose I line it with something so that the
walls are not too hot and the hole doesn't collapse.

1.  Describe the behavior of an object dropped down the hole.

2.  Describe the atmospheric pressure encountered in the hole.  Is it
sea level all the way down, or what?

palmer (04/08/83)

	The gravity in the hole will be directly proportional to the distance
from the center, so the solution to this problem (ignoring air resistance)
will be exactly the same as a mass on a spring (simple harmonic motion,
r = R sin wt)
	Plugging in the numbers for the earth, I get w=1.24E-3 seconds,
or a period of 84 minutes.
	All this assumes that the Earth is uniform (no dense iron core)
Since this is not true, the actual period will be slightly shorter,
since the gravity does not fall off as rapidly.

	To calculate the air pressure, just take the weight of the column
of air above you.  8km of air at standard pressure and gravity exerts
one atmosphere of force.  You can run the equations through Macsyma if
you want, but I doubt that the air pressure in the center of the tunnel
would be much less than 100,000 atmospheres.

		The double major
		David Palmer

mambo (04/09/83)

If you drop something down the hole in the middle of the earth it will
exhibit oscillatory motion. (Introduction to Mechanics - 11.201)
Assuming that the atmosphere does eventually fill the hole, the object
will come to rest at the center of the earth after a period of time.

What the atmosphere looks like in the hole I'm not quite sure of. Don't
let my mechanics teacher know though.

				Fred - Bell Labs, Murray Hill
					(coop: Northeastern University,
						Physics Major)

student (04/15/83)

There is also another effect to worry about, the Coriolis Effect.
(Don't nag me about spelling!) Unless the hole runs through the
axis or rotation that hole had better curved. If an object is
dropped down it will curve, as seen from the top of hte hole,
against the rotation of the earth. This means that the curve must
be symmetric with respect to the center of the earth.

	If the hole is through the axis of rotation, and ignoring the
effects of friction, the object will undergo simple harmonic
motion. With friction it undergoes damped harmonic motion.

Sincerely;
Greg Hennessy;
..decvax!ucbvax!unmvax!nmtvax!student