If you live in the USA and you drill a hole all the way through the Earth
to the other side (don't try this at home), then the Indian Ocean will pour
into the hole before you have a chance to do any experiments with it.
But this is our "gedanken" (thought)-experiment, we own it, and we can
add any additional helpful rules to it that we need. So let's say that we got
the government of India to help us with our experiment, and all the time
we were drilling, they had ships out in the Indian Ocean building a wall
around the spot we're aiming for. The wall is a cylinder, 6-inches across
the open end and about 5 miles long ... whatever it has to be to reach the
bottom and settle 1 foot into the mud down there. The wall is completed
2 weeks before the tip of our drill reaches the Earth's surface on the other
side, and the Indian Navy Corps of Engineers uses that 2 weeks to pump
all the water out of that cylinder, so that when the tip of our drill pops out
of the ocean floor, there's nothing but sunshine above it.
Now we start the experiment. The President of The United States and
several hundred scientists, important people, celebrities and dignitaries
are all gathered around the hole in the ground. The Chief Scientist on
the Project hands the stone to the POTUS, and she bends down and
gently drops it into the hole.
The stone falls into the hole, going deeper and deeper, down to where
the sun don't shine, and nobody can see it any more. People wait around
for a while, staring into the hole, but there's nothing seen or heard.
They get bored and start to leave, first one or two people at a time ...
those with the shortest attention spans. Then in small groups, and
eventually everybody gives up and leaves. There's nobody left there
86 minutes later. The stone reappears in the hole, quietly, for just an
instant, rising to exactly the same height as the President's hand was
when she let it go, stopping for an instant, and then just as quickly and
quietly falling back down into the hole, to repeat the whole journey.
Here's what happened to the stone when it was dropped:
-- It fell straight down toward the center of the Earth.falling faster and faster,
gaining speed all the time but with less and less acceleration.
-- It reached its maximum speed as it reached the center of the Earth.
I regret that just now I can't tell you what that speed was, because I don't
know it. But whatever it was, it depended only on the Earth's mass, and
it would have been the same speed for ANY stone that was dropped into
the hole and could fit through without scraping the sides.
-- As the stone passed the center of the Earth, it began to lose speed,
with small deceleration at first, but at a growing rate as it continued farther
from the Earth's center.
-- It arrived at the surface on the other side of the globe 43 minutes after
it was dropped into the hole. As it approached the surface, its speed shrank
to zero, just as its acceleration peaked at 9.8 m/s², and it stopped, for just
an instant, at the surface. In that instant, it was in exactly the same position
and situation as at the moment it was dropped from the hand in the USA, and
if there had been another hand there to grab it, it could have been grabbed
and placed on display in the Museum of Geology at Tech Mahindra's head-
quarters near Mumbai. But there was no hand there, and no sooner had it
appeared at the mouth of the hole and hesitated briefly, than it began to fall
back into the hole, just as if it had been dropped from THIS side.
-- After another 43 minutes, the stone reappeared at the mouth of the hole
in the USA and stopped for an instant. It was 86 minutes since the original
drop. The sound equipment and the lighting had all been taken down, the
technicians were gone, the reporters and their cameramen were all at the
bars, and there were only a few movers left at the scene, dismantling the
VIP bleachers and loading them into the rented trucks. One of them was
leaning against a truck, catching his breath and wiping his brow, when
something caught his eye. He noticed a stone slowly rising from under-
ground toward the mouth of the hole in the ground. Just as the stone
slowly reached the surface, he reached down, plucked it out of the hole,
dropped it into his pocket, climbed into the driver's seat of the truck, and
headed for the rental garage.
The stone did exactly the dance of a pendulum, but without the string ...
minimum speed with maximum potential energy and acceleration at the
ends, maximum speed and kinetic energy with minimum acceleration in
the middle, and a period of 86 minutes.
===> Same period as a satellite in the lowest possible Earth orbit ...
one that skims the Earth's surface just above the mountain peaks, if
there were no atmosphere. 86 minutes. Both for the same reasons,
but which I don't think I could explain like I used to, even if you wanted
to hear it.