|If you traveled through the center of the earth,
you might feel like you are falling downwards, but
when you reach the surface on the other side,
would you still feel like falling?
|Question Date: 2015-06-10
This is a fun one. Gravity pulls toward the center
of the Earth. If you drilled a hole directly
through the center and out the other side, and sat
unmoving at the perfect center you would be
weightless, since gravity pulls toward that point.
We're assuming no heat here, since the heat would
really kill you. If you stood on one side and
jumped in, you would accelerate down toward the
center being pulled by gravity. However,
gravity would decrease as you get closer to the
center since less and less mass would be pulling
you in. At the center, you'd again be
weightless but this does not mean you would stop
moving, just that there would be no force making
you go faster. You would shoot past the center and
up partway to the other side. Essentially, you
would spring back and forth hundreds of miles
around the center of the Earth until wind
resistance slowed you down at the dead center.
If there were also no wind resistance (say you
pumped the air out of the tunnel and made a
vacuum), you would spring back and forth around
the center of the Earth forever. Lost wing
resistance looks funny, but here's a video of a
feather and a bowling ball being dropped in a
vacuum. Guess which one lands first...?
When you are falling, it feels like you are in
zero gravity. This is because the force of gravity
is acting equally on all parts of your body at
once, so no part of you is compressed, unlike if
you are standing on the ground. The effect is the
same as if you are in orbit around the Earth.
Yes, you would still be falling when you
reached the surface on the other side. If you were
in an enclosed container and falling so that you
couldn't look out, you would have no way of even
knowing that you had reached the other side.
To tackle this question, let’s review what we
know about gravity. Earth’s mass pulls down on you
with a certain gravitational force, which is equal
to your mass multiplied by the acceleration. (That
acceleration is 9.98 m/s2 at the
Earth’s surface.) This force decreases quickly as
you move away from the surface, in an inverse
square (1/r2) relationship.
If you have a pen and paper, you can sketch a
graph with distance from the center of the earth
as your x-axis (always a positive value) and force
due to gravity on your y-axis (which is also
always positive). Mark a spot to represent
conditions on the Earth’s surface – somewhere in
the middle of the x- and y-axes. Draw a curved
from your point heading right that never quite
touches the x-axis. This represents the decreasing
force as you move away from the Earth’s center.
Now, we need to consider another point – what
is the force due to gravity at the very center of
the Earth (where x=0)? If you could stand at
the very center, you would still be attracted to
the Earth’s mass, but it would be pulling you
about equally in all direction. Thus, the force
you feel would be zero – you would feel weightless
at the Earth’s center! So, you can now mark a
point on your graph at the origin (x=0, y=0).
To find out what it would feel like to travel
to the center of the Earth, we have to connect
these points. We know that the force due to
gravity must be greater than zero. We also know
that the relationship must be a continuous
function – the line we draw on the graph can’t
have any gaps or jumps, and it can’t overlap
itself. The simplest case is a straight line
between the points – does this trend make sense?
As you travel beneath the Earth, you are attracted
to the mass below you but also to the mass above
and beside you. The forces directing you up and to
the side would lessen the force you feel going
downward, so the net force (y on your graph)
should be decreasing. So, your steadily decreasing
line makes sense if the mass of the Earth was
equally spread out.
How does your graph compare to the green
line on this graph from Wikipedia?
click here please
The dark blue line takes into account the
differences in the Earth’s density.
So, what would this feel like? If you
jumped into a shaft that went all the way through
the Earth, you would fall toward the center of
the Earth but the rate of acceleration would
decrease as you got closer to the center. (You’d
still keep moving faster as you moved closer to
the center but wouldn’t get faster at the same
rate.) As you passed the center of the Earth, you
would feel a force slowing you down, pulling you
back toward the center. Eventually, you would fall
back toward the center and repeat the process of
falling until you float weightless in the center
of the Earth.
Interestingly, the experience might not be like
you expect. Gravity works by pulling objects
towards something with mass. Because of this,
we feel we are pulled toward the center of the
Earth. So you would fall towards the center of the
Earth, but once you pass the center, you would
then slow down and start "falling" in the opposite
direction, back towards the center again. You'd
never make it out to the surface on the other side
of the Earth.
However, if you assumed there's no air
resistance and so the transfer of energy is 100%
efficient (and if the distance from the center of
the Earth is exactly the same to your starting
point as the opposite surface of the Earth), then
you would speed up as you approach the center of
the Earth (falling), and then shoot past the
center, and then continually slow down as you're
pulled back towards the center, but you'll
eventually reach the surface on the other side and
arrive with zero speed, because all energy would
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