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Re: physics question

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RainNina is not online. RainNina
Joined: 08 Apr 2015
Total Posts: 684
25 Apr 2015 06:26 PM
what happens if we were to just dig a hole straight through the centre of the earth that goes all the way down and comes out the other side
ignoring the fact that we would be burnt by the crust or whatever it is
and then someone jumped down that hole
what would happen
lol

- Ninarain | Add 27k to post count.
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maikaze is not online. maikaze
Joined: 14 Apr 2015
Total Posts: 79
25 Apr 2015 06:26 PM
you go to china dumbass
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RainNina is not online. RainNina
Joined: 08 Apr 2015
Total Posts: 684
25 Apr 2015 06:27 PM
>you go to china dumbass


DURRRRRRR

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maikaze is not online. maikaze
Joined: 14 Apr 2015
Total Posts: 79
25 Apr 2015 06:27 PM
its simple geography like the earth is round or something right
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RainNina is not online. RainNina
Joined: 08 Apr 2015
Total Posts: 684
25 Apr 2015 06:28 PM
>its simple geography like the earth is round or something right

nah its flat

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LordValkrie is not online. LordValkrie
Joined: 25 Feb 2012
Total Posts: 11344
25 Apr 2015 06:28 PM
"Ignoring the crust or whatever"
*Committing suicide brb*

It's called the core sweet heart. And since gravity pulls everything to the center I have no idea. You might die instantly from the force idk I'm speculating.

:Gallantry 2iC:
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RainNina is not online. RainNina
Joined: 08 Apr 2015
Total Posts: 684
25 Apr 2015 06:29 PM
LOL core, crust same thing AMIRIGHT

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tech4you is not online. tech4you
Joined: 04 Mar 2015
Total Posts: 123
25 Apr 2015 06:30 PM
Gravity is pulling you to the surface. So you would fall, neer the other side and fall again. Keeps repeating.
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ClanNotGuilds is online. ClanNotGuilds
Joined: 24 Dec 2008
Total Posts: 25571
25 Apr 2015 06:31 PM
you would be pulled to the centre of the earth
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Teapotus is not online. Teapotus
Joined: 06 Jul 2012
Total Posts: 2305
25 Apr 2015 06:32 PM
This physics video should help.

https://www.youtube.com/watch?v=DORLNFBXqJ8
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Forenz is online. Forenz
Joined: 31 Oct 2009
Total Posts: 7481
25 Apr 2015 06:32 PM
you slide and reach the center, and then go back up because of gravity poles or something

vsauce made a video about it i think
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ripint is not online. ripint
Joined: 28 Mar 2009
Total Posts: 11198
25 Apr 2015 06:32 PM
if hell existed u'd find it eventually
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meankiller7 is not online. meankiller7
Joined: 23 Dec 2011
Total Posts: 12241
25 Apr 2015 06:32 PM
you'd just keep falling till you ran out of force and stayed in middle
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RainNina is not online. RainNina
Joined: 08 Apr 2015
Total Posts: 684
25 Apr 2015 06:36 PM
>This physics video should help.

it all makes sense to me now.

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HarbingerXII is not online. HarbingerXII
Joined: 25 Jun 2014
Total Posts: 2115
25 Apr 2015 06:37 PM
Stupid oder get off CnG please.
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ripint is not online. ripint
Joined: 28 Mar 2009
Total Posts: 11198
25 Apr 2015 06:38 PM
https://www.youtube.com/watch?v=21tR5wyTeSY
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Scorpiosis is not online. Scorpiosis
Joined: 11 Nov 2010
Total Posts: 3039
25 Apr 2015 06:40 PM
you would crash into hell and then be trapped there for eternity

duh
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DataCrysis is not online. DataCrysis
Joined: 15 Sep 2012
Total Posts: 2546
25 Apr 2015 06:42 PM
Assuming we disregard the thing that would cause us to burn up?
the Earth would have no magnetization, and thus no gravity.
Furthermore the atmosphere would diminish in a matter of minutes.
So you'd wind up floating off and die eventually due to lack of oxygen.
But don't worry the effects of not having a spinning mantle would kill you long before that happened.
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Milnaria is not online. Milnaria
Joined: 29 Apr 2014
Total Posts: 7536
25 Apr 2015 06:47 PM
Let's suppose, just for sake of argument that you had a drill capable of plowing below where you are standing right now and grinding its way straight through the middle of the planet to the other side. Where would you end up?

Surf on the Google map below, find where you want to dig your hole and click there. After this, click on "Start Digging..." and you will see the place where you going to end up.

Scientifically speaking it would be impossible to dig a tunnel through to the other side of the world, but it’s fun to pretend! If you attempted to dig a hole to the other side of the Earth, you would be digging through:
» More than 12 000 kilometres of solid rock and molten magma
» Rock reaching temperatures up to 6000 ºC and
» Extreme pressures up to 300 million times greater than the pressures we experience on the surface of the Earth!

Also, the Earth is not a perfect sphere. It is slightly flattened at the poles, and bulges a little at the equator due to the Earth’s spin. So technically, if you dig a tunnel through to the other side of the globe, you would not come out at the place shown on a Google Map which is an almost perfect sphere.

If you did somehow manage to dig a hole to the other side of the Earth, would you fall through?
Again, theoretically no! The Earth continues to spin as you fall, gravity changes as you fall to the Earth’s centre and friction would slow you down. If you ignored all of these factors, scientists think it would take about 42 minutes to fall through the tunnel.


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Milnaria is not online. Milnaria
Joined: 29 Apr 2014
Total Posts: 7536
25 Apr 2015 06:48 PM
Want to really get away from it all? The farthest you can travel from home (and still remain on Earth) is about 7,900 miles (12,700 kilometers) straight down, but you'll have to journey the long way round to get there: 12,450 miles (20,036 kilometers) over land and sea.
Why not take a shortcut, straight down? You can get there in about 42 minutes -- that's short enough for a long lunch, assuming you can avoid Mole Men, prehistoric reptiles and underworld denizens en route. Granted, most Americans would end up in the Indian Ocean, but Chileans could dine out on authentic Chinese, and Kiwis could tuck into Spanish tapas for tea [sources: NOVA; Shegelski].
Of course, you'd be in for a rough ride. First, you'd have to pass through 22-44 miles (35-70 kilometers) of continental crust (3-6 miles/5-10 kilometers on the ocean floor) followed by 1,800 miles (2,900 kilometers) of mantle. After that, you'd have to traverse a Mars-sized outer core of liquid iron churning as hot as the sun's surface (10,000 degrees F, or 5,500 degrees C), then a solid, moon-sized inner core, and, some studies suggest, a liquid innermost core [sources: Angier; Locke; NOVA].
For sake of argument (and survival) let's pretend the Earth is a cold, uniform, inert ball of rock. While we're at it, let's ignore air resistance.
At the Earth's surface, gravity pulls on us at 32 feet (9.8 meters) per second squared. That means that, for each second you fall, you speed up by 32 feet per second -- but only near Earth's surface. Gravity is a function of mass, and mass is a property of matter. On the surface, all of Earth's matter lies below your feet but, as you fall, more and more of it surrounds you, exerting its own gravity. These horizontal tugs counterbalance each other and cancel out, but the increasing proportion of mass above your head exerts a growing counterforce to the proportionately decreasing mass below, so your acceleration slows as you near the core. At the planet's center, your acceleration due to gravity is zero -- Earth's mass surrounds you, gravity cancels out and you are weightless [sources: Locke; Singh].
You're still moving at a heck of a clip, though, so don't expect to stop there. Halfway to the center, your speed hits 15,000 mph (24,000 kph); 21 minutes after jumping in, you blow past the center at 18,000 mph (29,000 kph). Another 21 minutes later, with gravity slowing you as you go, you reach the far side and stop briefly in midair. Unless someone catches you, you'll then head back the way you came and start all over again. In our idealized case, this will continue indefinitely, like a pendulum or a spring, in a process called harmonic motion
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Milnaria is not online. Milnaria
Joined: 29 Apr 2014
Total Posts: 7536
25 Apr 2015 06:49 PM
It's funny you should ask this question. I remember a homework assignment in college in which we were asked a similar question. The question we had was, what would happen if you dug a hole all the way through the earth(from one side to the other, right through the middle) and dropped an object into the hole? The answer is as follows.

We dig the proverbial hole to China. We toss a stone into the hole. The stone is pulled down towards the center of the earth. It falls all the way to the middle of the earth once it reaches the middle, theres no more pull of gravity. But the stone is going pretty fast, and there's nothing at the middle of the earth to make it stop (since we dug all the stuff out). So the stone would keep on moving, going straight on up the other side of the hole, towards China. It would go up a ways, then (due to the pull of gravity) fall back in the other direction, back towards the center. This back and forth oscillation around either side of the middle point of the earth continues for a while. Eventually it stops, because all the while there's air that slows down the motion of the stone. The stone would stop right in the center of the earth.

In the homework problem I mentioned earlier, we were asked to assume that the earth has a uniform density throughout, and that there's no air resistance. (Physicists often make unrealistic assumptions like this.) We then found that the stone would oscillate forever, without stopping. Each time it moved back and forth, it would come all the way up to the surface of the earth, before falling back down again, and each cycle of oscillation would take about an hour and a half. In other words, if you dropped the stone in the hole, an hour and a half later it would come back up to the same spot you dropped it from. Pretty cool, but keep in mind that it wouldnt actually happen like that because the air resistance that we conveniently ignored actually has a significant effect. It would actually happen more like I described in the second paragraph, above.


Answer 2:
You might have a little difficulty digging a hole to Earth's center,
since the core is molten, but the idea is intriguing.If you tried
instead to dig a hole to the center of a body that does not have a
molten core, like a small moon, you could actually test your
hypothesis. In either case, molten or not, at the center of a
spherical body of uniform density, the gravitational attraction is
evenly distributed in all directions. The net result is that if you were
to crawl to the center, as you approached the center you would feel
progressively lighter. At the center, you would float. Now, imagine
that you bore a hole straight through the center from one side of
the small moon to the other. If you stood at one mouth of the hole
and dropped a rock into the hole, what do you think would happen?


Answer 3:
You would indeed float at the center of the earth (though I dare say it would be hot at the core of the earth!). You might not want to jump all the way from the surface, though, unless you dug your hole all the way to the other side of the planet, because you'd hit the bottom of your hole still falling.

Here's a question for you to try: Pretend the earth is a uniformly dense perfect sphere of matter, and drill a hole straight through the earth(small enough that it doesn't affect the gravitation much). Try using Newton's laws of mechanics and gravitation to relate motion through the hole to the motion of a weight attached to a spring.


Answer 4:
The simple answer to your question is that it would be very difficult to dig a hole to the center of the Earth because the immense pressure at depth would cause the sides of your hole to collapse. The interior of the Earth is also very hot so you would get cooked on the way down. Of course that's no fun and doesn't get to the core of your question.

The mass of the Earth exerts a force on everything, pulling objects towards its center which is why we fall until we run into some immovable object between us an the Earth's center (for example, the ground). If there were a hole all the way to the center of the Earth, we would fall, accelerating
until we reached terminal velocity (where the resistance of the air prevents us from going any faster). The problem is, we have momentum when falling so we would go right through the center of the Earth. If everything is being pulled toward the center of the Earth and our hole goes all the way through the Earth, what do you think will happen after we fall past the center of the Earth? Will we shoot out the other side or slow down?


Answer 5:
Ah, a very good question. This is often asked in a Physics class.
Because of the way gravity works, the gravitational force that an object feels (say you) due to another object (say the Earth) is proportional to the mass of each object. However, if you are traveling through a tunnel in the Earth, then the gravitational force that you feel is not proportional to the entire mass of the Earth but to the amount of the mass that is contained within a sphere that is centered at the center of mass of the Earth and has a radius equal to the distance you are from the center.

I know this is very wordy. To put it another way: as you travel through your tunnel towards the center of the Earth, the amount of gravitational force you experience decreases from the surface value (your weight, in pounds for example) until at the center there is no gravitational force on you at all. A way to picture this is that if you are at the center of mass of the Earth there is an equal amount of
matter surrounding you in all directions. Why would you be pulled in a particular direction?

So let's say you jump into your tunnel. You start falling freely and accelerate towards the center of the Earth due to the force of gravity. As you fall, your speed keeps increasing but more so at the beginning than as you approach the center because the amount of gravitational force pulling on you is decreasing. When you reach the center, your speed is not increasing at all but you are still moving very fast. So what happens? Do you get stuck in the center?
Nope. You overshoot the center and keep on moving. Now gravity is pulling you in the direction opposite to your motion and thus slows you down. A little at first and then increasingly as you get closer to the surface until finally, at the surface, you pop out and your speed is just around zero. If you want to, you can jump back in and pop out on the other side again.

This of course assumes that you can dig the tunnel and survive the heat during the trip. It also assumes there is nothing opposing your motion such as air resistance. What do you think would be different if there was air in the tunnel to oppose your motion?
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Milnaria is not online. Milnaria
Joined: 29 Apr 2014
Total Posts: 7536
25 Apr 2015 06:50 PM
This is a terrific, thought-provoking question. Thanks again, Louis.

First of all, no, it’s not possible. Sorry to disappoint. After all, you would have to dig through:

More than 8,000 miles of solid rock and molten magma.
Temperatures up to 6000 degrees.
Extreme pressures up to 300 million times more than what we experience on the surface of the Earth.
But, let’s say that somehow it was possible. That a hole, going straight through our planet, did exist. What would the properties of that hole be?

Firstly, falling or jumping straight down the hole is more difficult than it sounds. After about a mile of falling, you would crash into the side of the hole and likely never even make it to the other side. But why?

Because of the Coriolis Effect. The surface of Earth is constantly spinning at more than 1,000 miles per hour. If you go deeper into the Earth, it’s still moving all around you, but the mass inside doesn’t have as far to travel. It’s a bit like the lanes on a running track. The inside lane is shortest, and they get lengthier as you move out. So, if you jumped into the hole, you would soon be traveling faster than the sides of the hole around you, causing you to crash into the sides.

The only way to make it work, would be to dig the hole straight through Earth’s poles. Then the Coriolis Effect wouldn’t apply, and this hypothetical gets much more interesting.

Without the Coriolis Effect getting in the way, you would fall straight down, being pulled by gravity the same as if you jumped off of a building or bride or other high platform. And, with nothing to stop your rate of speed, you would soon be traveling at 6 miles per second. Yikes.

But, as you approached the center of the Earth, something wild would happen. The mass above you would begin to cancel out the attraction of the mass below you, meaning that the downward pull would weaken until you reach the center. And this is where things get crazy.

Once you reach the center, you would experience NO gravitational pull. Achieving, in effect, weightlessness. You would just float, being pulled equally by gravity in all directions. That said, you would still be traveling at an unparalleled speed, so you’d zip right through that awesome feeling pretty quickly.

As you pass through Earth’s center, still moving at 6 miles per second, the process would begin to reverse. And the pull would strengthen again, until you popped out on the other side of the globe about 40 minutes later.

So, supposing this impossibility were actually possible, it sounds pretty cool, right? You would be able to travel to the other side the world while experiencing weightlessness and the speed of sound. And the whole trip would take less than an hour.
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DataCrysis is not online. DataCrysis
Joined: 15 Sep 2012
Total Posts: 2546
25 Apr 2015 06:50 PM
Mil's answer took a different approach but it still seems just as (if not) more correct than my answer.
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Milnaria is not online. Milnaria
Joined: 29 Apr 2014
Total Posts: 7536
25 Apr 2015 06:50 PM
Suppose you could drill a hole through the Earth and then drop into it. How long would it take you to pop up on the other side of the Earth?

Your initial acceleration would be the surface acceleration of gravity


but the acceleration would be progressively smaller as you approached the center. Your weight would be zero as you flew through the center of the Earth. For our hypothetical journey we will assume the Earth to be of uniform density and neglect air friction and the high temperature of this trip.



For a spherically symmetric mass, the net gravity force on an object from that mass would be only that due to the mass inside its radius, and that would act as if it were a point mass located at the center. When this is analyzed in detail, you find that the gravity at any radius r less than REarth will be linearly proportional to the distance from the center.

Gravity force of spherical shell On mass outside the shell
On mass inside the shell
Taking positive r as outward from the center of the Earth:


This is the same form as Hooke's Law for a mass on a spring. It would cause the trans-Earth traveler to oscillate back and forth through the center of the Earth like a mass bobbing up and down on a spring. The angular frequency and period for this oscillation are


For this case the period of oscillation is


The traveler accelerates toward the center of the Earth and is momentarily weightless when passing through the geometric center at about 7900 m/s or almost 17,700 miles/hr. The traveler would pop up on the opposite side of the Earth after a little more than 42 minutes. But unless he or she grabs something to hold on, they will fall back for a return journey and continue to oscillate with a round-trip time of 84.5 minutes.


As a further feature of this fanciful journey, suppose a satellite could be put in a circular orbit about the Earth right above the surface. Ignoring air drag and the terrific sonic boom that would accompany such an orbit, suppose it passed overhead just above the falling person as they popped up out of the hole. The period of such an orbit would be such that it would be passing overhead every time the oscillating person popped up on either side of the Earth.

The period of the orbit is calculated from


which is the same as the period of the oscillating body.

Sanity check on the hole-through-the-Earth example

OK, if you have analyzed this example, you might well have observed that the forward momentum of the dropped object relative to the center of mass of the Earth would mean that it would almost immediately collide with the forward wall of the hole, so the whole example is really a swindle in terms of what would happen in the real world. So for this to work, the dropped object would have to bounce elastically off the front and rear walls, and would be oscillating back and forth very rapidly as it approached the center of the earth. After all, your initial horizontal speed is nominally 465 m/s relative to the center, using an equatorial radius, so that gives a fairly rapid oscillation back and forth between the walls of our idealized well as you approach the center. Neglecting the fact of how hot the center is, and the fact that your object would melt, and your hole would close - Oh, well, this is all silliness to begin with. But blithely proceeding in the face of real-world facts, if you maintained the hole and the elastic collisions, things would get more extreme on the way up toward the opposite side of the Earth since the elastic presumption would imply that the velocity perpendicular to the radius would approach twice the 465 m/s, so if the object emerged from the hole, it would go zinging off at 930 m/s, almost mach 3. So it's best not to stand close to the hole.

So the hole through the center of the Earth really doesn't work, but this example has generated some interesting comments. Having swept all these difficulties under the rug in posting this example, it yet gives some interesting correlations to orbital velocities and surprisingly to Hooke's law.
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Milnaria is not online. Milnaria
Joined: 29 Apr 2014
Total Posts: 7536
25 Apr 2015 06:52 PM
This is a beautiful question, in a small part because it’s an interesting thought experiment with some clever math, but mostly because of all the reasons it couldn’t be done and wouldn’t work. Right off the bat; clearly a hole can’t be drilled through the Earth. By the time you’ve gotten no more than 30 miles down (less than 0.4% of the way through) you’ll find your tunnel filling will magma, which tends to gunk up drill bits (also melt everything).


Jumping into a hole drilled through the Earth. What’s the worst that could happen?

But! Assuming that wasn’t an issue, and you’ve got a tube through the Earth (made of unobtainium or something), you still have to contend with the air in the tube. In addition to air-resistance, which on its own would drag you to a stop near the core, just having air in the tube would be really really fatal. The lower you are, the more air is above you, and the higher the pressure. The highest air pressure we see on the surface of the Earth is a little under 16 psi. But keep in mind that we only have about 100 km of real atmosphere above us, and most of that is pretty thin. If the air in the tube were to increase in pressure and temperature the way the atmosphere does, then you’d only have to drop around 50 km before the pressure in the tube was as high as the bottom of the ocean.

Even worse, a big pile of air (like the atmosphere) is hotter at the bottom than at the top (hence all the snow on top of mountains). Temperature varies by about 10°C per km or 30 °F per mile. So, by the time you’ve fallen about 20 miles you’re really on fire a lot. After a few hundred miles (still a long way from the core) you can expect the air to be a ludicrously hot sorta-gas-sorta-fluid, eventually becoming a solid plug.

But! Assuming that there’s no air in the tube, you’re still in trouble. If the Earth is rotating, then in short order you’d be ground against the walls of the tunnel, and would either be pulverized or would slow down and slide to rest near the center of the Earth. This is an effect of “coriolis forces” which show up whenever you try to describe things moving around on spinning things (like planets). To describe it accurately requires the use of angular momentum, but you can picture it pretty well in terms of “higher things move faster”. Because the Earth is turning, how fast you’re moving is proportional to your altitude. Normally this isn’t noticeable. For example, the top of a ten story building is moving about 0.001 mph faster than the ground (ever notice that?), so an object nudged off of the roof can expect to land about 1 millimeter off-target. But over large changes in altitude (and falling through the Earth counts) the effect is very noticeable: about halfway to the center of the Earth you’ll find that you’re moving sideways about 1,500 mph faster than the walls of your tube, which is unhealthy.


The farther from the center you are, the faster you’re moving.

But! Assuming that you’ve got some kind of a super-tube, that the inside of that tube is a vacuum, and that the Earth isn’t turning (and that there’s nothing else to worry about, like building up static electricity or some other unforeseen problem), then you would be free to fall all the way to the far side of the Earth. Once you got there, you would fall right through the Earth again, oscillating back and forth sinusoidally exactly like a bouncing spring or a clock pendulum. It would take you about 42 minutes to make the trip from one side of the Earth to the other.


The clever math behind calculating how an object would fall through the Earth: As you fall all of the layers farther from the center than you cancel out, so you always seem to be falling as though you were on the the surface of a shrinking planet.

What follows is interesting mostly to physics/engineering majors and to almost no one else.

It turns out that spherically symmetric things, which includes things like the Earth, have a cute property: the gravity at any point only depends on the amount of matter below you, and not at all on the amount of matter above you. There are a couple of ways to show this, but since it was done before (with pictures!), take it as read. So, as you fall in all of the layers above you can be ignored (as far as gravity is concerned), and it “feels” as though you’re always falling right next to the surface of a progressively smaller and smaller planet. This, by the way, is just another reason why the exact center of the Earth is in free-fall.

The force of gravity is F = -\frac{GMm}{r^2}, where M is the big mass, and m is the smaller, falling mass. But, since you only have to consider the mass below you, then if the Earth has a fixed density (it doesn’t, but if it did) then you could say M = \rho \frac{4}{3}\pi r^3, where ρ is the density. So, as you’re falling F = -\left(\frac{Gm}{r^2}\right)\left(\rho \frac{4}{3}\pi r^3\right) = -\left(\frac{4}{3}G\rho \pi\right) mr.

Holy crap! This is the (in)famous spring equation, F = – kx! Physicists get very excited when they see this because it’s one of, like, 3 questions that can be exactly answered (seriously). In this case that answer is r(t) = R\cos{\left(t\sqrt{\frac{4}{3}G\rho \pi} \right)}, where R is the radius of the Earth, and t is how long you’ve been falling. Cosine, it’s worth pointing out, is sinusoidal.

Interesting fun-fact: the time it takes to oscillate back-and-forth through a planet is dependent only on the density of that planet and not on the size!
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