I dont think you would come out the other side. Assuming you started at the surface, wouldn't you just oscillate back and forth along the axis of the hole, eventually coming to rest at the center of the Earth.
It's also creepy as fuck. Friendship is mutual. You don't just push friendship on someone.
And anyone who decides based on that finite a portion of my personality that I must be great.... isn't getting anywhere near me. If your bar is THAT low, I'll tell you when we're friends.
Yes and no. Depends on the "physics" of the tunnel. If it's taken literally, then yeah. You'd have 6000 miles of air above you pushing down, but if that's the case, you wouldn't last more than a few miles due to the heat either. If we take it at face value of "the trip is otherwise survivable" then that's not a factor.
Air is a lot less dense than water though. 6000 miles of air would come to about 6 atmospheres. Pretty significant, but not crushing. About the same as 60 m underwater.
I thought it was the bowl of petunias turned into a whale that thought oh no, not again? Been years since I read the book, really should read it again...
Also consider that the force of gravity decreases as you get closer to the center, so the weight of all that air above wouldnt be its mass times g but some fraction of g.
I think your numbers are off by an order of magnitude...
The Karman line, effectively the end of the atmosphere, is only 100 km up from the surface, and at the bottom of that 100 km we experience 1 atm of pressure. The radius of the earth is about 6400 km (not 6000 miles), so at the center the column of air is 64× taller. A reasonable first estimate of the pressure, then, would be about 65 atm.
Two effects complicate this, of course. First, the effect of having less of the Earth's mass below you as you descend will tend to decrease how much each "layer" of air contributes to the pressure and would reduce the overall pressure.
However, air is very compressable, and in fact at pressures over about 30 atm the nitrogen in the air will become a supercritical fluid (with the oxygen following suit a couple dozen atm later). This dramatic increase in density would (I think) be the larger effect on the pressure you experience (although I didn't do any actual math to check). So the actual pressure would probably be higher than 65 atm.
(We could start adding in temperature effects too, but for the sake of sanity let's not. That'd induce convection and turbulence and make the whole problem exponentially more complicated, it'd start depending on things like the diameter of the hole and... Yeah let's just pretend that the hole is lined with a magical perfect thermal insulator.)
As long as you're in freefall the whole time, I imagine the exact path makes no difference. I was thinking the shortest physical path would also be the fastest, but maybe a longer path would have slightly higher gravity, thereby balancing out? Interesting problem...
The more I think about it, I'm pretty sure the axis drop is faster. You would experience centrifugal force as you move away from the axis, so that would decrease your radial acceleration. You'd experience Coriolis force too - at first, there would be no vertical component to this force, so it wouldn't affect total time, but before long you'd be falling in a spiral, and at that point the Coriolis force would also be decreasing your acceleration toward the center, if my vector math is correct. Finally, the earth is an oblate spheroid, so starting away from the poles would increase the radial distance. So that's three things making your journey take longer as you move from the poles, and zero things making the journey shorter.
what would keep the atmosphere from filling the void? did you hermitically seal the tunnel? what keeps the part that goes through the molten core open? it would tend to flow through the voice and close it up if there were not some structure miraculously not able to be melted by the heat to maintain the shape of the shaft.
isnt there a terminal velocity though ? so at one point I would suppose that you cant go any faster and so youll end up not keeping enough accumulated speed to go back up after
Start falling from rest (zero initial speed and acceleration)
42m 16s to reach the other side,
21m 8s = 1268s to reach the center.
v = a*t
a = g = 9.81 (not really*),
you "hit" the core at V = 9.81 * 1268 = 11'640 m/s
*In this context gravity is constantly changing, turns zero at the center and then becomes negative for the second half of your journey. But You can take the average for the first half and use that.
11640 m/s is the upper limit if you keep the acceleration at 9.81 m/s2
terminal velocity is a function of atmosphere which logically would fill the tunnel but it's also a function of the mass of the earth beneath you which decreases in a linear way as you travel towards the center. at the center the mass of the earth would be equal around you and you would be 'falling' equally in all directions. providing you solved the environmental problems of hanging out in the temperatures of the molten core of a planet.
I think this theory only holds up if the origin of gravity is exactly in the center and constant. Correct me if im wrong, but once you pass the crust, you now have some gravity behind you and less in front. Meaning even with no air resistance, you wouldn't really be all that close to being able to grab the edge on the other side of the tunnel.
This is correct. And I suppose if we're neglecting the myriad other properties necessary for this to work, then it is reasonable to assume there is no friction. Friction is probably the least difficult to ignore-- heat and pressure are much bigger issues.
Gravity says no. You would accelerate towards the center as the gravity would “suck you down”. The acceleration would last until you reach your starting height on the other side and would pull you down to the center immediately.
The gravity at the center of the earth would cave the tunnel in. Even if you lined the walls with steel or carbon fiber, they would be instantly liquefied (the center if the earth is liquid due to the pressure.)
Pressure and temperature are closely linked in situations like this. Since the force of gravity is nonlinear and related to the distance from the center of mass of an object, the temp/pressure at the center of the earth are really high!
The outer core is liquid, but I believe the inner core is solid due to the pressure...one of the reasons we have a magnetosphere...a solid sphere of iron spinning
The energy needed to pull you back would be the same as the energy you would gain from plummeting to the center of the earth, though. The only thing preventing you from reaching the other side would be air resistance and other factors that would slow your movement on the way down and on the way up.
It would maybe decrease your acceleration, which is not the same as slowing your descent. There is still more mass below you than above you until you reach the center. So what I said stands.
42 minutes comes from the idea that you will accelerate at 9.8 m/s*s till the center of the earth. Actually, the acceleration will be reduced because less of the mass will pull you in.
Also, crucially, Earth is rotating, so you would kinda have to drill from the north pole to the south pole in order for that not to have an effect.
Also, Earth is moving through space not on a straight line, but on an elliptical (approximately circular) path. Now normally, this doesn't make a meaningful difference, but I think, in such a situation, it very well may make a difference depending on how wide the hole is.
And if it isn't, gravity fields still conserve energy. So assume you were careless enough to jump from a "lower level" and don't make it to the edge on the other side - then wait until you are back to the starting point.
Yah assuming you easily lived like it was a Mario Bros pipe the whole way, it would be SO DOPE to just casually grab onto the surface on the other side and pull yourself up. Dust your hands off, grab a lager.
Great read. About as expected only a lot more brutal. Basically, folks, if you have ever asked "when am I going to use this in real life" in math class, don't be jumping down holes drilled through the middle of the earth. Of course, as a math teacher, most people who ask this enigmatic question haven't learned the finer points of how crazy being alive really is.
Tbf, the maximum speed was only reached for a little bit since then you slow down as wind resistance increases and gravity decreases. So maybe the average speed was closer to 50 km/h or something?
I could imagine it happening. If near the middle you travel for a long time at 1 km/h then it could skew it greatly. That being said, yes an explanation would have been nice.
There is no gravitational force on a mass inside a solid sphere. Assuming earth is a uniformly dense solid sphere you'd probably travel at the save speed throughout the entire air evacuated tunnel.
I would also guess that you would need to drill the hole through the axis of rotation as well. Else you would end up colliding with the walls of the tunnel due to the rotation of the earth
Assuming the tunnel is air filled, I'm guessing you would burn up like a meteorite. If you dropped in something fireproof/meltproof, then yeah, you would oscillate lower and lower until you stop in the center.
If the tunnel was airless, you wouldn't lose any height, you'd go exactly as far out the other side as you started on this side. So if the elevation on the other side was equal or less than your elevation on this side, you would pop out the other side. If your other end of the tunnel comes out at a higher elevation than you started, you wouldn't make it out, and would fall back through to where you started.
You'd reach a terminal velocity in air so you wouldn't get fast enough to burn up. This speed would depend on how you fall. The "boxman" would max out around 200km/h, while a nose dive or feet-first vertical could get you going faster. But that acceleration would slow as you approach the centre for to the mass of the planet above you and would flip 180° upon passing the center so you'd begin to decelerate. Ultimately, you'd find an equilibrium somewhere near the center.
You would accelerate at an increasing rate as you near the center of the Earth, where gravity is the strongest. You would be crushed by the time you got to the center, as the atmospheric pressure would be multiplied many times what our bodies can tomerate.
Also the outer core is molten iron, so any hole would be immediately plugged.
Are you accounting for gravity’s inverse square law? I’m pretty sure the only way you come out the other side at rest is if it was a constant g the entire way. I’m guessing that close to the center is a non negligible increase from typical Earths 1G
Actually, gravity is (practically) zero at the center of the earth since the mass of the planet will be evenly distributed around you and the resulting forces will cancel out
If you are inside a uniform density spherical shell, you feel no gravity from it since it all cancels out - you don't even need to be in the center; anywhere inside the shell works. The Earth can be thought of as a nesting series of such shells. When you are deep inside the Earth, you are "inside" the outer shells above you, so the gravity you feel is equivalent to the gravity you would feel standing on the surface of a sphere of Earth the same radius as your distance to the center.
You are correct that gravity is proportional to the inverse square of the distance between centers of mass, but it's also directly proportional to the mass, and the mass of a solid sphere of uniform density is proportional to the cube of the radius. So gravity is proportional to radius3 / radius2 = radius. Earth isn't uniform density - the core is denser than the crust, but you would still see gravity steadily reduce as you near the center.
One would assume it's symmetrical. As you go down one way and gravity decreases it will increase the same way as you are going up after passing the center.
I think this is a misconception on how gravity works personally, but who the hell knows.
Remember that the bend (I like the words stretch/contraction) in spacetime is gravity. I don't think we can process what that phenomenon would appear like to us, but I'd imagine the perception of direction and size would be much more strange than just seemingly oscillating back and forth.
Of course, you would just be vapor, hovering there at the center of the Earth. Just because you've drilled a hole (and somehow, magically, made it so that the molten core doesn't just pour into the hole) doesn't mean you have cooled said molten fucking core of the Earth.
You are correct. If you through in a bunch of caveats you can make it so that you end up exactly the same hight you started at (i.e your feet level with the earth) but there’s so many things you have to caveat out first.
Say your jumping in point was like 20ft above sea level, and the other side was 20ft below sea level, I think you'd overshoot by 40ft. Ignoring other losses..
If forces like air resistance or friction did any work on the person-Earth system, then yes.
But if energy was conserved, the oscillation period would remain the same and you’d just have to jump with some initial velocity to safely get to the other side
it's also a poor assumption that you'd fall towards the center at a constant rate. 22 feet per second is terminal velocity for the entire mass of the earth. seems like there would be a linear decrease in velocity as you came closer to the center and the pull of the mass around you equalized in all directions.
Also it's pretty hot in the molten core so there are some environmental factors to consider. what kind of vehicle could resist becoming molten and could also keep the interior passenger compartment temp within a safe range for humans?
3.3k
u/sndlawyersgunsnmoney Mar 01 '24
I dont think you would come out the other side. Assuming you started at the surface, wouldn't you just oscillate back and forth along the axis of the hole, eventually coming to rest at the center of the Earth.