I wonder… How does gravity affect you inside the earth?
In very simple thoughts: You fall down to the middle of the earth and accelerate (ok, friction would get you to the stated terminal velocity) and the decelerate on your way “up” on the other side.
A bit more complicated: But this is just a hole, meaning there’s mass all around us. So this attracts us. But right in the center, we should be attracted by all mass around us in all directions. So I guess it pulls is into the center of mass? Or maybe it cancels all out and there is no gravity?
That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.
This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.
So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).
The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.
Yes, in the center of Earth gravity cancels itself out. Even if there’s a huge hole making it asymmetric.
With the parachute open, you’ll fall slower and slower until you barely go past the center and then continue to slow down while you oscillate around it. At 32 km/h, you would need about 3 months to get there, but with all the slowing down you’ll probably stay on the path for a few years.
This is getting well outside my area but my understanding is that if you were approaching the center of the earth gravity would gradually decrease until you have effectively no net pull at the core. This is because the mass above you is still attracting you too so at the core you’re pulled equally in all directions. Using the same principle you’d essentially be free-floating if you found yourself in a hollow “shell” planet, presumably because the pull from whichever area of the shell is close to you is offset by there being more shell pulling you away.
I wonder… How does gravity affect you inside the earth?
In very simple thoughts: You fall down to the middle of the earth and accelerate (ok, friction would get you to the stated terminal velocity) and the decelerate on your way “up” on the other side.
A bit more complicated: But this is just a hole, meaning there’s mass all around us. So this attracts us. But right in the center, we should be attracted by all mass around us in all directions. So I guess it pulls is into the center of mass? Or maybe it cancels all out and there is no gravity?
That is a really interesting question. The exact acceleration depends on the density profile of the earth. But you are correct there is no gravitational pull in the center of the earth, it cancels out.
This is actually true for every spherically symmetric shell - gravity cancels out everywhere inside the shell. Something probably every physics undergrad had to prove as homework. See https://en.wikipedia.org/wiki/Shell_theorem for more information.
So when calculating gravity you only have to take into account the part of the earth below you, everything above you cancels out (yes the earth is not a perfect sphere but this is a pretty good approximation).
The end result for a large hole through the earth is oscillating around the center and slowing down until you are stuck in the middle. Oh and you would also be melting, it’s still ~6000° C down there.
Yes, in the center of Earth gravity cancels itself out. Even if there’s a huge hole making it asymmetric.
With the parachute open, you’ll fall slower and slower until you barely go past the center and then continue to slow down while you oscillate around it. At 32 km/h, you would need about 3 months to get there, but with all the slowing down you’ll probably stay on the path for a few years.
This is getting well outside my area but my understanding is that if you were approaching the center of the earth gravity would gradually decrease until you have effectively no net pull at the core. This is because the mass above you is still attracting you too so at the core you’re pulled equally in all directions. Using the same principle you’d essentially be free-floating if you found yourself in a hollow “shell” planet, presumably because the pull from whichever area of the shell is close to you is offset by there being more shell pulling you away.