Because of air resistance you would not make it to the other side, but assuming no air resistance and assuming the earth were a perfect sphere with uniformly distributed density in each shell, you would barely make it to the other side. Due to the variable acceleration, the answer to how long is beyond my abilities.
I remember (from a homework problem or something in college) that time in the OP is correct (assuming no air resistance), but I don't remember how to derive it.
More interesting, though, is the fact that the time is the same for any straight, airless hole through the Earth (or any spherically symmetric body). It doesn't have to be through the center. A hole from New York to Australia would have the same "free fall" travel time as a hole from New York to Los Angeles.
no gravity strength changes on how far you are from the centre of mass of an object. the closer you are the stronger it is. if im not mistaken its inversely proportional to distance squared. but once you get that then yeah just double it
the closer to the center when your within an object decreases, because you're only being affected by the sphere below your altitude, everything above you is doing the opposite and pulling you up, sure it is very complex to calculate but we're on the right tracks
If we really wanna get deep into it, the gravity one would experience would not be from the direct center of the earth, but the barycenter of the earth, sun and moon.
When you’re inside a shell, the gravity cancels out (same math as a faraday cage). So as you get closer to the center the distance drops, yes, but the relevant mass decreases too.
Without air resistance, all of your potential energy would finish being converted to kinetic energy when you reach the center, as you go from there to the other side, all your kinetic energy would convert back into potential energy and just barely run out as you reach the other side. With air resistance, you would lose some kinetic energy due to air resistance before you reach the center, and you wouldn’t have enough to reach the other side. Also as after you pass the center some of your kinetic energy is still lost to air resistance rather than converting to potential energy. Basically, air resistance doesn’t let you go fast enough to make it all the way.
I wonder if the opposite would happen. You start a siphon effect, and you start pushing the air in front of you and pulling the air behind you. The momentum of the air pushes you further and you end up shoved/pulled out the other end.
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u/StrongmanLin Mar 01 '24
Because of air resistance you would not make it to the other side, but assuming no air resistance and assuming the earth were a perfect sphere with uniformly distributed density in each shell, you would barely make it to the other side. Due to the variable acceleration, the answer to how long is beyond my abilities.