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If somehow there was a tunnel straight through the center of the earth and we dropped a capsule through it, what will happen to the capsule? Would the tunnel shoot the capsule into space?
That's an excellent question. Assuming there were a tunnel from one side of the Earth to the other, going through the center, and you dropped a capsule into the tunnel, it would accelerate due to the Earth's gravity as it traveled toward the center.
But once it passed the center, the Earth would be pulling it back toward the center, so it would be slowing down, not speeding up. Neglecting friction and other inconvenient complications such as the rotation of the Earth, the capsule would just make it to the other side of the Earth, arriving there with zero velocity. It would then fall back into the tunnel, and regain its starting point with zero velocity.
If undisturbed, this back and forth motion would continue indefinitely. So your idea of using the tunnel as a mechanism to launch the capsule into space unfortunately would not work.
There is a great PhysicsCentral poster that deals with falling through the center of the Earth, and it's accompanied by an online explanation of the physics with more detail than I can go into here.
Alan Chodos, PhD
Associate Executive Officer
American Physical Society
Tedd from Texas