Journey Through the Center of the Earth

You've thought about it: what would happen if we made a hole through the center of the Earth, all the way to the other side? For starters, if you do this in the USA, the other side of the hole would end up in the southern Atlantic Ocean, not in China!

But what if you were to jump into this hole? Neil DeGrasse Tyson explains the sequence of events.

There is still something that bothers me about this hypothetical scenario. I'm not actually sure why you would 'fall' in the first place? Anyone can help me here?

On a related note, the other day I also heard on my local NPR station that if you were to send an object into orbit from the place you started your journey through the center of the earth at the same time you started falling, you would both reach the other side at exactly the same time, and back again, ad infinitum. Doesn't that tickle your mind?
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