If you had a straight hole through the centre of the earth (USA to China for example, or here to NZ) and you could avoid the extreme heat as you went down, then I think you would just float somewhere around the middle. When you were in the middle, you would be being pulled by gravity from the earth in all directions at the same time – but this would cancel itself out so you would feel like you were floating in space!
There is a bit of pull from the moon and sun etc and some bits of the earth are heavier than others, but you would be somewhere near the middle.
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wentwardroyalchant commented on :
but surely you would burn and die before you even got there?