There would absolutely positively be no 'felt' gravity acting on something at the center of the earth. There would however be mind boggling pressures and extreme temperatures.
For a potential (if not feasible) way to actually get something to the center of the earth, check out:
http://news.bbc.co.uk/1/hi/sci/tech/3021255.stm
Really, it's interesting.
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"Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill
"All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence
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