It matters what kind of the velocity do you mean. If you mean to put some object to the center of earth, you'll get weightlessness because the net force acting on your object will be equal to zero. If you mean the center of earth movement, that isn't closed scientific problem, but it seems to be immovable. Donald Argus of NASA’s Jet Propulsion Laboratory says that if you changed the velocity of the Earth’s center a millimeter (0.04 inches) per year, you would change the estimate of sea level by less than one millimeter, but even half a millimeter would be important.
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