Question

Where does the center of gravity of the atmosphere of the lie?

Answer 1

The center of gravity of Earth lies at the center of Earth. Its because at that point, the mass of the Earth is equally distributed in all the directions, thus pulling equally in all directions. Hence the net pull is zero.

As the distance from the centre decreases, the acceleration due to gravity also decreases.

At the center the distance is zero, hence gravity is zero.