What is the nature of motion of an object falling freely under the action of gravity?

When a body is falling freely under gravity it has motion with constant acceleration (acceleration due to gravity,g). This is valid till the height is very small as compare to the radius of the earth, as in that case the acceleration due to gravity is nearly constant. If the body is falling from a height comparable to the radius of the earth, then in that case the body has motion with increasing acceleration. This is because the acceleration due to gravity decreases as we move upward from the surface of the earth.