The radius of the earth is 6368 km. For all objects near the surface of the earth the distance from the center is nearly constant, and the magnitude of the gravitational acceleration vector is therefore approximately constant. We denote the gravitational acceleration vector by g . Over small distances, when the curvature of the earth's surface can be neglected, the direction of the gravitational acceleration vector is also nearly constant. Near the surface of the earth g is the same for all objects.
All objects accelerate at approximately the same rate.
Freely falling objects are therefore objects, which are moving with constant acceleration g . You drop a ball from a window on an upper floor of a building. It strikes the ground with speed v. You now repeat the drop, but you have a friend down on the street, who throws another ball upward with the same speed v. Your friend throws the ball upward at the same time you drop yours from the window. At some location the balls pass each other.