What happens to the force of earths gravity as distance from earth increases?

As we are told by Newton's Law of Universal Gravitation, the force of gravity is inversely proportional to the square of the distance between the centers of the two objects in question. As a result, the attraction of gravity becomes less, as the distance from Earth increases. Note that since the Earth is quite large, about 4,000 miles in diameter, you are not going to notice a change in gravity if you travel away from the Earth by a small distance, such as you can do by climbing a mountain. You will still be approximately the same distance from the center of the Earth.