How Smooth Is Planet Earth?

At first glance, the Earth does not seem like an overly smooth planet. It is covered in mountains, ridges, canyons, land masses, and oceans. However, the Earth only appears as rough as it does because of its size. The Earth has a diameter of 7,917 miles (12,742 kilometres), yet if you were to shrink it down to the size of a standard billiard ball, the Earth would actually be smoother. 

Smoothness Of Earth

Defining how smooth something is can be somewhat strange, yet one way to do it is to define it based on a ratio of pits and bumps to an object's size. For example, a standard billiard ball has a diameter of 2.5 inches and has no pits or bumps greater than 0.005 inches in height or depth. That means that the ratio of pits and bumps to size for a billiard ball is 0.005 to 2.5, or 0.002. Thus we can define the average smoothness of a billiard ball as being 0.002. To compare Earth to a billiard ball, we can do the same thing but for the entire Earth by using the tallest peak and the deepest trench. On Earth, the tallest mountain is Mt. Everest at 5.5 miles in height, and the deepest point on Earth is the Marianas Trench at 11 miles deep. In order to determine whether or not the Earth is smoother than a billiard ball, we can simply multiply the Earth’s diameter by the smoothness of a billiard ball to determine the maximum size/depth something must be in order for the Earth to be smoother. When we multiply 7,917 by 0.002, we get 15.8 miles, which is larger than both the height of Mt. Everest and the depth of the Marianas Trench. Since the tallest and lowest points on Earth are smaller, the Earth is actually smoother than a billiard ball. If you were to shrink the Earth down to 2.5 inches in diameter, it would be smoother. 

Problems

There are some issues with the numbers calculated above, the most notable of which is that the definition for smoothness uses an object's size and roundness, and it does not necessarily tell us how smooth the object itself would feel. For example, if you had a ball of sandpaper the same size as a billiard ball with the same maximum size of pits and bumps, it would be defined as being as smooth as a billiard ball, yet it would feel nowhere near as smooth. Although the size of Earth’s mountains and trenches show that, if it were shrunk to the size of a billiard ball, it would be smoother, the Earth likely would not feel as smooth.