Billiard balls are pretty darn smooth and according to the World Pool-Billiard Association have a tolerance of +/- 0.0127 cm. Essentially, this means that a ball must not have any bumps or indentations greater than 0.127mm- which is about the width of a strand of hair.
If we find the ratio of the diameter of the ball (6.35cm) and the size of the allowable surface coarseness (.0127cm) we get a ratio of around .002 (.0127/6.35). So, this means for the Earth to be deemed as smooth as a billiard ball it’s diameter to tolerance ratio must be equal to or less than .002.
So.. is it?? *drum roll*
The average diameter of the Earth is around 12,742 km. If we use the ratio from above we can find out what the allowable “tolerance” would be to achieve billiard ball smoothness, as follows: 12,742 x .002= 25.482km.
Essentially, this means that we have over 25km to play with regard deviations in topography- so let’s take a look at the highest and lowest points on the planet:
The highest point on land is the peak of Mount Everest at 8.84 Km above sea level- well within the 25km range. (Or, if you want to get technical, the highest point on the Earth is Mt. Chimborazo in Ecuador in the Andes mountain chain. It’s about 2.4 kilometers higher than Mt. Everest due to the Earth being an oblate spheroid and bulging around the equator, but is still less than than 25km)
The lowest point is the Mariana Trench at around 11.03 Km below sea level- also within the 25km range.
So, there you have it. If you could shrink the Earth down to the size of a billiard ball it would actually be smoother!!