The idea of shrinking Earth down to the size of a billiard ball is a classic thought experiment used to challenge our perspective on planetary scale. From our human vantage point, towering mountain peaks and deep oceanic trenches dominate the landscape, leading to the perception that our planet must be incredibly rough and jagged. This local view, however, is highly misleading when considering the Earth’s true dimensions. To determine if the Earth’s topography compromises its overall spherical form, we must apply a precise scale.
Defining the Standard of Smoothness
To properly assess Earth’s surface, we must establish a rigorous standard for comparison, which the regulation billiard ball provides. A high-quality pocket billiard ball has an average diameter of \(5.7\) centimeters (\(2.25\) inches) and must adhere to remarkably tight manufacturing specifications. The World Pool-Billiard Association sets a strict diameter tolerance of plus or minus \(0.005\) inches (\(0.127\) millimeters) for these balls. This narrow range dictates the maximum allowable deviation from a perfect sphere, encompassing both the overall roundness and any localized surface imperfections like pits or bumps.
This tolerance is the metric against which Earth’s surface variation will be judged. The ratio of the maximum allowable bump or dent to the ball’s diameter is about \(0.00222\), representing an extremely high level of precision. The \(0.005\) inch limit provides the official constraint for the maximum shape distortion. Any object scaled to this size must have its features fall within this tiny margin to be considered a regulation ball.
Measuring Earth’s Extreme Topography
To measure the Earth’s surface “roughness,” we identify the two most extreme points of its solid crust. The highest point is the summit of Mount Everest, rising approximately \(8.8\) kilometers above sea level. The deepest point is the Challenger Deep within the Mariana Trench, plunging roughly \(11\) kilometers below sea level. Combining these two extremes gives Earth a total vertical relief, or maximum height variation, of about \(20\) kilometers.
This \(20\)-kilometer range represents the maximum possible deviation from the average planetary radius. The Earth’s average diameter is approximately \(12,742\) kilometers. This maximum relief distance is the figure we use when scaling the entire planet down. This \(20\)-kilometer vertical distance is the total variation that must be accounted for on our scaled model.
The Scaled Comparison: Smoother Than You Think
The analogy requires scaling the Earth’s average diameter of \(12,742\) kilometers down to the \(5.7\)-centimeter diameter of a billiard ball. We then apply the Earth’s maximum vertical relief of \(20\) kilometers to this miniature model. The \(20\)-kilometer difference between the highest peak and the deepest trench translates to an astonishingly small feature on the scaled model.
The ratio of Earth’s maximum relief (\(20\) kilometers) to its diameter (\(12,742\) kilometers) is approximately \(0.00157\). Applying this ratio to the \(5.7\)-centimeter billiard ball diameter results in a scaled relief of only \(0.089\) millimeters (\(0.0089\) centimeters). This minuscule \(0.089\)-millimeter variation is the size of the bump or dent that Mount Everest or the Mariana Trench would represent on the miniature Earth. For context, this is less than the average thickness of a human hair.
This scaled roughness is significantly smaller than the official \(0.127\)-millimeter (\(\pm 0.005\) inch) maximum deviation allowed for a regulation billiard ball. If the Earth were shrunk down, its mountains and trenches would not be detectable by a quality control inspection using the ball’s specifications. If a billiard ball were proportionally as rough as the Earth’s topography, the maximum allowable “bump” would be \(28.3\) kilometers tall, much larger than Earth’s actual \(20\) kilometers of relief. This confirms that, based purely on surface texture, the Earth is substantially smoother than a regulation billiard ball.
Beyond Roughness: The Equatorial Bulge
While the Earth’s surface texture is exceptionally smooth when scaled, the planet has a large-scale imperfection distinct from its topography. Because the Earth rotates, centrifugal force causes the planet to bulge outward at the equator, resulting in an oblate spheroid shape. This is a deviation from sphericity—perfect roundness—rather than a measure of smoothness—surface texture.
The Earth’s diameter at the equator is about \(43\) kilometers greater than its diameter measured pole-to-pole. This means the radius at the equator is roughly \(21.5\) kilometers larger than the radius at the poles. This \(21.5\)-kilometer difference must be checked against the billiard ball standard to see if the Earth is round enough to qualify.
The Earth’s deviation from a perfect sphere due to the bulge is still less than the \(28.3\)-kilometer scaled-up tolerance for the billiard ball’s shape. Therefore, even when accounting for the massive equatorial bulge, the Earth remains within the official regulations for a regulation billiard ball. The bulge is a fundamental feature of the planet’s shape, but it does not make the Earth too “out of round” to pass the billiard ball standard.