Considering its size, the earth has a very smooth surface

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

11 May 2025

There is a short YouTube video featuring the renowned astrophysicist, Neil deGrasse Tyson, in which he claims that, if the earth was scaled down to the size of a regular classroom globe, its surface would be smoother than the smoothest billiard (pool) ball ever made. A reader who wishes to remain anonymous sent me the video and asked whether this claim is accurate.

Now, the real earth has a diameter of about 12,800km. Most of the surface (over 70 per cent) is covered by water which is quite smooth – the waves rise up just a few metres. The classroom globe measures about 30cm across. The scaling ratio is determined as follows:

First, we convert 12,800km of the real earth to metres (12,800,000m) and then to centimetres (1,280,000,000cm); then we dive the result by the 30cm of the classroom globe. The answer is 42,666,667. That is, every unit of length on the classroom globe represents 42.7 million units of the real planet.

While the water surface is smooth, the dry land has many mountains, hills and valleys. The highest feature above the water surface is Mt Everest which is goes up to about 8.8km above sea level. This is equal to 8,800m of 880,000cm. So, on a classroom globe, this mountain would rise 880,000 divided by 42,66,667, or 0.02cm above the oceans.

Now 0.02cm is a very small distance; it is 0.2mm. To get an idea, take a look at a ruler or measuring tape, identify a millimetre and imagine it divided into five equal parts. 0.2mm is one of those subdivisions. It is smaller than a quarter of a millimetre and about half the size of a grain of regular table salt.

Still; how does this compare to a billiard ball? Well, a scientist by the name David Alciatore measured the unevenness of billiard balls in a laboratory at the State University of Colorado in 2013. He found that the largest imperfections were about 5 micrometres. A micrometre is a millionth of a metre or a thousandth of millimetre. Thus, this is about 0.005mm.

Clearly, the largest imperfections on a billiard ball are much smaller than those on the classroom globe. However, as Dr Alciatore notes, the billiard ball has too many of them across its surface while most of the globe is almost perfectly smooth – water bodies and plainlands. Therefore, the classroom globe can be said to be much smoother than the billiard ball.