Unruled Notebook

In the Principia (1687), Newton gave this argument:

The Earth is spinning about its axis perpendicular to the Equator.

(Recall Newton proved Kepler’s Laws of planetary motion in his Principia. Newton didn’t exactly use words like Equator, axis etc., but essentially said this. Anyway, the text we read in current reprints of Principia is the English translation of what he wrote in Latin; so no more nit picking in these lines please).
Suppose two wells are dug, one from the Polar surface and the other from the Equatorial surface, respectively, to the center of the Earth (see Figure) and filled with water.

The weight of the water in these wells must be equal, otherwise, the ‘excess’ water will ‘splash’ out of the Earth.

The weight of water in each of these wells is equal to the mass of water times the effective acceleration. The effective acceleration is the gravitational acceleration (recall, Newton explained how gravity works in the Principia) minus the acceleration due to ‘centrifugal force’ (whoops!) brought about by the spinning of the Earth. This effective acceleration, due to the action of the centrifugal force, is slightly less in the Equatorial direction than in the polar direction, where the action of the centrifugal force is absent.

Since the weight of the water in these wells must be equal, to offset the decrease in the effective acceleration, there should be more mass of (incompressible) water in the equatorial well. This is possible only if the equatorial well is ‘longer’ than the polar one. So, the Earth, due to its spinning about an axis perpendicular to the Equator, should be an oblate spheroid, with a bulge in the equatorial direction and a flattening near the Poles!

A mere ‘thought experiment’. A remarkable feat of reasoning.

There is an interesting follow-up story attached to this gem of scientific thinking. This is reported by Subrahmanyam Chandrashekar while discussing star shapes.

When Newton proposed this argument in his Principia, there was Giovanni Domenico Cassini in France, who thought the other way. Cassini, with his measurement of the meridian arc within France, thought that the Earth is elongated at the Poles and shortened at the Equator. Being the first director of the Paris observatory, the discoverer of, among other astronomical things, the 4,700 mile gap between the A and B rings of Saturn, called the Cassini division, Cassini was a big-shot in France. So the fight for who is right continued even after the death of both of these giants.

An expedition, under the captaincy of Pierre Louis Maupertius, was launched in 1738 to the Arctic region to measure the radius of the Earth. The result showed that the polar radius of the Earth (6,363,806.283 m) is shorter than the equatorial one (6,397,300 m).

Newton was right!

It seems, upon hearing this result, Voltaire chided the group that went to the Arctic on why they needed to go to the Arctic to know something that Newton knew without looking out of his window.

Such rare genius shaped (Science on) this Earth, otherwise burdened mostly by myopic mortals.