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We know the Earth isn't a sphere: that is, the equatorial circumference isn't equal to the polar circumference. When (and how) was this discovered?

I can put a lower bound of around the 3rd century BC, when Greek astronomy showed that the Earth was round rather than flat, and an upper bound of 1791, when the French Academy of Sciences specified a quadrant of meridian in the definition of the meter. An uncertainty of 2000 years is rather large, though.

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  • $\begingroup$ could you reference your lower bound please? The Earth is very nearly spherical and I would have thought you could detect deviations only over large distances (larger than size of Mediterranean anyways). $\endgroup$
    – user5245
    Commented Jan 28, 2017 at 3:35
  • $\begingroup$ I'm assuming that "the Earth's shape deviates from spherical" could not have been discovered before "the Earth's shape is a sphere", and the Greeks started accumulating (or at least recording) solid evidence for a spherical Earth in the 300s BC. $\endgroup$
    – Mark
    Commented Jan 28, 2017 at 3:40
  • $\begingroup$ agreed... It must have been by direct measurement. Local variations of $g$ would be subject to first order to local changes in densities, and measuring the variation would require a lot of technology. The navigational clocks weren't that good until the 1800s so even measurements over navigational distances are unlikely to be the clincher before the French. So by elimination that leaves you with a bound closer to your upper bound. $\endgroup$
    – user5245
    Commented Jan 28, 2017 at 3:50
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    $\begingroup$ Would most people have realised quite early on, that the earth is not round\a sphere? I mean, there are plenty of mountains and valleys on the earth, which precludes it from being a sphere. And yes, I know what you mean, but it seems quite hard to draw a line here. $\endgroup$
    – Gerhard
    Commented Jan 29, 2017 at 14:20
  • $\begingroup$ You can see John Greenberg, The Problem of the Earth's Shape from Newton to Clairaut: The Rise of Mathematical Science in Eighteenth-Century Paris and the Fall of 'Normal' Science (1995). $\endgroup$
    – Mauro ALLEGRANZA
    Commented Jan 31, 2017 at 9:00

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Discarding the ungrounded speculations (for example, Columbus claimed that Earth has a "bulge"), scientific theories which predicted deviation of Earth's shape from the sphere were proposed in he late 17th century. The correct theory was due to Newton. There was a competing theory predicting that equator is shorter than meridian (either by Descartes himself, or by his followers). To decide which theory is correct, several expeditions were sent by the French Academy to measure arcs of meridians. The first expedition did this in Peru (modern Equador) in 1735-45. Before they finished in Peru, the second expedition (to Lapland, Sweden, 1736) returned with a conclusive result that Newton's theory was correct. The results were published in the book of Maupertuis, La figure de la Terre in 1738. It was translated into English in the same year.

This result was one of the first major tests of the theory of universal gravitation. (See How did Newton come up with his formula?).

EDIT. Of course this was only the beginning. Since then geodesists made many more precise measurements, and mathematicians also investigated the question in great depth. Mathematically, the question is about equilibrium of rotating liquid body; it was finally solved only in 20th century (by Chandrasekhar in 1970).

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    $\begingroup$ Specifically, it seems to have been introduced in Newton's Principia of 1687: "Proposition XVIII. Theorem XVI. That the axes of the Planets are less than the diameters drawn perpendicular to the axes (online) $\endgroup$
    – njuffa
    Commented Jan 28, 2017 at 8:34

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