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I'm quite interested to know the history of the study of the Earth's departure from spherical symmetry. What were the first methods used to model the non-spherical geometry of the Earth? For example, there are geodesy satellite and missions used now to determine the gravity field of the Earth but that is "recent" technology. They obviously had other methods prior to this.

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Isaac Newton was the first to put it together and realized the Earth had an oblate shape in 1687. See 1672 - Wikipedia.

In 1666 Robert Hooke reasoned that pendulums could measure variation in gravity, but this remained unobserved until 1671, when Jean Richter observed that pendulums kept different time near the equator (French Guiana compared to Paris).

Around that time, 1673, Christian Huygens observed that the wide swing of a pendulum would move in a very slight oval, so to make pendulum clocks more accurate, the swings were kept to a low angle and the swing kept perpenducular That, however, has to do with the Earth's rotation, but not your question specifically.

Newton was the first to put it all together that the observed gravitational fluctuation was due to the equatorial bulge and faster speed of rotation near the equator. Article here also credits him with being the first.

Also, related: https://en.wikipedia.org/wiki/History_of_geodesy

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    $\begingroup$ Very nice answer! I just skimmed the article's Europe subsection. It looks like Newton's contribution was an Earth-shape-prediction and it wasn't until 100 years later that there was an experimental confirmation. Those are two different types of "determinations". The differences in pendulum speeds could possibly be caused by other things, but the later zenith measurements were much more geometrical in nature. $\endgroup$ – uhoh Aug 7 '17 at 15:32
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Although userLTK's answer is right in addressing the when it was realised that the Earth should be an oblate and not an sphere - mostly by indirect means - the first direct measures of the departure from sphericity were by means of grade measurement.

In short, by measuring difference of astronomical latitude between two points (that is, elevation of the celestial North pole) along a given meridian and the topographical distance between those two points we can compute local radius of curvature of that meridian. By comparing local radius of curvature at different latitudes, we can adjust and ellipse or even test whether the Earth shape is actually an ellipsoid.

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