Newton began his quantitative derivation of Earth’s figure in 1686, after learning about work by the French physicist Jean Richer. In 1671, Richer had traveled to Cayenne, the capital of French Guiana in South America, and experimented with a pendulum clock. Richer found that the clock, calibrated to Parisian astronomical time (48°40’ latitude), lost an average of 2.5 minutes per day in Cayenne (5° latitude). This was surprising, but it could be explained by the theory of centrifugal motion, recently developed by Christian Huygens: The theory suggested that the centrifugal effect is strongest at the equator, so the net effective surface gravity would decrease as you moved from Paris to Cayenne[1].
Newton accepted Huygens’s theory but realized it meant something strange: If Earth is a sphere and its centrifugal effect is strongest at the equator, gravity would vary across Earth’s surface, and the ocean would bulge up at the equator — a proposition that Newton considered absurd.
Paul Mainwood Degrees in Physics and Philosophy, Doctorate in Philosophy of PhysicsAuthor
By itself, that argument isn’t convincing. A centrifugal force term for a body rotating around an axis at a constant speed is given by F=mω2r. So while a body on earth rotating once every 24 hours and that same body on a merry-go-round rotating once every 24 hours gives you the same first two terms, there’s still that
r term that’s different. And it’s a fairly big difference, when you think about the radius of the earth. So we still need to show that both are tiny compared to existing forces we know are at work, like gravity.
They are of course. On a merry-go-round of radius 5 metres, you get a force term of around 2.6*10^−9 times that of gravity. And on the surface of the earth with a radius 6371km, you get a force of 3.4*10^−3 times that of gravity. Both effects are small compared to gravity, but it is much bigger in the case of the Earth: a little over a million times bigger (unsurprisingly, since the radius of the earth is a little more than a million times larger than the radius of a merry-go-round.)
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*Lucifers' Heretic of Apostacies of Consensi*
'Once the individual is constantly fed the signals of their impotence and
insignificance, it is quite natural for them to reach no further than what
they can take hold of, if only with their hands or feel with their tangible
senses.The only submission that exists in one's potential is one's
unaddressed limitations.'*
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