Newton knew the length of two meridional arcs that he could use for this calculation, measured by surveyors in England and France. To derive Earth’s figure based on this theory, Newton first had to calculate the ratio between gravitational acceleration and centrifugal force at the equator (a 1-to-290.8 ratio), based on the period of Earth’s diurnal rotation and estimates of Earth’s equatorial diameter. He proposed modeling planets as rotating fluids in equilibrium, where the planet’s shape is stable while the force generated by its rotational motion, and the gravitational attraction between its particles, acts on it. To resolve this, he proposed that the solid Earth had behaved like a fluid throughout its formation, gradually bulging up at the equator because of the centrifugal effect. 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. 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.

Richer found that the clock, calibrated to Parisian astronomical time (48☄0’ latitude), lost an average of 2.5 minutes per day in Cayenne (5° latitude). In 1671, Richer had traveled to Cayenne, the capital of French Guiana in South America, and experimented with a pendulum clock.

Newton began his quantitative derivation of Earth’s figure in 1686, after learning about work by the French physicist Jean Richer. Here, I reconstruct Newton’s derivation and its significance. The work changed physics.īut buried in the Principia is an often-overlooked triumph: Newton’s derivation of Earth’s figure - that is, the calculation of its shape, size, and surface gravity variation, part of a field later known as geodesy - which was crucial to his argument for universal gravitation.

Isaac Newton’s landmark 1687 work, “Philosophiæ Naturalis Principia Mathematica,” laid the groundwork for classical mechanics, describing the laws of gravitation and predicting astronomical phenomena, like the movement of planets. To argue for universal gravitation, Newton had to become a “geodesist.”

Flat earth gravity theory