In other words, Newton did not aim to establish Earth’s figure once and for all. Rather, he gave approximations, which would allow for adjustments to the assumptions he made in his derivation. With Newton’s early derivation, for example, he assumed the rotating Earth has a homogeneous density. But when his predictions and Richer’s measurements in Cayenne and Gorée disagreed, he modified this assumption in the first edition of the Principia. If Earth is denser at its center, he suggested, the ellipticity of Earth’s equilibrium figure and its surface gravity variation will differ.
With this methodology, Newton passed the torch to future researchers, inviting them to develop hypotheses that would work with these initial measurements, and could then be tested with increasingly precise measurements.
In line with Newton’s methodology, geodesists eventually produced convergent measurements of Earth’s ellipticity based on variation in latitudinal surface gravity and curvature. For about two and a half centuries, they used the theories of gravitation and hydrostatic equilibrium to model Earth’s figure, motion, and constitution, and gradually revised these parameters in light of new measurements. By 1909, all major ellipticity measurements converged within 297.6±0.9, implying that density increased inward. By 1926, Viennese astronomer Samuel Oppenheim concluded that these results offered overwhelming evidence for Newtonian gravity on Earth, vindicating both Newton’s theory of gravitation and his methodology.
Miguel Ohnesorge is a doctoral student at the University of Cambridge and visiting fellow at Boston University’s Philosophy of Geoscience Lab. Ohnesorge won the APS Forum of the History and Philosophy of Physics’ 2022 essay contest; this article is adapted from his winning essay.
[i] The only published discussions of the work’s methodological importance are in Schliesser and Smith 2000 and Smith 2014, who do not reconstruct Newton’s derivation. Todhunter 1873 and Greenberg 1996 discuss the derivation in plain English, without methodological contextualization. Chandrasekhar 2003 also reconstructs the derivation in modern algebra, which contains some minor but confusing mistakes and ambiguities.
[ii] Newton’s derivation for the attraction of perfectly spherical and spheroidal compound bodies is given in Book 1, Prop. 91, coroll. 1 and 2 and reconstructed in its original notation at go.aps.org/geodesy.
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