Earth’s figure and gravitation - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 323

5
Earth's figure and gravitation
The study of Earth's figure and gravitation goes back to the very roots of the phys-
ical sciences. We begin with a description of its very interesting historical roots.
5.1 Historical development
Although ancient Greek and Egyptian philosophers and astronomers believed the
Earth to be spherical and had made rough measurements of its size, the modern
theory of the Earth's figure originates with the work of Newton. Using his newly
developed laws of dynamics and gravitation, and making the remarkable assump-
tions that the Earth's figure is nearly an oblate spheroid (the surface generated by an
ellipse revolved about its minor axis) and that the Earth behaves as a fluid, he was
able to show that the ellipticity of figure is directly given by the ratio of centrifugal
force to gravitational force at the equator. As a result of the neglect of the concen-
tration of mass towards the Earth's centre, Newton's estimate of the ellipticity was
more than 30% too large. However, the oblate spheroid continues as the figure of
reference for geodesy, and the assumption of hydrostatic equilibrium remains as
the basis of much of the modern theory. Perhaps Newton's most important contri-
bution, though, was his unequivocal demonstration that any theory of the Earth's
figure must take account of both its gravitation and its rotation.
Newton published his calculation in the first edition of the Principia in 1687,
but the meridian arc length per angular unit of geographical latitude, as measured
on European baselines, appeared to increase with increasing latitude, implying that
the Earth was prolate rather than oblate. It was not until expeditions had been dis-
patched by the French Academy to Peru and Lapland that the matter was settled in
Newton's favour in the 1740s.
In 1743, a few years after his return as a member of the Lapland expedition,
Clairaut published a theory that related the latitudinal increase of gravity (grav-
itational plus centrifugal force) to the ellipticity and the ratio of centrifugal to