Why the Earth Is a Squashed Sphere
📐 Measuring the Earth
Question
How do we know the Earth is a slightly squashed sphere - and not a perfect ball, or a flat disc?
Five independent kinds of measurement all agree. (1) Pendulums: a Foucault pendulum (1851, Paris) swings in a fixed plane while the ground turns under it - the rotation rate depends on latitude, zero at the equator, a full turn per day at the pole. (2) Gravity: g is about 0.5% stronger at the poles than the equator, because you are closer to the centre of mass. (3) Arc surveys: the 1735-36 French expeditions to Peru and Lapland showed a degree of latitude is longer near the equator - exactly what a squashed sphere predicts. (4) Rotation: a spinning body bulges at the equator. (5) Satellites: every orbit ever flown is only possible around a ball.
The math
Oblateness f = (a − b)/a = 1/298.257 (WGS-84): equatorial radius a = 6,378.137 km, polar radius b = 6,356.752 km. The equatorial diameter is 42.77 km (~43 km) larger than the polar one. g = 9.780 m/s² at the equator vs 9.832 m/s² at the poles.
Why it matters
A flat-disc model fits none of these measurements. A squashed sphere fits all five - and predicts the exact 43 km difference in diameters that NASA and every surveying agency report.