Gresham College Lectures The Shape of Gravity: Why On Earth Are Planets Spherical? - Alain Goriely
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Apr 17, 2026 
Alain Goriely, mathematician and Oxford professor known for mathematical modelling of growth and mechanics. He explores why planets are round, historical measurements of Earth’s shape, rotating-fluid solutions like Maclaurin and Jacobi forms, stability vs exotic shapes, elastic-planet models and collapse, and implications for Mercury and rocky exoplanet sizes.
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One Parameter Controls Rotating Fluid Planet Shapes
- For a rotating fluid planet the single governing parameter is m = omega^2/(pi G rho), controlling shape transitions from sphere to increasingly oblate Maclaurin spheroids.
- McLaurin's curve links eccentricity to rotation until bifurcation points appear.
Jacobi Ellipsoids Explain Fast Rotators Like Haumea
- Jacobi discovered a bifurcation from Maclaurin spheroids to triaxial ellipsoids, explaining bodies like Haumea that rotate fast and are non-axisymmetric.
- The Jacobi branch meets Maclaurin at a critical rotation where stability changes.
Poincaré's Bifurcations Led To Many Unstable Shapes
- Poincaré predicted further bifurcations to pear-shaped and more exotic equilibria, sparking decades of research, but later work (Cartan) showed many of these exotic branches are unstable.
- Chandrasekhar later consolidated stability results into a definitive treatment.