Alain Goriely University of Oxford Mathematical Institute: ON THE SHAPE OF GRAVITATING PLANETS

A classic problem of elasticity is to determine the possible
equilibria of a planet modelled as a homogeneous compressible spherical
elastic body subject to its own gravitational field. In the absence of
gravity the initial radius is given and the density is constant. With
gravity and for small planets, the elastic deformations are small enough
so that the spherical equilibria can be readily obtained by using the
theory of linear elasticity. For larger or denser planets, large
deformations are possible and surprising behaviours emerge as will be
revealed during this talk.