  A theoretical and experimental study of the spin-over mode induced by the
elliptical instability of a flow contained in a slightly deformed rotating
spherical shell is presented. This geometrical configuration mimics the liquid
rotating cores of planets when deformed by tides coming from neighboring
gravitational bodies. Theoretical estimations for the growth rates and for the
non linear amplitude saturations of the unstable mode are obtained and compared
to experimental data obtained from Laser D\"{o}ppler anemometry measurements.
Visualizations and descriptions of the various characteristics of the
instability are given as functions of the flow parameter.
