The classical model of an isolated self-gravitating gaseous star is given by the Euler-Poisson system. For any value of the adiabatic index between 1 and 4/3, we construct an infinite-dimensional family of collapsing solutions to the Euler-Poisson system with inhomogeneous densities. The collapse occurs along a prescribed space-time surface in Lagrangian coordinates, and the mass is continuously absorbed at the origin. The leading order singular behaviour is described by an explicit collapsing solution of the pressureless Euler-Poisson system. This is a joint work with Yan Guo (Brown) and Juhi Jang (USC).