  Goldreich-Weber solutions constitute a finite-parameter of expanding and
collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses
of this family correspond to compactly supported density profiles suitably
modulated by the dynamic radius of the star that expands at the self-similar
rate $\lambda(t)_{t\to\infty}\sim t^{\frac23}$ and linear rate
$\lambda(t)_{t\to\infty}\sim t$ respectively. We prove two results: any
linearly expanding Goldreich-Weber star is nonlinearly stable, while any given
self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly
stable against irrotational perturbations.
  The codimension-4 condition in the latter result is optimal and reflects the
presence of 4 unstable directions in the linearised dynamics in self-similar
coordinates, which are induced by the conservation of the energy and the
momentum. This result can be viewed as a codimension-1 nonlinear stability of
the moduli space of self-similarly expanding Goldreich-Weber stars against
irrotational perturbations.
