= Vertical stellar orbit in a uniform slab
{title2=$\omega_z^2=4\pi G\rho$}
A test <star> inside an infinite planar slab of uniform <mass density> $\rho$ experiences acceleration $\ddot z=-4\pi G\rho z$. Reflection symmetry gives zero vertical <gravitational field> at the mid-plane, and integrating the gravitational <Poisson equation> gives the field linear in height. The interior orbit is therefore <simple harmonic motion>; release from rest at any height within the slab gives its first mid-plane crossing after $\pi/(2\sqrt{4\pi G\rho})$. Finite radial extent, a varying vertical <mass density> or leaving the slab changes this result.
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