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CFringanalysis

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 We can then look to where this outward ram pressure equals the pressure of the ambient medium. The ambient medium is not in HSE, so it will begin to fall inward toward the cylinder. We can approximate this a uniform collapse, which will specify density and velocity as a function of distance away from the cylinder, thus giving a ram pressure of the ambient medium. At that radius where these ram pressures are equal, we can expect a ring will build up.
+'''Uniform Collapse of the ambient'''
+Ignoring the pressure of the ambient, the local acceleration of a gas parcel at a distance r away from the origin for a uniform density sphere is given by:
+[[latex($\frac{d^2r}{dt^2} = -G\frac{M_r}{r^2}$)]]
+Integrating this equation under the boundary conditions, the initial velocity [[latex($\frac{dr}{dt}=0$)]] and the initial radius is the radius of the sphere [[latex($r=r_0$)]], leads to an equation that describes the radius of the outer sphere over time,
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