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UniformCollapse

-              v1
+              v2
+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:
+'''Homologous Collapse of a uniform density sphere '''
+Ignoring the pressure forces in the gas (which is valid when the gas is Jeans unstable, i.e. [[latex($E_{grav}>>E_{kin}$)]]), 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,
+Integrating this equation under the boundary condition, the initial velocity [[latex($\frac{dr}{dt}=0$)]] at the initial radius of the sphere [[latex($r=r_0$)]], leads to an equation that describes the radius of the outer sphere over time (i.e. over the course of collapse), and the velocity at this radius over time.