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UniformCollapse

-              v17
+              v18
 This last point is useful for solving integrating the equation. Since the mass is constant in any shell (i.e. shell by the way here is used to mean concentric sphere), we can replace [[latex($M_r$)]] in the equation by [[latex($M_r = \frac{4}{3} \pi r_0^3 \rho_0$)]]. 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. We will look at these equations next.
 '''Position equation'''
 …
 [[Image(position.png, 40%)]]
+[[br]]'''''Radius of concentric spheres over time.''''' '''This plot shows the size of the outer radius of a collapsing sphere over time. The blue line shoes the outer most radius, [[latex($r_0=10$)]], the yellow is a sphere of same initial density but half the radius, and so on. From this plot, we can see that the shells do not cross over time, that the collapse speeds up over time, and that they all collapse to 0 radius in a free fall time.
+Next, by using the values of r(t),t in the velocity equation, we can see study the velocity profiles of collapsing uniform spheres.
 '''Velocity equation'''