| | 43 | [[br]]'''''Radial velocity of collapsing uniform density sphere over time''''' '''At t=0, the sphere is static, and the velocity of the sphere is everywhere 0 (blue line). At the next time, we see that the radius of the sphere has shrunk, and that the velocity of the gas in the sphere is fastest at the outer edge, but goes to 0 linearly as you approach the origin (orange line). Each of these lines are evenly spaced in time, which shows the growing acceleration of the sphere. The red line is approaching the free fall time. As you can see from the velocity equation, at this point r->0, and we are getting a singularity in the velocity. This is why the line is tending toward an infinite slope. ''' |
