| 33 | 33 | [[br]]'''''Velocity of outer radius over time.''''' '''This plot shows that for initial concentric spheres of the same density, by varying outer radius, spheres with larger radii have steeper velocity profiles over time. Note this velocity is the velocity out the outer edge of the sphere. The free-fall time here, as can be seen where all of the curves begin to asymptote, is about [[latex($t_{ff} \approx .24$)]]. The smallest sphere plotted has an initial radius of [[latex($\frac{1}{1000}r_0$)]] (this is the green line), whereas the velocity of the outer most sphere within initial radius [[latex($r_0$)]] is the blue line. Note that this shows that all shells continue to accelerate over time, that the furthest away shells have the highest initial acceleration, all consistent with the discussion above. |
