Q:  Why doesn't the initial size of the cloud appear in this equation?

          Because the time doesn't depend on the initial size -- just
             the density!  Larger clouds have stronger gravitational
             forces, but also a larger distance to fall .... and those
             two factors turn out to cancel each other exactly.

          Pretty cool.


  Q:  Suppose that a cloud of 1 solar mass, M = 1.99 x 10<sup>30</sub> kg,
          has an initial radius of 0.1 pc, R = 3 x 10<sup>15</sup> m.

          Roughly how long will it take this cloud to collapse?

                         M
              rho  =  --------------   =   1.76 x 10^(-17) kg/m^3
                      (4/3) pi R^3


                           3 pi
              tff  =  ( ----------- )  =   1.6 x 10^(13) s
                         32 G rho

                                       =   500,000  yr