### Problem

Solve equation (2.16) and obtain equations (2.23) and (2.24).
In the present case, at , since the energy is negative. Equation (2.19) shows us becomes equal to zero (the gas collapses) if as well as at . Equation (2.21) indicates it occurs at the epoch of
 (2.26)

where represents the average density inside of , that is . This is called free-fall time'' of the gas. This gives the time-scale for the gas with density to collapse. In the actual interstellar space, the gas pressure is not negligible. However, gives a typical time-scale for a gas cloud to collapse and to form stars in it.

Kohji Tomisaka 2012-10-03