Solve equation (2.16) and obtain equations (2.23)
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
Free-fall. x-axis and y-axis represent and
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.