Does anyone know how to solve this problem for an isothermal collapse of molecular gas say at T = 10K. I would like to look at how the density "p",M(r), and P changes with time at this stage of protostellar developement.(in one dimension)

eqn of motion: GM(r)/r^2 + (1/"p")(dP/dr) = -(d^2r/dt^2)

mass conservation: dM(r)/dr = 4(pi)r^2"p"

eqn of state: P = R_g"p"T/"u"

where "p" is the density, M(r) is the mass inside the radius r, "u" is a constant=2, P is the pressure and all the dirivitives are actually partial derivitives.

Boundary Conditions: P(t) = constant or R(t)=constant

There is standard literature on the subject in Graduate level astrophysics curriculuum. The first work on the subject was by Hyashi. I think the standard "best" text is Stellar Evolution by Martin Schwartzschild. I would start there. By the way, rotation is important. The problem gets to be at least 2D rather quickly. Non-gravitational effects (i.e. radiation) also become important. The problem gets quite tricky.