How Long Does an Interstellar Cloud Take to Contract?

[knhlove]

Problem:"An interstellar cloud with a radius of 10parsecs and a mass of 10000 M_sun is contracting. How long does this take? (The cloud itself has no pressure)

 

[qraal]

Problem:"An interstellar cloud with a radius of 10parsecs and a mass of 10000 M_sun is contracting. How long does this take? (The cloud itself has no pressure)

Assuming it begins at zero velocity and constant density then its freefall time is ~sqrt(R^3/GM) but the size you've quoted sounds a tad excessive for the mass you quote if it's a gravitationally bound mass. The cloud is only about double the average ISM. But let's use those numbers because it's going to collapse at some temperature assuming no other masses interfering with it. So the radius is 2062648 AU and the mass is 10,000 suns. Thus free-fall time in Gaussian years is sqrt(2062648^3/10,000) = 29.6 million years.