A large, spherical, and very diffuse cloud of molecular hydrogen sits in empty space. The radius of the cloud is \(r_0\) and the molecules are initially at rest. Let \(t_0\) be the time it takes for this cloud to completely collapse, i.e. the time it takes for a molecule at \(r_0\) to free-fall into the origin. Similarly, let \(t_1\) be the time it takes for a cloud of radius \(r_1=4r_0\) to collapse. What is \(t_1/t_0\)?
Details and assumptions
- The entire cloud is collapsing in this process.
- Both clouds have the same mass.