Stars are created when a cloud of particles/dust/whatever collapses under its own gravity.

 

I've read this in several places, but none of them tells me exactly how dense a cloud of particles must be in order to collapse.

 

What are the numbers here?

 

If a cloud were close to the right density, could humans (in theory) jump-start the process?

As far as I know, there doesn't seem to be "The Equation" for this. Most of the studies are numerical, either by using computers to by brute force solve equations of gravitation, or empirical studies of supernovae. As for whether we can, I'm sure we can...with the right technology. I'm waiting for them to make the first experimental black hole (no joke, I read that black holes can be of nearly any size as long as the Schwarzschild condition is met)

in theory if we really wanted to and had the logistical capabilities we could probably create a star, we already jump start the process in fusion reactors.

 

 

the odds are it would be next to impossible to use a similar technique to create a star that we use in fusion reactors

Jeans Criterion;

2<K>+<U>=0

 

Basically you need to balance the kinetic energy (K) of the gaseous cloud (which is proportional to temperature ) against the potential energy (U) which in this case is gravitational.

 

A qualative interpretation is that a hot cloud (>K) will need to be denser (>U) in order to undergo gravitational collapse, Alternatively a cooler cloud can collapse more easily (ie over a smaller radius) as it needn't contain as much mass to balance the equation.

 

It is quite easily for us to influence the collapse by either adding matter or by cooling the cloud.