Gravitational collapse of a cloud of hydrogen

[closet mathemetician]

I often hear that stars form when giant clouds of hydrogen start to collapse under gravitational forces, so I started thinking about this.

Gravity depends on the masses and distances of objects. So how many atoms of hydrogen would you need, and at what average distance would the atoms need to be spaced in order for a cloud of hydrogen to start collapsing upon itself?

The collapse begins to happen toward the center of mass of the cloud. At what point do you stop viewing the picture as a bunch of individual particles spread out over a space, and start viewing it as a single “object” with a center? I assume this would have something to do with the center of mass calculation?

The mass of a hydrogen atom is so small that the gravitational attraction of two hydrogen atoms to one another is ridiculously small at any distance. How can such a small acceleration due to gravity, even with lots of atoms, result in such an avalanche of acceleration toward one center point?

 

[diazona]

You'd be surprised. Even the tiny gravitational force between two distant hydrogen atoms is able to pull them together given enough time. And the closer they get, the harder they pull and the faster they fall together. Now remember that stars contain astronomically huge numbers of atoms, probably almost 10^60 for the sun (if I remember some numbers correctly), and you may start to see how the gravitational forces add up. (Keep in mind also that all gravity is attractive, not like electromagnetic forces which can be repulsive or attractive and can cancel out)

 

[closet mathemetician]

Ok, so say you have 10^60 atoms. If they are spread out over a large enough volume they won't begin to collapse, right? So at what average distance do they need to be for the attraction to begin to accelerate them together?

What I'd like to do is actually do (or see) a calculation of an example of this.

 

[Stonebridge]

Find out using Google, the typical separation of hydrogen atoms in space.
Calculate the attraction between two hydrogen atoms at that distance apart. Newton's Law of gravitation.
Calculate the acceleration. F=ma
Calculate how long it would take for that distance to, say, half.
(Approximation needed here!)
Remember that the time scale in this case is hundreds of millions of years.

 

[Lsos]

It's probably more difficult that this. Even at extremely low temperatures, the atoms vould have a certain velocity to them which could very well overcome any gravitational attraction...

 

[closet mathemetician]

So thinking about this more, I'm looking at the electric field as an analogy. In texts on the electric field, when you have a group of charged particles, the strength of the electric field at any particular point in space is equal to the vector sum of the individual field vectors of each particle at that point.

I'm guessing it would work the same way for gravity. You have particles, each with a gravitational field surrounding it pointing inward toward each particle's center. Also, the magnitude of the field vectors becomes greater as you move closer to the particle. So if you have a bunch of particles, the closer they are, the greater the magnitude of the resultant vector.

If the particles are farther away, where the field vectors are "shorter", the resultant vector would have a smaller magnitude.

I'm guessing, and I'd like to verify this, but if you have LOTS of particles packed into a spherically symmetrical volume, and distributed fairly evenly, the resultant vector sum of all those individual field vectors would point inward toward the center of the ball.



Oh, and I did google (first thing I did) but I couldn't find anything exactly on point here. Found lots of stuff talking about gravitational collapse and black holes, but I'm more interested in the very beginning of the process, how all of these small individual particles start to congregate together.

 

[closet mathemetician]

Ok, did find something:

http://physics.gmu.edu/~jevans/astr103/CourseNotes/ECText/ch17_txt.htm#17.1.

Section 17.5. This explains things pretty well.