Gravitational collapse of a cloud of hydrogen

• closet mathemetician
In summary, stars form when giant clouds of hydrogen collapse under gravitational forces. The collapse begins towards the center of mass of the cloud and is dependent on the mass and distance of hydrogen atoms. The gravitational force between two distant hydrogen atoms may seem small, but when combined with an astronomically large number of atoms, it can result in a significant acceleration towards the center. The distance at which this acceleration begins depends on the average distance between hydrogen atoms. Similar to the electric field, the gravitational field of each particle points inward towards its center, and the resultant force becomes stronger as particles get closer together. Therefore, as more particles accumulate in a spherical volume, the resultant force points towards the center of the cloud, causing it to collapse. This process can
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?

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)

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.

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.

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...

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.

1. What is gravitational collapse of a cloud of hydrogen?

Gravitational collapse of a cloud of hydrogen refers to the process by which a large, dense cloud of hydrogen gas collapses under its own gravity, eventually leading to the formation of a star.

2. How does gravitational collapse occur?

Gravitational collapse occurs when the force of gravity acting on a cloud of hydrogen gas is greater than the internal pressure pushing outward. As the cloud collapses, it becomes more dense and the temperature increases, eventually reaching a point where nuclear fusion can occur.

3. What factors influence the rate of gravitational collapse?

The rate of gravitational collapse is influenced by the size and mass of the cloud, as well as the initial density and temperature. The presence of other materials, such as dust and heavier elements, can also affect the rate of collapse.

4. What is the end result of gravitational collapse?

The end result of gravitational collapse is the formation of a star. As the cloud of hydrogen gas collapses, the temperature and pressure at the core increase, causing nuclear fusion to begin. This process generates energy, which counteracts the force of gravity and stabilizes the star.

5. Can a cloud of hydrogen collapse without forming a star?

Yes, it is possible for a cloud of hydrogen to collapse without forming a star. If the initial mass and density are not high enough, the core may not reach the necessary temperature and pressure for nuclear fusion to occur. This can result in the formation of a brown dwarf or a gas giant planet instead of a star.

• Special and General Relativity
Replies
1
Views
374
• Mechanics
Replies
36
Views
14K
• Introductory Physics Homework Help
Replies
6
Views
2K
• Special and General Relativity
Replies
2
Views
805
• Astronomy and Astrophysics
Replies
35
Views
4K
• Classical Physics
Replies
2
Views
2K
• Astronomy and Astrophysics
Replies
1
Views
905
• Classical Physics
Replies
16
Views
939
• Other Physics Topics
Replies
15
Views
2K
• Mechanics
Replies
22
Views
2K