How To Calculate The Binding Energy Of Spiral Galaxies

[Dubbelosix]

I showed in previous work that we can apply a binding energy term into the Friedmann equation. I did so without showing how you actually derive it. To do so, goes like the following:

 

 

The gravitational field inside a radius [math]r = r(0)[/math] is given as

 

[math]\frac{dM}{dR} = 4 \pi \rho R^2[/math]

 

and the total mass of a star is

 

[math]M_{total} = \int 4 \pi\rho R^2 dR[/math]

 

and so can be understood  in terms of energy (where [math]g_{tt}[/math] is the time-time component of the metric),

 

[math]\mathbf{M} =  4 \pi  \int \frac{\rho R^2}{g_{tt}} dR = 4 \pi \int \frac{ \rho R^2}{(1 - \frac{R}{r})} dR[/math]

 

The difference of those two mass formula is known as the gravitational binding energy:

 

[math]\Delta M = 4 \pi \int  \rho R^2(1 - \frac{1}{(1 - \frac{R}{r})}) dR[/math]

 

Distribute c^2 and divide off the volume we get:

 

[math]\bar{\rho}_{spiral} = \rho c^2  - \frac{ \rho c^2}{(1 - \frac{R-{spiral}}{r_{spiral}})}[/math]

 

I have removed the [math]4 \pi[/math] from the equation which is really there for spherical systems. In our case, we have taken work by Arun who shows that he calculates the binding energy of spiral galaxies in arguably a naive way. 

Edited April 5, 2017 by Dubbelosix

[henryy123]

hi

   Disks are a common astrophysical phenomenon and galactic disks owe their origins to the same fundamental process as other astrophysical disks: conservation of angular momentum in a system collapsing under gravity eventually leading to arrest of the collapse by rotational support. Understanding the physical properties of galactic disks therefore requires knowledge of their angular momentum content and the gravitational potential in which they form.

 

 

 

 

 

 

 

Thanks

 

 

 

 

http://www.contenthoop.com/magnetic-science-fun/8187/] MAGNETIC SCIENCE FUN

Edited April 10, 2017 by henryy123