Jump to content
Science Forums

How To Calculate The Binding Energy Of Spiral Galaxies


Recommended Posts

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 by Dubbelosix
Link to comment
Share on other sites

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
 
 
 
 
Edited by henryy123
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
×
×
  • Create New...