Hi Astro forum... I have got something to clarify which came across my mind as I was trying to answer few problems.So without any further delay , let's start :(adsbygoogle = window.adsbygoogle || []).push({});

For simplicity we will assume that dark matter doesn't influence the center of mass of galaxy A. Now let's say galaxy A has mass 'M' concentrated at the center with a separation distance of 'r' from the edge. In this case with simple arithmetic manipulation we get :

[itex]V_{escape}[/itex] = [itex]\sqrt{GM/r}[/itex]

Now I know that at shorter separation distances gravitational forces overwhelm ( i.e are greater) than cosmological constant , and then using Hubble's law v = [itex]H_{0}[/itex] r( assuming redshift is inteperted as doppler shift) .. so far it all makes sense...

But if I am asked to prove that Vesc >> v ... I was thinking of something as following:

[itex]V_{escape}[/itex] = [itex]\sqrt{GM/r}[/itex]

Squaring both sides to get:

[itex]V_{escape}^2[/itex] = [tex]2GM/r[/tex]

which gives r = [itex]2GM/ V_{escape}^2[/itex]

Now as said previously v = [itex]H_{0} r[/itex]

so v = [itex]H_{0} 2 GM / V_{escp^2} [/itex]

[itex]V_{escp^2} = H_{0} *2 GM / v [/itex]

Gives us [itex]V_{escp} \propto[/itex] [itex]v^{-1/2}[/itex]

Is this suffice enough to prove Vesc >> v ? am I on the dot on this one ?

Any input is appreciated.

-ibysaiyan

EDIT: Oh why are my latex command showing up.. hm..

edit2: latex error fixed

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# Galaxy expansion & cosmological constant

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