A confusing “elegant formula”

[Kramer]

A confusing “elegant formula”
( Sure “ confusing” only for a lay man)

It is about formula of “critic density of universes matter”

( m * ( Ho * R ) ^ 2 ) / 2 = ( G * m / R ) * ((4 * pi / 3 ) * ( R ^ 3 * ρ c ))

 

 

( Ho * R ) ^ 2 = ( ( 4 * pi ) / 3 ) * ( G * R ^ 2 * ρc ) ) * 2

My confusion is here:
On the left side we have Hubbles square velocity “ (Ho * R )” caused by ????!!!.(B.B)
On the right hand we have square velocity “ ( G * R ^ 2 * ρc ) “ caused by gravity.
-The “ B.B velocity is a radial velocity.
-The gravity velocity is a tangential circular, cyclic velocity.
Doesn’t it is a mistake the sign of equivalence, when they are two perpendicular vectors?
May be the specialist will give a hand about where I am wrong?

[Strange]

It would be useful if you could provide a link to where this is explained/derived.

 

 

The gravity velocity is a tangential circular, cyclic velocity.

 

I'm not sure why you say that.

 

As far as I can tell (without working through it in detail) it is comparing the outward acceleration (from the big bang model - the FLRW metric) with the inward acceleration due to gravity. If the latter is larger, then the universe will eventually collapse. If the former is larger, then the universe will continue expanding. This, I think, depends on the density of the universe.

 

I may have that wrong, as it is a bit off-the-top-of-my-head...

 

More here: http://astronomy.swin.edu.au/cosmos/C/Critical+Density

Edited July 13, 2014 by Strange

[swansont]

It would be useful if you could provide a link to where this is explained/derived.

 

Indeed. If it were an equation for the critical density of universe, one might expect it to be solved for ρ_c

 

( Ho * R ) ^ 2 = ( ( 4 * pi ) / 3 ) * ( G * R ^ 2 * ρ_c ) ) * 2 => Ho² = 8πG/3 * ρ_c

 

or ρ_c = 3Ho²/8πG

 

Which is indeed the critical density equation

http://en.wikipedia.org/wiki/Critical_density_(cosmology)#Density_parameter

 

An expression for the critical density is found by assuming Λ to be zero (as it is for all basic Friedmann universes) and setting the normalised spatial curvature, k, equal to zero. … [T]he substitutions are applied to the first of the Friedmann equations

 

More explanation can be found here:

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/fried.html

 

A confusing “elegant formula”

( Sure “ confusing” only for a lay man)

 

One generally does not study GR without a solid background in physics, i.e. it's graduate-level physics.

 

-The gravity velocity is a tangential circular, cyclic velocity.

 

It is?

Edited July 14, 2014 by swansont
fix hyperphysics url

[Kramer]

 

Swanson

Kramer, on 13 Jul 2014 - 10:45 AM, said:

-The gravity velocity is a tangential circular, cyclic velocity.

It is?
-------------

------ I think it is. It is uncontested that velocity of planets around tha sun depend only by:

Vplanet = (G* Msun / Distance sun-planet) ^ 0.5

and the velocity of the sun depends only by the distance of the sun toward the center of galaxy where supposed to be a massive black body with mass = 1.7*10^41 kg.
I think it is a big mistake to confound gravity velocity of the “ force of gravity “--- which is in the “direction of force”, with the velocity of “inertial gravity” ---- which is perpendicular with direction of force, even they have the same formula.
The velocity of gravity force is always accompanied with its nemesis electromagnetic anti - force and appears only when their equilibrium (of stationary status) is compromised by electromagnetic force of run-away status (photons).

And here is the aim of this post.

[swansont]

 

Swanson

Kramer, on 13 Jul 2014 - 10:45 AM, said:

-The gravity velocity is a tangential circular, cyclic velocity.

It is?

-------------

------ I think it is. It is uncontested that velocity of planets around tha sun depend only by:

 

Vplanet = (G* Msun / Distance sun-planet) ^ 0.5

 

and the velocity of the sun depends only by the distance of the sun toward the center of galaxy where supposed to be a massive black body with mass = 1.7*10^41 kg.

 

This might matter if the critical density was a description of planetary mechanics. But it's not, so that point is moot. You might note that the speed formula derived for a circular orbit requires additional constraints — that's where the detail of a tangential speed comes in. The assumption of a central mass and a circular orbit. Not in the idea of gravity itself.

 

For the critical density equation, the expansion and contraction are in opposite senses. Either subtracting them or equating their magnitudes seems perfectly reasonable.

[Kramer]

 

Swanson
….. circular orbit requires additional constraints — that's where the detail of a tangential speed comes in. The assumption of a central mass and a circular orbit. Not in the idea of gravity itself.

Does it mean that “central mass” is irrelevant for the idea of gravity?

I see where is it driving at:
1- Mass of particles (alias gravity) is not matter. It is a property injected by the “field of gravity”.

2- It is "irrelevant" that mass particles, we see, to exist in "cosmic bodies" via their gravity, even that those cosmic bodies are integrated in galaxies, cluster of galaxies.

For an argument about the idea of “creation” of the universe, matter will be nothing else but a few atoms in cubic km. as it was nothing before “creation”.
I quit this post with a moto borrowed by somebody:

For those who believe, no explanation is necessary. For those who do not believe, no explanation will suffice.

[Strange]

Does it mean that “central mass” is irrelevant for the idea of gravity?

No, it means that tangential movement is required for orbits. Gravitational force works purely radially (contrary to your assertion).

 

 

For an argument about the idea of “creation” of the universe, matter will be nothing else but a few atoms in cubic km. as it was nothing before “creation”.

 

There is no science related to the "creation" of the universe. And what does it have to do with the subject anyway?

 

 

For those who believe, no explanation is necessary. For those who do not believe, no explanation will suffice.

 

That seems irrelevant to science. Although I suppose you could replace "believe" with "understand".

[swansont]

Swanson

….. circular orbit requires additional constraints — that's where the detail of a tangential speed comes in. The assumption of a central mass and a circular orbit. Not in the idea of gravity itself.

 

Does it mean that “central mass” is irrelevant for the idea of gravity?

No. It means a central mass is irrelevant for the discussion of expansion of the universe, which is what the critical density equation is related to.

 

I see where is it driving at:

1- Mass of particles (alias gravity) is not matter. It is a property injected by the “field of gravity”.

What?

 

2- It is "irrelevant" that mass particles, we see, to exist in "cosmic bodies" via their gravity, even that those cosmic bodies are integrated in galaxies, cluster of galaxies.

For an argument about the idea of “creation” of the universe, matter will be nothing else but a few atoms in cubic km. as it was nothing before “creation”.

Again, what?

 

I quit this post with a moto borrowed by somebody:

For those who believe, no explanation is necessary. For those who do not believe, no explanation will suffice.

That's religion, not science.

[Mordred]

critical density of the universe is the calculated value that will gradually halt expansion and then start to collapse, a critically dense universe is a perfectly fat universe in terms of energy-density to pressure relations. k=0

 

see these articles for more details.

http://cosmology101.wikidot.com/universe-geometry

page 2 with the FRW metric portion.

http://cosmology101.wikidot.com/geometry-flrw-metric/

 

http://arxiv.org/pdf/hep-ph/0004188v1.pdf :"ASTROPHYSICS AND COSMOLOGY"- A compilation of cosmology by Juan Garcıa-Bellido
http://arxiv.org/abs/astro-ph/0409426 An overview of Cosmology Julien Lesgourgues

 

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis (this is covered in the preliminary review chapter 2)

Edited July 16, 2014 by Mordred