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moment of inertia of isothermal spheroid?

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  moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-02 10:30 -0800
    Re: moment of inertia of isothermal spheroid? Sylvia Else <sylvia@email.invalid> - 2018-12-03 10:52 +1100
      Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 10:33 -0800
        Re: moment of inertia of isothermal spheroid? Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com.INVALID> - 2018-12-03 20:00 +0100
          Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 12:57 -0800
            Re: moment of inertia of isothermal spheroid? JanPB <filmart@gmail.com> - 2018-12-03 13:27 -0800
              Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 13:41 -0800
                Re: moment of inertia of isothermal spheroid? JanPB <filmart@gmail.com> - 2018-12-03 14:11 -0800
            Re: moment of inertia of isothermal spheroid? Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com.INVALID> - 2018-12-03 22:38 +0100
        Re: moment of inertia of isothermal spheroid? Sylvia Else <sylvia@email.invalid> - 2018-12-04 10:05 +1100
    Re:moment of inertia of isothermal spheroid? Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com.INVALID> - 2018-12-03 20:30 +0100
      Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 12:32 -0800
        Re: moment of inertia of isothermal spheroid? Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com.INVALID> - 2018-12-03 22:43 +0100
          Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 14:02 -0800
            Re: moment of inertia of isothermal spheroid? Libor Striz <poutnik4REMOVEnntp@CAPITALSgmail.com.INVALID> - 2018-12-03 23:08 +0100
              Re: moment of inertia of isothermal spheroid? Mole Santiago <msb@awwnuvs.an> - 2018-12-03 22:18 +0000
              Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 14:26 -0800
        Re: moment of inertia of isothermal spheroid? Tom Roberts <tjroberts137@sbcglobal.net> - 2018-12-03 16:46 -0600
          Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-03 15:28 -0800
          Re: moment of inertia of isothermal spheroid? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-12-04 01:19 +0100
            Re: moment of inertia of isothermal spheroid? Mole Santiago <msb@awwnuvs.an> - 2018-12-04 14:58 +0000
            Re: moment of inertia of isothermal spheroid? alsor@interia.pl - 2018-12-04 09:19 -0800

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#478779 — moment of inertia of isothermal spheroid?

Simple mathematical problem:

1. what is a moment of inertia of isothermal sphere?

I = x M R^2, x = ?

An isothermal sphere is a sphere with a mass density:
rho(r) = k/r^2; where k is a constant.

2. the same, but now for flattened version of the same sphere:

Iz = ?
Iy = Ix = ?

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#478816

On 3/12/2018 5:30 am, alsor@interia.pl wrote:
> Simple mathematical problem:
> 
> 1. what is a moment of inertia of isothermal sphere?
> 
> I = x M R^2, x = ?
> 
> An isothermal sphere is a sphere with a mass density:
> rho(r) = k/r^2; where k is a constant.
> 
> 2. the same, but now for flattened version of the same sphere:
> 
> Iz = ?
> Iy = Ix = ?
> 
If it's simple, why don't you have the answer?

Looks like an exercise in calculus.

Sylvia.

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#478903

W dniu poniedziałek, 3 grudnia 2018 00:52:20 UTC+1 użytkownik Sylvia Else napisał:
> On 3/12/2018 5:30 am, alsor@interia.pl wrote:
> > Simple mathematical problem:
> > 
> > 1. what is a moment of inertia of isothermal sphere?
> > 
> > I = x M R^2, x = ?
> > 
> > An isothermal sphere is a sphere with a mass density:
> > rho(r) = k/r^2; where k is a constant.
> > 
> > 2. the same, but now for flattened version of the same sphere:
> > 
> > Iz = ?
> > Iy = Ix = ?
> > 
> If it's simple, why don't you have the answer?
> 
> Looks like an exercise in calculus.
> 
> Sylvia.

Then go, calculate this.

Iz(f) = ?
ect.

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#478910

alsor@interia.pl Wrote in message:
> W dniu poniedziałek, 3 grudnia 2018 00:52:20 UTC+1 użytkownik Sylvia Else napisał:
>> On 3/12/2018 5:30 am, alsor@interia.pl wrote:
>> > Simple mathematical problem:
>> > 
>> > 1. what is a moment of inertia of isothermal sphere?
>> > 
>> > I = x M R^2, x = ?
>> > 
>> > An isothermal sphere is a sphere with a mass density:
>> > rho(r) = k/r^2; where k is a constant.
>> > 
>> > 2. the same, but now for flattened version of the same sphere:
>> > 
>> > Iz = ?
>> > Iy = Ix = ?
>> > 
>> If it's simple, why don't you have the answer?
>> 
>> Looks like an exercise in calculus.
>> 
>> Sylvia.
> 
> Then go, calculate this.
> 
> Iz(f) = ?
> ect.
> 

Why should others solve for you simple tasks ?
Are you that lazy ?
Or, do you rather try to set a trolling bait ?

-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#478932

W dniu poniedziałek, 3 grudnia 2018 20:00:07 UTC+1 użytkownik Libor Striz 


> >> If it's simple, why don't you have the answer?
> >> 
> >> Looks like an exercise in calculus.
> >> 
> >> Sylvia.
> > 
> > Then go, calculate this.
> > 
> > Iz(f) = ?
> > ect.
> > 
> 
> Why should others solve for you simple tasks ?
> Are you that lazy ?
> Or, do you rather try to set a trolling bait ?

This is for educational purposes mainly;
it's a bit of a real science for blind idiots:
stupid students and other pseudo-scientists,
which dominate this place, talking still about nothing for 20 years.

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#478935

On Monday, December 3, 2018 at 12:57:48 PM UTC-8, al...@interia.pl wrote:
> W dniu poniedziałek, 3 grudnia 2018 20:00:07 UTC+1 użytkownik Libor Striz 
> 
> 
> > >> If it's simple, why don't you have the answer?
> > >> 
> > >> Looks like an exercise in calculus.
> > >> 
> > >> Sylvia.
> > > 
> > > Then go, calculate this.
> > > 
> > > Iz(f) = ?
> > > ect.
> > > 
> > 
> > Why should others solve for you simple tasks ?
> > Are you that lazy ?
> > Or, do you rather try to set a trolling bait ?
> 
> This is for educational purposes mainly;

I doubt it.

> it's a bit of a real science for blind idiots:

Ah, yes, of course, it is only just to boost your ego after
you had your butt beaten here several times.

> stupid students and other pseudo-scientists,

Keep talking.

> which dominate this place, talking still about nothing for 20 years.

Have you even been here for 20 years?

--
Jan

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#478940

W dniu poniedziałek, 3 grudnia 2018 22:27:53 UTC+1 użytkownik JanPB napisał:

> > This is for educational purposes mainly;
> 
> I doubt it.

Even the simple geometric calculus
is pussylion times better for education than
the relativistic pseudoscience,
especially with the yours totally brainless interpretation you serve here.
 
> > which dominate this place, talking still about nothing for 20 years.
> 
> Have you even been here for 20 years?

Almost.
I not need so many time to realize what is going on here - army of imbeciles still talking about nothingness.. within their own brains. :)

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#478949

On Monday, December 3, 2018 at 1:41:59 PM UTC-8, al...@interia.pl wrote:
> W dniu poniedziałek, 3 grudnia 2018 22:27:53 UTC+1 użytkownik JanPB napisał:
> 
> > > This is for educational purposes mainly;
> > 
> > I doubt it.
> 
> Even the simple geometric calculus
> is pussylion times better for education than
> the relativistic pseudoscience,

Crackpot talk. Not even wrong.

--
Jan

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#478938

alsor@interia.pl Wrote in message:
> W dniu poniedziałek, 3 grudnia 2018 20:00:07 UTC+1 użytkownik Libor Striz 
> 
> 
>> >> If it's simple, why don't you have the answer?
>> >> 
>> >> Looks like an exercise in calculus.
>> >> 
>> >> Sylvia.
>> > 
>> > Then go, calculate this.
>> > 
>> > Iz(f) = ?
>> > ect.
>> > 
>> 
>> Why should others solve for you simple tasks ?
>> Are you that lazy ?
>> Or, do you rather try to set a trolling bait ?
> 
> This is for educational purposes mainly;
> it's a bit of a real science for blind idiots:
> stupid students and other pseudo-scientists,
> which dominate this place, talking still about nothing for 20 years.
> 


Such words say about you a lot.


-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#478960

On 4/12/2018 5:33 am, alsor@interia.pl wrote:
> W dniu poniedziałek, 3 grudnia 2018 00:52:20 UTC+1 użytkownik Sylvia Else napisał:
>> On 3/12/2018 5:30 am, alsor@interia.pl wrote:
>>> Simple mathematical problem:
>>>
>>> 1. what is a moment of inertia of isothermal sphere?
>>>
>>> I = x M R^2, x = ?
>>>
>>> An isothermal sphere is a sphere with a mass density:
>>> rho(r) = k/r^2; where k is a constant.
>>>
>>> 2. the same, but now for flattened version of the same sphere:
>>>
>>> Iz = ?
>>> Iy = Ix = ?
>>>
>> If it's simple, why don't you have the answer?
>>
>> Looks like an exercise in calculus.
>>
>> Sylvia.
> 
> Then go, calculate this.
> 
> Iz(f) = ?
> ect.
> 

I'm occupying my time with things that interest me. This doesn't. You 
apparently want to know the answer, so do it yourself.

Sylvia.

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#478921

alsor@interia.pl Wrote in message:

> 
> An isothermal sphere is a sphere with a mass density:
> rho(r) = k/r^2; where k is a constant.

Such condition is unreal.
No matter can have such a density profile
and there is no reason to call it isothermal.



-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#478928

W dniu poniedziałek, 3 grudnia 2018 20:30:05 UTC+1 użytkownik Libor Striz napisał:
> alsor@interia.pl Wrote in message:
> 
> > 
> > An isothermal sphere is a sphere with a mass density:
> > rho(r) = k/r^2; where k is a constant.
> 
> Such condition is unreal.
> No matter can have such a density profile
> and there is no reason to call it isothermal.

Wrong!
The isothermal distribution
is just the most in reality!

Simply:
temperature of any real body converges to a constant:
T = const, over its whole volume, 
because this is a state of a thermodynamical equilibrium of the body.

Gravitational case - the Sun or other big masses:

T = const is unavoidable, due to a convection, thermal conduction, ect.

Hence:
a gravitational potential must preserve this condition too:

U(r) = kT = const

So, what distribution this provides?

U(r) = Gm(r)/r = const;

thus: m(r) ~ r, simply!

Hence: rho(r) ~ 1/r^2;

because:
m(r) = rho(r) dV = rho(r) 4pi r^2 dr = k/r^2 4pi r^2 dr = 4pik dr ~ r

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#478941

alsor@interia.pl Wrote in message:
> W dniu poniedziałek, 3 grudnia 2018 20:30:05 UTC+1 użytkownik Libor Striz napisał:
>> alsor@interia.pl Wrote in message:
>> 
>> > 
>> > An isothermal sphere is a sphere with a mass density:
>> > rho(r) = k/r^2; where k is a constant.
>> 
>> Such condition is unreal.
>> No matter can have such a density profile
>> and there is no reason to call it isothermal.
> 
> Wrong!
> The isothermal distribution
> is just the most in reality!
> 
> Simply:
> temperature of any real body converges to a constant:
> T = const, over its whole volume, 
> because this is a state of a thermodynamical equilibrium of the body.
> 
> Gravitational case - the Sun or other big masses:
> 
> T = const is unavoidable, due to a convection, thermal conduction, ect.
> 
> Hence:
> a gravitational potential must preserve this condition too:
> 
> U(r) = kT = const
> 
> So, what distribution this provides?
> 
> U(r) = Gm(r)/r = const;
> 
> thus: m(r) ~ r, simply!
> 
> Hence: rho(r) ~ 1/r^2;
> 
> because:
> m(r) = rho(r) dV = rho(r) 4pi r^2 dr = k/r^2 4pi r^2 dr = 4pik dr ~ r
> 

Try to find errors in your analysis.


-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#478946

W dniu poniedziałek, 3 grudnia 2018 22:43:20 UTC+1 użytkownik Libor Striz napisał:
> alsor@interia.pl Wrote in message:
> > W dniu poniedziałek, 3 grudnia 2018 20:30:05 UTC+1 użytkownik Libor Striz napisał:
> >> alsor@interia.pl Wrote in message:
> >> 
> >> > 
> >> > An isothermal sphere is a sphere with a mass density:
> >> > rho(r) = k/r^2; where k is a constant.
> >> 
> >> Such condition is unreal.
> >> No matter can have such a density profile
> >> and there is no reason to call it isothermal.
> > 
> > Wrong!
> > The isothermal distribution
> > is just the most in reality!
> > 
> > Simply:
> > temperature of any real body converges to a constant:
> > T = const, over its whole volume, 
> > because this is a state of a thermodynamical equilibrium of the body.
> > 
> > Gravitational case - the Sun or other big masses:
> > 
> > T = const is unavoidable, due to a convection, thermal conduction, ect.
> > 
> > Hence:
> > a gravitational potential must preserve this condition too:
> > 
> > U(r) = kT = const
> > 
> > So, what distribution this provides?
> > 
> > U(r) = Gm(r)/r = const;
> > 
> > thus: m(r) ~ r, simply!
> > 
> > Hence: rho(r) ~ 1/r^2;
> > 
> > because:
> > m(r) = rho(r) dV = rho(r) 4pi r^2 dr = k/r^2 4pi r^2 dr = 4pik dr ~ r
> > 
> 
> Try to find errors in your analysis.

I leaved this one oversimplicity-type of error for you.

Fully and general derivation is based on the Virial theorem,
so I simplified it a bit, for obvious reason:
this version must be limited accordingly for the great relativistic (in)competence.

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#478948

alsor@interia.pl Wrote in message:
> W dniu poniedziałek, 3 grudnia 2018 22:43:20 UTC+1 użytkownik Libor Striz napisał:
>> alsor@interia.pl Wrote in message:
>> > W dniu poniedziałek, 3 grudnia 2018 20:30:05 UTC+1 użytkownik Libor Striz napisał:
>> >> alsor@interia.pl Wrote in message:
>> >> 
>> >> > 
>> >> > An isothermal sphere is a sphere with a mass density:
>> >> > rho(r) = k/r^2; where k is a constant.
>> >> 
>> >> Such condition is unreal.
>> >> No matter can have such a density profile
>> >> and there is no reason to call it isothermal.
>> > 
>> > Wrong!
>> > The isothermal distribution
>> > is just the most in reality!
>> > 
>> > Simply:
>> > temperature of any real body converges to a constant:
>> > T = const, over its whole volume, 
>> > because this is a state of a thermodynamical equilibrium of the body.
>> > 
>> > Gravitational case - the Sun or other big masses:
>> > 
>> > T = const is unavoidable, due to a convection, thermal conduction, ect.
>> > 
>> > Hence:
>> > a gravitational potential must preserve this condition too:
>> > 
>> > U(r) = kT = const
>> > 
>> > So, what distribution this provides?
>> > 
>> > U(r) = Gm(r)/r = const;
>> > 
>> > thus: m(r) ~ r, simply!
>> > 
>> > Hence: rho(r) ~ 1/r^2;
>> > 
>> > because:
>> > m(r) = rho(r) dV = rho(r) 4pi r^2 dr = k/r^2 4pi r^2 dr = 4pik dr ~ r
>> > 
>> 
>> Try to find errors in your analysis.
> 
> I leaved this one oversimplicity-type of error for you.
> 
> Fully and general derivation is based on the Virial theorem ...

You ignore  behaviour of  matter.


-- 
Libor Striz aka Poutnik ( a pilgrim/wanderer/wayfarer)

"Humour is the only effective weapon against stupidity."
Miloš Forman


----Android NewsGroup Reader----
http://usenet.sinaapp.com/

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#478952

Libor Striz wrote:

>>> Try to find errors in your analysis.
>> 
>> I leaved this one oversimplicity-type of error for you.
>> Fully and general derivation is based on the Virial theorem ...
> 
> You ignore  behaviour of  matter.

Matter cannot possibly behave. Logic circuitry however does. Time or event 
driven. You shall absolutely bring your country in shame, aint you.

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#478954

W dniu poniedziałek, 3 grudnia 2018 23:08:08 UTC+1 użytkownik Libor Striz 

> >> Try to find errors in your analysis.
> > 
> > I leaved this one oversimplicity-type of error for you.
> > 
> > Fully and general derivation is based on the Virial theorem ...
> 
> You ignore  behaviour of  matter.

The galaxies are quite isothermal already.

And I have showed very nice observational data:

the Sun and any big masses provide a rotational flatness:
f = 3/4 a/g; perfectly.

so, now there is no problem to resolve
whether these bodies are isothermal too or not.

Try to calculate something, instead of still talking about your great inabilities.

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#478956

On 12/3/18 2:32 PM, alsor@interia.pl wrote:
> An isothermal sphere is a sphere with a mass density:
>>> rho(r) = k/r^2; where k is a constant.

Apparently you don't know what the words you use actually mean: 
"isothermal" means constant temperature, not that particular mass 
density -- or any other: a truly isothermal sphere is unlikely (unless 
it is small), and would have a mass density determined by the equation 
of state for its composition.

> Libor Striz wrote:
>> Such condition is unreal.
>> No matter can have such a density profile
>> and there is no reason to call it isothermal.

Yes. That pole at r=0 is unphysical.

> temperature of any real body converges to a constant:
> T = const, over its whole volume,

This is just plain false:
  1) The earth gets downright hot deep in its interior (> 5,000 C).
  2) The sun varies in temperature from ~ 10,000 C to ~ 15,000,000 C.

> because this is a state of a thermodynamical equilibrium of the body.

Few if any astronomical bodies are in thermal equilibrium.

A basketball sitting on a shelf is in thermal equilibrium, but not when 
it is being dribbled (hint: it bounces).

> Gravitational case - the Sun or other big masses:
> T = const is unavoidable, due to a convection, thermal conduction, ect.

NONSENSE! You're just making stuff up and pretending it is true.
IT ISN'T.

Tom Roberts

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#478962

W dniu poniedziałek, 3 grudnia 2018 23:46:19 UTC+1 użytkownik tjrob137 napisał:

> > An isothermal sphere is a sphere with a mass density:
> >>> rho(r) = k/r^2; where k is a constant.
> 
> Apparently you don't know what the words you use actually mean: 
> "isothermal" means constant temperature, not that particular mass 
> density -- or any other: a truly isothermal sphere is unlikely (unless 
> it is small), and would have a mass density determined by the equation 
> of state for its composition.

The isothermal sphere term is a standard in astrophysics.

So, You learned something new - revelation! :)
 
> > Libor Striz wrote:
> >> Such condition is unreal.
> >> No matter can have such a density profile
> >> and there is no reason to call it isothermal.
> 
> Yes. That pole at r=0 is unphysical.

Don't worry about this:
in the center of the sun
there stays proudly a single atom or neutron, hence the density is very well limited. :)

> temperature of any real body converges to a constant:
> T = const, over its whole volume,

This is just plain false:
  1) The earth gets downright hot deep in its interior (> 5,000 C).
  2) The sun varies in temperature from ~ 10,000 C to ~ 15,000,000 C.

The earth is a tiny mass compared to any star or a big planet: Jupiter, Saturn, ...

And not incidentally the earth flatness is intermediate:

1. solid uniform sphere: 5/4, 
2. earth has: 1
3. the big planets and stars have: 3/4

So, the Earth density is intermediate between of: 
uniform and isothermal = ?

it's just linear approximately!
Correct?

Of course: density at earth surface is about 2-3 g/c3,
further it grows slowly - just linearly!,
and finally reaches in a core 8-9.

Hence the earth temperature must still increase, to the center,
because here a gradient of the temperature
compensates the deficit of a density gradient!

Simple? :)

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#478966

Tom Roberts wrote:
> On 12/3/18 2:32 PM, alsor@interia.pl wrote:
>> temperature of any real body converges to a constant:
>> T = const, over its whole volume,
> 
> This is just plain false:
>   1) The earth gets downright hot deep in its interior (> 5,000 C).

Yes, the inner core temperature is estimated to be 5600 K.

>   2) The sun varies in temperature from ~ 10,000 C to ~ 15,000,000 C.

The effective temperature is ca. 5700 K (your approximation for the core
temperature is correct; it is ca. 1.57 × 10⁷ K), so the range is even larger
than that.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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