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Re: moment of inertia of isothermal spheroid?

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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


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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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