> On Jul 6, 8:23 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
> wrote:
>> tadchem <tadc...@comcast.net> wrote
>> innews:6dd26197-65fb-4e5d-85bd-662578
> 4a7...@k30g2000hse.googlegroups.com:

>> > On Jul 5, 5:48 pm, John Schutkeker
>> > <jschutke...@sbcglobal.net.nospam> wrote:
>> >> I followed the procedure at the following site,

>> >>http://www.astro.utu.fi/~cflynn/Stars/l4.html

>> >> and I believe that I've correctly added a centripetal force term
>> >> to the derivation of the differential equation for stellar
>> >> hydrostatic equilibrium.  That equation relates dP/dr to d_rho/dr,
>> >> where P is th
> e
>> >> hydrostatic pressure, rho is the mass density and r, of course, is
>> >> the radial coordinate.  

>> >> I added the centripetal force, rho*w^2*r, as a second body force
>> >> term in equation (11) on that site, making that equation into

>> >> dP/dr=rho(r)*w^2*r*sin(theta)-G*m(r)*rho(r)/r^2,

>> >> where w is omega, the rotational frequency of the star, which is
>> >> allowed to
>> >> vary with the latitude on the star, as w=w(theta).

>> >> The middle part is pretty much just algebra, and the answer I got
>> >> was

>> >> (1/r^2)*d[(r^2/rho)(dP/dr)]/dr+4*pi*G*rho=[3w^2+2*w*r*dw/dr]*sin
>> (theta
>> >> ).

>> >> Actually, you can tell by the presence of a dw/dr term that I
>> >> allowed w to
>> >> vary as a function of both r and theta, but I have no idea whether
>> >> the is necessary to understand the physics, so I kept it for
>> >> completeness and just in case.

>> >> If I were to put in the compressible equation of state for a
>> >> fluid, P=K*rho^gamma, my result would be an improved Lane-Emden
>> >> equation.
>  I
>> >> haven't done that yet, but so far it looks straightforward, and I
>> >> plan to do it within the day or two.

>> >> In summary, I need to know whether the above equations and
>> >> derivation look
>> >> familiar to the people in this group, and does anybody know if
>> >> this particular approach to the problem has ever been taken
>> >> before.  I have to
>> >> know whether I have just reinvented the wheel, so I can start
>> >> thinking about whether to get the entire derivation published,
>> >> rather than just the
>> >> first and last equations.  :b

>> >> Any reasonable input would be greatly appreciated.  TIA.

>> > You might try a more realistic equation of state.  The one you have
>> > is
>> > an ideal thermodynamic gas equation with considerations made for
>> > heat capacities (gamma = Cp / Cv is the adiabatic index - the ratio
>> > of specific heats).  This might be sufficient for gases at
>> > densities well
>> > below those found at the critical point, but at higher densities,
>> > the fluid becomes 'incompressible'.

>> > You might try a 'hardened' equation - one which has special
>> > considerations for high pressures, in which drho/dP is less
>> > variable at higher pressures.

>> I googled "hardened equation of state," but nothing came up.  Can you
>> write down that equation for gamma, or give me a reference to a place
>> where I might look it up, either online or in a printed journal
>> article?

> My bad...
> Try "stiffened equation of state".  <31 hits>

> This will give you an entré into non-ideal fluid behavior.