> > 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 the
> >> 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?