> 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.