The P = Kρ - P - pressure.
- ρ - density.
- γ - a constant.
Assuming such a constant exists, the gas is polytropic.
The model is used in modeling stars and Gas Planets.
In some circumstances, an The Lane-Emden Equation is: 1 d —— —— (E where: - n - a constant, determined by a function of the constant γ above.
- θ - a function of density and the constant n.
- E - a function of the radius and some cleverly-chosen constants.
As such, it spells out the density by radius, and from that, the pressure at any radius can be determined by the earlier equation.
Solutions to the equation are known to astrophysicists as equation,astrophysics)http://www.astro.caltech.edu/~jspineda/ay123/notes/2011/ay123_polytropes_sep2010.pdf http://www.ast.cam.ac.uk/~bdavies/Stars2/Stars2_Lecture1.pdf |