Lane Emden Equation
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High Quality Content by WIKIPEDIA articles! In astrophysics, the Lane Emden equation is Poisson's equation for the gravitational potential of a self-gravitating, spherically symmetric polytropic fluid. It is named after the astrophysicists Jonathan Homer Lane and Robert Emden.Note that solutions to the Lane Emden equation for a given polytropic index n are known as polytropes of index n. Physically, hydrostatic equilibrium connects the gradient of the potential, the density, and the gradient of the pressure, whereas Poisson's equation connects the potential with the density. It should be clear…mehr

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High Quality Content by WIKIPEDIA articles! In astrophysics, the Lane Emden equation is Poisson's equation for the gravitational potential of a self-gravitating, spherically symmetric polytropic fluid. It is named after the astrophysicists Jonathan Homer Lane and Robert Emden.Note that solutions to the Lane Emden equation for a given polytropic index n are known as polytropes of index n. Physically, hydrostatic equilibrium connects the gradient of the potential, the density, and the gradient of the pressure, whereas Poisson's equation connects the potential with the density. It should be clear then if we know nothing about the gas other than the way pressure and density vary with respect to one another, we can reach a solution, in principle.