Lane–Emden equation
Dimensionless astrophysics equation / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Lane-Emden equation?
Summarize this article for a 10 year old
In astrophysics, the Lane–Emden equation is a dimensionless form of Poisson's equation for the gravitational potential of a Newtonian self-gravitating, spherically symmetric, polytropic fluid. It is named after astrophysicists Jonathan Homer Lane and Robert Emden.[1] The equation reads
where is a dimensionless radius and is related to the density, and thus the pressure, by for central density . The index is the polytropic index that appears in the polytropic equation of state,
where and are the pressure and density, respectively, and is a constant of proportionality. The standard boundary conditions are and . Solutions thus describe the run of pressure and density with radius and are known as polytropes of index . If an isothermal fluid (polytropic index tends to infinity) is used instead of a polytropic fluid, one obtains the Emden–Chandrasekhar equation.