Coordinates, Mass Distribution, and Gravitational Field in Spherical Stars
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For gaseous, non-rotating, single stars without strong magnetic fields, the only forces acting on a mass element come from pressure and gravity. This results in a spherically symmetric configuration. All functions will then be constant on concentric spheres, and we need only one spatial variable to describe them. It seems natural to use the distance r from the stellar centre as the spatial coordinate, which varies from r = 0 at the centre to the total radius r = R at the surface of the star. In addition, the evolution in time t requires a dependence of all functions on t. If we thus take r and t as independent variables, we have a typical “Eulerian” treatment in the sense of classical hydrodynamics. Then all other variables are considered to depend on these two, for example the density ϱ = ϱ (r, t)
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