The calculation of atmospheric pressure at the summit of Mount Everest carried out in Example 13.3 used the model known as the isothermal atmosphere, in which gas pressure is proportional to density: p = γp, with γ constant. Consider a spherical cloud of gas supporting itself under its own gravitation and following this model.
a) Write the equation of hydrostatic equilibrium for the cloud, in terms of the gas density as a function of radius, ρ(r).
b) Show that ρ (r) = A/r2 is a solution of this equation, for an appropriate choice of constant A. Explain why this solution is not suitable as a model of a star.
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