SAO 2020, Подбор за GeCAA · структурирани задачи — Задача 1. Stars

GeCAA Selection Test Structured Question Paper · 4 т.

Условие

Suppose we have an equation of state for stars:

where $P$ is the pressure, $\rho$ is the density, and $A$ is a constant. Such a solution is called a polytrope, and one can estimate an approximate relationship between the mass $M$ and density $\rho$ of the form $M \propto R^{\alpha}$.

Find $\alpha$. State any assumptions you made.

Hint: The hydrostatic equilibrium condition given by $\frac{dP}{dr} = -\frac{GM_r\rho_r}{r^2}$ may be useful.

Отговори

Решение

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Оригинал в Архива: GeCAA Selection Test Structured Question Paper.pdf · официални решения: GeCAA Selection Test Structured Question Solutions.pdf