2019年USAAAO决赛第4题

英文题目

4. (7 points) Consider a star with mass M and radius R. The star’s density varies as a function of radius r according to the equation $$ρ(r) = ρ_{center}(1-\sqrt{r/R})$$, where $$ρ_{center}$$ is the density at the center of the star. Derive an expression for $$\dfrac{dP}{dr}$$ in terms of G, M, R, and r, where P is the pressure at a given radius r.