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{c}

If $\rho=\rho_c\theta^n$, $r=\alpha\xi$, and $\xi_1$ is the first zero of the Lane-Emden function, then a spherical polytrope has
$$
M=4\pi\alpha^3\rho_c\left[-\xi_1^2\theta'(\xi_1)\right].
$$


Lane-Emden mass formula

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 317 / 3 / ii / Solution

Lane-Emden mass formula

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Lane-Emden mass formula

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