Answer to Question #304120 in Astronomy | Astrophysics for Rohan

Question

Neutron stars are some of the densest objects in the universe. They form during supernova ex plosions and are very small compared to other astronomical objects. You can assume 5 * 10 ^ 17 kg/m³ as the average density of a neutron star. The Earth has a total mass of about 5.97*10^ 24 kg

What would be the diameter of the Earth if it had the density of a neutron star?

Answer 1

Let us determine the volume of neutron star: $V=\frac43 \pi R^3.$ We should obtain an estimate for R.

The density $\rho = \dfrac{M}{V},$ so $V=\dfrac{M} {\rho}.$

The volume will be $V=\dfrac{5.97\cdot10^{24}}{5\cdot10^{17}} = 1.19\cdot10^7\,\mathrm{m^3}.$

The radius will be $R= \sqrt[3]{\dfrac{V}{\frac43\pi}} = 142\,\mathrm{m}.$

The diameter will be 284 m.