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.