Question

Neutron star density. a typical neutron star has a mass of about 1.5m☉ and a radius of 10 kilometers. calculate the average density of a neutron star, in kilograms per cubic centimeter. compare the mass of 1 cm3 of neutron star material to the mass of mount everest ( 5 1010 kg).

Answer 1

(a) One solar mass is equal to $2\cdot 10^{30}kg$, so the mass of the neutron star is 1.5 times this value:
$M=1.5 M_s =1.5 \cdot 2\cdot 10^{30}kg=3\cdot 10^{30}kg$

The radius of the star is $r=10 km=10000 m$, so its volume is
$V= \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (10000 m)^3 = 4.2 \cdot 10^8 m^3$

So, the density of the neutron star is
$d= \frac{M}{V} = \frac{3 \cdot 10^{30}kg}{4.2 \cdot 10^8 m^3}=7.1 \cdot 10^{21} kg/m^3$

(b) We want to find the mass of 1 cm^3 of neutron star. The volume is
$V=1 cm^3 = 1 \cdot 10^{-6}m^3$
so, by using the density we found at point (a), we can calculate the mass of 1 cm^3 of neutron star:
$m=dV=(7.1 \cdot 10^{21}kg/m^3)(1 \cdot 10^{-6}m^3)=7.1 \cdot 10^{15} kg$

So, 1 cm^3 of neutron star has more mass than Mt Everest (whose mass is $5 \cdot 10^{10}kg$).