## For Educators

### Calculating a Neutron Star's Density

A typical neutron star has a mass between 1.4 and 5 times that of the Sun. It cannot be more massive than this or gravity will overwhelm it and it will become a black hole! The radius of a neutron star may be between 10 and 20 kilometers.

Suppose we have a neutron star that has a radius of 15 kilometers and
a mass of 1.4 times that of the Sun. (The Sun's mass is 2.0 x 10^{30}
kilograms.) What is the neutron star's density?

Remember, density (D) = mass ÷ volume and the volume (V) of a sphere is
(4/3)r^{3}.

^{3}

=14137.2 km

^{3}

Can we compare the density of a neutron star, which is made up of neutrons, to the density of a single neutron?

By shooting particles at a neutron, we can find out its cross-sectional area,
and thus its radius and volume. From this we find that the volume of a neutron
is approximately 5.6 x 10^{-54} km^{3} and the mass of a
neutron is 1.67 x 10^{-27} kg, calculate the density.

These answers are remarkably close!