Question

A neutron star consists of neutrons at approximately nuclear density. Estimate, for a 10-km-diameter neutron star its mass number, its mass, the acceleration of gravity at its surface. Estimate its mass number. Estimate its mass. Estimate the acceleration of gravity at its surface.

Answer 1

Given the diameter of the neutron star = 10 km

Nuclear density is about 10^18 kg/m³.
The mass per proton is about 1.67×10^−27kg

You should be able to figure it from that.

First, calculate the volume of the star. V = 4/3 pi r^3
r = 5000 m
V = ~ 5.24 x 10^11 m³

Mass = volume * density
5.24e11 m³ * 1e18 kg/m³ = 5.24e29 kg
(about 130,000 times the mass of the earth)

Mass number = mass(kg) / mass per neutron
5.24e29 kg / 1.67e−27kg/n = ~3.14e56


Gravity at surface: F =GmM/R^2

M is the mass of the star, m is the mass of whatever - we'll set it to one, since we're finding force per kilogram. R is the radius of the star, G is a constant, 6.67x10^-11 N m^2/kg^2

F = 6.67e-11 N m^2/kg^2 * 5.24e29 kg / (5000m^2) = ~
1.4e12 N/kg

Earth's gravity is about 9.8 N/kg, so we could also express it as 1.43e11 times earth's gravity.