Question

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun, but a much smaller diameter.
If you weigh 650 N on the earth, what would you weigh on the surface of a neutron star that the same mass as our sun and a diameter of 20.0 km?

Answer 1

We need to convert diameter into SI units:
km --> m
20.0 km (1000 m/1 km) = 20000 m

We have to convert the weight into mass before we can apply it to the weight elsewhere.
F = force
m = mass
a = acceleration

F = ma --> m = F/a
m = (650 N)/(9.810 m/s^2)
m = 66.26... kg

Now we must use Newton's law of universal gravitation in order to find the weight of the person on a neutron star. We are assuming that all of your mass is located within the center of you, and that the distance between that center and the surface of the star is negligible.

m1 = mass of you
m2 = mass of neutron star
r = radius = diameter/2

F = G(m1 * m2)/r^2
F = (6.67 * 10^-11 ((N*m^2) / kg^2))*(66.26 kg * 1.99*10^30 kg)/(20000/2 m)^2
F ≈ 8.79*10^13 N

Your weight on the surface of the neutron star is 8.8*10^13 N.