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.

A)If you weigh 670 on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 18.0 ?
Take the mass of the sun to be = 1.99×1030 , the gravitational constant to be = 6.67×10-11 , and the acceleration due to gravity at the earth's surface to be = 9.810.

Answer 1

The mass of the star is M = 1.99*10^30 kg
The radius of the star is R = 18 km
The universal gravitational constant G = 6.67*10^-11 Nm^2/kg^2
The acceleration due to gravity on the Earth's surface g = 9.81 m/s^2

The acceleration due to gravity on the surface of the star is
a(star) = GM/R^2
a(star) = (6.67*10^-11 Nm^2/kg^2)(1.99*10^30 kg)/(18000 m)^2
a(star) = 4.09669*10^11 m/s^2

The mass of the person is
m = We/g
Where We are the weight of the person on the earth
g is the free-fall acceleration on the earth
m = 670 N / 9.810 m/s^2
m = 68.297 kg

Weight of the peraon on the star is
Ws = m*a(star)
Ws = 68.297*4.09669*10^11 m/s^2
Ws = 2.79*10^13 N