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 660 N on the earth, what would you weigh on the surface of a neutron star that has the same mass as our sun and a diameter of 20.0 km?

weight on the surface of neutron star will be 8.93 x 10^13 N

Explanation:

First, we need to find the acceleration due to gravity (gx) at the surface of the neutron star. The formula for the acceleration due to gravity is given as:

gx = GM/R²

where,

G = Universal Gravitational Constant = 6.67 x 10^-11 N. m²/kg²

M = mass of star = mass of sun = 1.989 x 10^30 kg

R = radius of star = 20 km/2 = 10 km = 10000 m

Therefore,

gx = (6.67 x 10^-11 N. m²/kg²) (1.989 x 10^30 kg) / (10000 m) ²

gx = 13.27 x 10^11 m/s²

Now, we calculate mass of body on earth:

Weight on earth = 660 N = m (g on earth)

660 N = m (9.8 m/s²)

m = (660 N) / (9.8 m/s²)

m = 67.35 kg

Hence, the weight of body on surface of neutron star (Wx) will be:

Wx = (m) (gx)

Wx = (67.35 kg) (13.27 x 10^11 m/s²)

Wx = 8.93 x 10^13 N