Neutron stars, such as the one at the center of the Crab Nebula, have about the

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 690 N 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 17.0 km ?

Take the mass of the sun to be ms = 1.99×1030 kg , the gravitational constant to be G = 6.67×1011 Nm2/kg2 , and the acceleration due to gravity at the earth's surface to be g = 9.810 m/s2 .

Express your weight wstar in newtons.

Explanation / Answer

here,

Weight on earth, we = 690 N
mass on earth, me = 690/9.81 = 70.336 kg

radius of sun, r = 17/2 = 8.5 km = 8.5*10^3 m

From Newton Law of Gravitation,
Force, F = G*me*ms/r^2 (ms = mass of sun)

F = ((6.67*10^11)*(1.99*10^30)*70.336)/(8.5*10^3)^2

F = 1.292*10^14 N

From Newton Second LAw,
F - Ws = 0 ( Ws = Weight on star)
F = Ws
Ws = 1.292*10^14 N

Bonus:
acceleration due to gravity on star,
g = F/m = 1.292*10^14/(1.99*10^30)

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