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 21.0 km ?

Take the mass of the sun to be ms = 1.99×10³⁰ kg , the gravitational constant to be G = 6.67×10⁻¹¹ N⋅m2/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.

Answer 1

weight on earth

W = m g

m = W / g

= 690 / 9.8

= 70.408 kg

if the person with mass m = 70.408 is om the surface of the nuetron star then the gravitational force of attraction between person and the nuetron star will be

Fg = G m₁ m₂ / r²

where

G = 6.67×10⁻¹¹ N⋅m2 / kg²

m₁ = 70.408 kg,

m₂ = 1.99×10³⁰ kg

r = 10.5 km

Fg = = m₁ g

m₁ g = G m₁ m₂ / r²

the acceleration on the surface of neutron star is

g = G m₂ / r²

= (6.67×10⁻¹¹) (1.99×10³⁰) / (10.5 x 10³)²

   = ......... m / s2

the weight on the neutron star will be

W = (m₂) g

= ......... N