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

Question

solb

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as out ton but a much smaller diameter If you weigh 655 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 15.0 km? Take the mass of the sun to be m_s = 1.99 times 10^30 kg the gravitational constant to be G = 6.67 times 10^-11 N middot m^2/kg^2. and the acceleration due to gravity at the earth's surface to be g = 9.810 m/s^2 Express your weight w_star in newtons.

Explanation / Answer

Your weight on earth, Wearth = 655 N

as                    Wearth = GMe m /Re^2 =mg        …………………………………..(1)

let weight on star, Wstar = ?

                      Wstar = GMs m /Rs^2            …………………………………….(2)

Dividing ………….(2)     by     ………………..(1)

                      Wstar / Wearth = (GMs m /Rs^2 ) / mg = GMs /gRs^2 = 6.67*10^-11 * 1.99*10^30 / 9.8*((15/2)*10^3)^2

                    Wstar / Wearth =24.08*10^10

                   Wstar =24.08*10^10 * Wearth =24.08*10^10 *655 =1.58*10^14N

Hence, you weight on star is 1.58*10^14 N

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