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 has the same mass our sun and a diameter of 190. km? take the mass of the sun to be ms= 1.99x10^30 kg. the gravitational constant to be G= 6.67x10^-11 N.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.

Answer 1

In earth ,weight = mg

which is equal to the Gravitational force between a person and earth

we know F_g =GM_em/R² ,where m is the mass of person , M_e mass of earth ,R is the radius of earth

so mg = GM_em/R²

g =GM_e /R² =9.81 m/s²

--------------------

On the neutron star value of g is different

R_n =190km/2 = 95000m ,M_n = 1.99*10³⁰kg

g_n = GM_n/R_n² = 6.67*10^-11 *1.99*10³⁰ /(95000)²

g_n = 1.4707*10¹⁰ m/s²

----------------------

Weight in Neutron star

Given weight on earth mg =690N

m = 690/9.81 = 70.3364kg

---------

Mass is same everywhere

so Weight on neutron star = mg_n = 70.3364 *1.4707*10¹⁰

W_n = 1.0344*10¹² N

ANSWER: W_n = 1.0344*10¹² N

------------------------------------