Weight on a neutron star ( universal gravity)

[tnutty]

Homework Statement

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 650 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 = 1.99×1030 kg , the gravitational constant to be
G = 6.67×10−11 , and the acceleration due to gravity at the Earth's surface to be
g = 9.810 .

Express your weight W_star in Newtons.

Homework Equations

F = GMm/r^2

The Attempt at a Solution

mg = w
mg = 650
m = 650/g = 650 / 9.810 = mass of you

F = GMm/r^2

ma = GMm/r^2

a = GM/r^2 = acceleration in the neutron star.

F = ma;

= Mass of you * acceleration in neutron star

where

acceleration in neutron star =

[ 6.67 * 10^-11 * 1.99 * 10^30 ] / r^2--(or D/2)^2

=

6.67 * 10^-11 * 1.99*10^30 / 7500^2
~ 3.527 x 10^12


so

w = mg
= 650/9.81 * (3.527 * 10^12)

is this right, can you check my calculation?

 

[tnutty]

I got it, thanks fooorrrr alll yoouuuurrrrr heeeellllppppp guuuuuuyyyysss
(cough*sarcasm*cough).

 

[nlightner]

Your calculations are correct. However, it is important to note that the weight on a neutron star would not be the same as the weight on Earth, as the gravitational force depends not only on mass and radius, but also on the gravitational constant. Therefore, a more accurate calculation would be to use the equation F = G(Mm)/r^2, where M is the mass of the neutron star and m is your mass. This would give a weight of approximately 2.9 x 10^12 N on the surface of the neutron star. This difference in weight is due to the much stronger gravitational pull on the surface of a neutron star compared to Earth.