Answer: [tex]W_{n}=5.724 (10)^{13})N[/tex]
Explanation:
The weight [tex]W[/tex] of a body or object is given by the following formula:
[tex]W=m.g[/tex] (1)
From here we can find the mass of the body:
[tex]m=\frac{W}{g}=67.346 kg[/tex] (2)
Where [tex]m[/tex] is the mass of the body and [tex]g[/tex] is the acceleration due gravity in an especific place (in this case the earth).
In the case of a neutron star, the weight [tex]W_{n}[/tex] is:
[tex]W_{n}=m.g_{n}[/tex] (3)
Where [tex]g_{n}[/tex] is the acceleration due gravity in the neutron star.
Now, the acceleration due gravity (free-fall acceleration) [tex]g[/tex] of a body is given by the following formula:
[tex]g=\frac{GM}{r^{2}}[/tex] (4)
Where:
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the gravitational constant
[tex]M[/tex] the mass of the body (the neutron star in this case)
[tex]r[/tex] is the distance from the center of mass of the body to its surface. Assuming the neutron star is a sphere with a diameter [tex]d=24km[/tex], its radius is [tex]r=\frac{d}{2}=12.5km=12500m [/tex]
Substituting (4) and (2) in (3):
[tex]W_{n}=m(\frac{GM}{r^{2}})[/tex] (5)
[tex]W_{n}=(67.346kg)(\frac{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(1.99(10)^{30}kg)}{(12500m)^{2}})[/tex] (6)
Finally:
[tex]W_{n}=5.724 (10)^{13})N[/tex]
