If you weigh 660 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 25.0 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 .

Explanation:

The weight of a body or object is given by the following formula:

(1)

From here we can find the mass of the body:

(2)

Where is the mass of the body and is the acceleration due gravity in an especific place (in this case the earth).

In the case of a neutron star, the weight is:

(3)

Where is the acceleration due gravity in the neutron star.

Now, the acceleration due gravity (free-fall acceleration) of a body is given by the following formula:

(4)

Where:

is the gravitational constant

the mass of the body (the neutron star in this case)

is the distance from the center of mass of the body to its surface. Assuming the neutron star is a sphere with a diameter , its radius is

Substituting (4) and (2) in (3):

(5)

(6)

Finally:

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