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 that has the same mass as our sun and a diameter of 17.0 km?

take the mass of the sun to be m_s = 1.99×1030 kg, the gravitational constant to be g = 6.67×10-11 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.

Explanation:

In order to solve this problem, we must start by finding our mass, which can be found by using the following formula:

when solving for the mass we get that:

which yields:

Now, generally when using the force of gravity equation on a planet, we take the r to be the distance between the center of the planet to its surface. This is the radius of the planet, since the problem provides us with the diameter, we can use it to find the radius:

so we get that:

we can convert this to meters so all our dimensionals are the same, so we get:

We can now find our weight at the star by using the force of gravity formula:

when plugging all the provided data in, we get:

which yields: