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 665 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 19.0 ?
Take the mass of the sun to be = 1.99×1030 , the gravitational constant to be = 6.67×10−11 , and the acceleration due to gravity at the earth's surface to be = 9.810 .

Express your weight in newtons.

1..29 x 10^14

To calculate your weight on the surface of a neutron star, we can use the formula for gravitational force:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force between two objects,
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.

In this case, we want to find the force between you (considered a point mass) and the neutron star. We already have the mass of the neutron star (same as our sun) and its diameter. We also have the mass of the sun.

1. Convert the diameter of the neutron star into its radius:
r = diameter / 2 = 19.0 km / 2 = 9.5 km = 9.5 x 10^3 m

2. Convert the mass of the sun to kilograms:
Mass of the sun = 1.99 x 10^30 kg

3. Convert your weight on Earth from pounds to kilograms:
Weight on Earth = 665 pounds x 0.4536 kg/pound

Now, let's put these values into the formula:

F = (G * m1 * m2) / r^2

F = (6.67 x 10^(-11) N * m^2 / kg^2) * (your weight in kg) * (mass of the sun) / (radius of the neutron star)^2

F = (6.67 x 10^(-11) N * m^2 / kg^2) * (your weight on Earth in kg) * (1.99 x 10^30 kg) / (9.5 x 10^3 m)^2

Now, plug in the given values and solve for F:

F = (6.67 x 10^(-11)) * (665 x 0.4536 kg) * (1.99 x 10^30 kg) / (9.5 x 10^3 m)^2

Evaluate the calculation and express your weight in Newtons.