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 665N 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 km?
Take the mass of the sun to be = 1.99×1030 kg , 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.
To find the weight on the surface of the neutron star, we can use the formula for gravitational force:
F = (G * M1 * M2) / r^2
where:
F is the gravitational force,
G is the gravitational constant,
M1 and M2 are the masses of the two objects,
r is the distance between the centers of the two objects.
In this case, we want to find the weight on the surface of the neutron star, so M1 will be the mass of the neutron star, M2 will be your mass, and r will be the radius of the neutron star (which is half the diameter).
First, let's calculate the mass of the neutron star using the mass of the sun:
Mass of the neutron star = Mass of the Sun = 1.99×10^30 kg
Next, let's calculate the radius of the neutron star:
Radius of the neutron star = Diameter / 2 = 19.0 km / 2 = 9.5 km = 9.5 * 10^3 m
Now, let's substitute these values into the formula to find the gravitational force on the surface of the neutron star:
F = (G * M1 * M2) / r^2
F = (6.67×10^-11 N m^2/kg^2 * 1.99×10^30 kg * 665N) / (9.5 * 10^3 m)^2
Calculating this equation will give us the weight on the surface of the neutron star.