How Much Would You Weigh on a Neutron Star?

[MissKaylaPaige]

Homework Statement

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 675 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 16.0 km?


Take the mass of the sun to be = 1.99×1030kg , the gravitational constant to be G= 6.67×10−11 , and the acceleration due to gravity at the Earth's surface to be g = 9.81

Homework Equations

mg=(Gmm_E)/(R_E)^2

I think??

The Attempt at a Solution

well I have not attempted it because the equation I have doesn't make sense when you include R_E^2 so I am unsure of the proper formulas??

 

[Edward G]

You need to change the M_e to M_n, the mass of the neutron star, and R_e to R_n, the radius of the neutron star. Everything should then work out fine.

 

[ogb p]

I would like to clarify that the equation you have provided, mg=(Gmm_E)/(R_E)^2, is the correct formula for calculating weight on a celestial body with a radius R_E and mass m_E. However, in this case, we are dealing with a neutron star, which has a much smaller diameter than Earth and therefore a much larger gravitational force. The equation for calculating weight on a neutron star would be mg=(Gmm_N)/(R_N)^2, where R_N is the radius of the neutron star and m_N is its mass.

To solve this problem, we can use the given information and the formula for the acceleration due to gravity, g=Gm_N/R_N^2, to find the weight on the surface of the neutron star.

First, we need to find the radius of the neutron star. We can use the given diameter of 16.0 km to calculate the radius using the formula R_N=d/2=8.0 km.

Next, we can plug in the values for the gravitational constant, mass of the sun, and radius of the neutron star into the equation g=Gm_N/R_N^2 and solve for the acceleration due to gravity on the surface of the neutron star. This gives us a value of g=1.93×10^12 m/s^2.

Finally, we can use the formula mg=(Gmm_N)/(R_N)^2 to calculate the weight on the neutron star. Plugging in the given weight on Earth (675 N), the gravitational constant, and the calculated acceleration due to gravity on the neutron star's surface, we get a weight of 1.30×10^16 N on the neutron star.

In conclusion, your weight on a neutron star with the same mass as our sun and a diameter of 16.0 km would be 1.30×10^16 N, which is significantly greater than your weight on Earth due to the strong gravitational force of the neutron star.