Neutron stars, such as the one at the center of the Crab...

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 $\mathrm{N}$ on the earth, what would you weigh on the surface of a neutron star that has the same mass as our sun and a diameter of 20.0 $\mathrm{km} ?$

Transcript

0:00 Hi there.

00:01 So for this problem, we are told that 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.

00:15 If your weight is given and that weight is equal to 675 neutrons on the earth.

00:27 So the question is, what will your weight on the surface? of a neutron star that has the same mass as our sond and a diameter that is given and that diameter is equal to 20 kilometers, which is the same as 20 times 10 to the 3 meters or just simply 20 ,000 meters.

00:56 Now with that said, the first thing that we need to obtain is your mass.

01:02 We know that the weight is defined as the mass times acceleration due to gravity.

01:08 Now, since we have the weight, we just simply solve for the mass, so that will be the weight divided by the acceleration due to gravity, so that will be 675 neutens, divided by the acceleration due to gravity, that is 9 .8 meters per second square.

01:24 So from this, we obtain a value of 68 .8 .5.

01:33 88 kilograms.

01:39 So this is your mass.

01:41 And now we know that what we need to use is the equation, the equation for the gravitational force, which is the gravitational constant.

01:59 And this times the mass of the neutron star, which is the same as the mass of the mass of the, the sun, we are told that.

02:09 And this times the mass that we just found.

02:12 And this divided by the radios of the, of this neutron star and to the square, of course...