How heavy would you be on neuron star

[Neutrino00]

I have a problem that I can't figure out, as do most people I guess, so here goes. A neutron star is 1,000 times smaller than the Earth and has 450,000 times the mass of the earth. How many times heavier would you be on the surface of a neutron star?

 

[David]

Here are the steps you need to get to the answer... Your weight is your mass times the gravitational field strength. $$W=mg$$. $$g$$ depends on the mass and radius of the object like this: $$g = \frac{GM}{r^2}$$

So for a particular person, their weight will scale as the mass of the planet/star and inversely with the radius squared. i.e. your mass will be greater by a factor of 450,000 due to the mass difference and greater by an additional factor of (1000)² due to the smaller radius.

 

[quicknote]

On the surface of a neutron star, you would be significantly heavier due to its incredibly high mass and small size. To calculate how much heavier, we can use the formula for gravitational force: F = G(m1m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, m1 would be your mass and m2 would be the mass of the neutron star. Since the neutron star has 450,000 times the mass of the Earth, we can substitute 450,000mE for m2, where mE is the mass of the Earth. We also know that the radius of a neutron star is about 10 kilometers, or 10,000 meters. Plugging in these values, we get:

F = G(m1)(450,000mE)/(10,000m)^2

Simplifying, we get:

F = 45Gm1/mE

This means that the gravitational force on you would be 45 times stronger on the surface of a neutron star compared to Earth. Since weight is a measure of the force of gravity on an object, you would weigh 45 times more on a neutron star than you do on Earth. So, if you weigh 150 pounds on Earth, you would weigh a staggering 6,750 pounds on a neutron star!

It's important to note that this calculation assumes that you are standing directly on the surface of the neutron star. In reality, the intense gravitational force and radiation on a neutron star would make it impossible for a human to survive on its surface. But hypothetically, if you were able to stand on a neutron star, you would definitely feel the effects of its extreme gravity.