Calculating the Radius of a Neutron Star

[sammyz]

The question is: Suppose the sun collapses into a neutron star. What will its radius be?

The question gave a brief backround explaining that stars are powered by nuclear reactions that fuse hydrogen and helium. When the hydrogen is used up the star collapses into a neutron star. The force of gravity becomes so large that protons and electrons are fused into neutrons. The entire star is then a tightly packed ball of neutrons with the density of nuclear matter.

I am not even sure how to begin. Any help would be appreciated. Thanks.

 

[mathman]

For starters, the sun is too small to end up as a neutron star - it would collapse to a white dwarf.

 

[Jheriko]

If you somehow had an enormous compressor to put the Sun in, you could squash it into being a neutron star. The how big would its radius be?

If i remember correctly there is some critical density that a star must attain for collapse into a neutron star so that the gravitation can overcome the degeneracy pressure. The easy way to find the answer is to take this critical density as an approximation to the real density, use it with the mass of the sun to find the volume if it was a neutron star, and then finally you can use the volume of a sphere, \frac{4}{3} \pi r^2, to get the radius out of that figure.

 

[scupydog]

The question is: Suppose the sun collapses into a neutron star. What will its radius be?

The question gave a brief backround explaining that stars are powered by nuclear reactions that fuse hydrogen and helium. When the hydrogen is used up the star collapses into a neutron star. The force of gravity becomes so large that protons and electrons are fused into neutrons. The entire star is then a tightly packed ball of neutrons with the density of nuclear matter.

I am not even sure how to begin. Any help would be appreciated. Thanks.

In a sense an atomic nucleus is like neutron star and the electron cloud would have been the size of the star before the collapse, therefore its diameter must have shrunk by approx 1/100,000 so if the sun with a diameter of 1,400,000k were converted to a nuetron star its diameter would be 14 kilometers hypotheically