Calculating the Radius of a Neutron Star

In summary, the question asks about the potential radius of a neutron star formed from the collapse of the sun. The process of collapse is explained, where the star becomes a tightly packed ball of neutrons with the density of nuclear matter. The suggested method for finding the radius is to use the critical density and mass of the sun to calculate the volume and then use the formula for the volume of a sphere to determine the radius. Another estimate is given by comparing the size of an atomic nucleus to a neutron star, making the hypothetical radius of a neutron star formed from the sun's collapse to be 14 kilometers.
  • #1
sammyz
2
0
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.
 
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  • #2
For starters, the sun is too small to end up as a neutron star - it would collapse to a white dwarf.
 
  • #3
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, [itex]\frac{4}{3} \pi r^2[/itex], to get the radius out of that figure.
 
  • #4
sammyz said:
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
 

1. How do you calculate the radius of a neutron star?

To calculate the radius of a neutron star, you need to use the mass and density of the star. The formula for calculating the radius is R = (3M)/(4πρ), where R is the radius, M is the mass, and ρ is the density.

2. What is the mass and density of a typical neutron star?

The mass of a neutron star is typically around 1.4 times the mass of the sun, or 2.8 x 10^30 kilograms. The density of a neutron star is incredibly high, with an average density of 10^17 kg/m^3.

3. How accurate are the calculations for the radius of a neutron star?

The calculations for the radius of a neutron star are fairly accurate, with an error margin of around 10%. However, there are still uncertainties in the measurements of mass and density of neutron stars, so the calculated radius may vary slightly.

4. Can the radius of a neutron star change over time?

Yes, the radius of a neutron star can change over time due to various factors such as accretion of matter, rotation, and magnetic fields. However, these changes are very small and difficult to measure.

5. How is the radius of a neutron star related to its gravitational force?

The radius of a neutron star is directly related to its gravitational force. The smaller the radius, the stronger the gravitational force will be. This is because the mass of the neutron star is concentrated in a smaller area, resulting in a stronger gravitational pull.

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