Calculating the Radius of a Neutron Star

In summary, the question asks for the radius of a neutron star formed from the collapse of the sun, with a background explanation of the fusion process. The density of nuclear matter (2.3*10^17 kg/m^3) is given, and the solution involves relating the mass of the sun to the volume and radius of the neutron star.
  • #1
sammyz
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Homework Statement



Suppose the sun collapses into a neutron star. What will its radius be? The questions also gives some backround explaining that stars fuse hydrogen into helium until they collapse into a neutron star. The protons and electrons fuse into neutrons with the density of nuclear matter.


Homework Equations





The Attempt at a Solution



I'm not sure exactly how to begin. I am assuming I am supposed to use the number for the density of nuclear matter which is 2.3 * 10^17 kg/m^3 but I do not know where to go from here. It would be nice to just get a hint. Thanks.
 
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  • #2
What you must assume is that the wntire mass of the sun gets condensed into an extrememly dense neutron core. You are given the density of a neutron star and thus it is easy to relate the mass to the volume and thus the radius as you assume the sun will condense into a sphere.

[tex]\rho_{core} = \frac{m_{sun}}{\frac{4}{3}\pi r^3}[/tex]
 

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

Scientists use a variety of methods to calculate the radius of a neutron star, including observations of the star's mass and luminosity, as well as theoretical models based on the properties of neutron stars.

2. What is the average radius of a neutron star?

The average radius of a neutron star is estimated to be around 10-15 kilometers, which is about the size of a small city.

3. 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 from a companion star, or the emission of energy through radiation.

4. How does the radius of a neutron star compare to other astronomical objects?

The radius of a neutron star is much smaller than other astronomical objects, such as planets or stars. For comparison, the radius of the Earth is about 6,371 kilometers, while the radius of the largest known star, UY Scuti, is estimated to be around 1,708 times that of the Sun.

5. Are there any challenges in accurately calculating the radius of a neutron star?

Yes, there are several challenges in accurately calculating the radius of a neutron star, including the extreme gravitational and magnetic fields present on these objects, as well as uncertainties in our understanding of the properties of matter at such high densities.

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