A neutron star is a star that has collapsed into a...

A neutron star is a star that has collapsed into a collection of tightly packed neutrons. Thus, it is something like a giant nucleus; but since it is electrically neutral, there is no Coulomb repulsion to break it up. The force holding it together is gravity. Suppose the Sun were to collapse into a neutron star. What would its radius be? Assume that the density is about the same as for a nucleus. Express your answer in $\mathrm{km}$.

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Key Concepts

Neutron Stars

Neutron stars are extremely dense stellar remnants formed by the gravitational collapse of massive stars. They are composed predominantly of neutrons and have densities comparable to that of atomic nuclei, which leads to their compact sizes despite having masses comparable to that of an ordinary star.

Nuclear Density

Nuclear density is a characteristic density of atomic nuclei, typically around 10^14 grams per cubic centimeter. This density scale is used as a benchmark when estimating the size of a neutron star, as their matter is compressed to similar densities during formation.

Mass-Radius Relationship in Spherical Bodies

For any spherical object with a uniform density, the mass, density, and radius are related by the formula V = M/? and V = (4/3)?r^3. This relationship allows one to calculate the radius by equating these expressions, which is essential for determining the size of objects like neutron stars from their mass and assumed density.

Gravitational Collapse

Gravitational collapse is the process by which a star or other astronomical object contracts under its own gravity. In the case of neutron stars, this collapse compresses the star's matter to extremely high densities, eliminating forces like Coulomb repulsion and resulting in a compact object dominated by gravity.

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