Stars are powered by nuclear reactions that fuse hydrogen into helium. The fate of many stars, once most of the hydrogen is used up, is to collapse, under gravitational pull, into a neutron star. The force of gravity becomes so large that protons and electrons are fused into neutrons in the reaction p⁺ + e^- → n + v. The entire star is then a tightly packed ball of neutrons with the density of nuclear matter.

a. Suppose the sun collapses into a neutron star. What will its radius be? Give your answer in km.

b. The sun’s rotation period is now 27 days. What will its rotation period be after it collapses? Rapidly rotating neutron stars emit pulses of radio waves at the rotation frequency and are known as pulsars.