(Solved): Problem 4. What is the significance of 8 solar masses in stellar evolution? 1. How does the death ...

Problem 4. What is the significance of 8 solar masses in stellar evolution? 1. How does the death of one very massive star give birth to perhaps hundreds of smaller ones soon thereafter? 2. Looking at the elements that make up our world, which are the products of low versus high mass stars? Problem 5. The Schwarzschild radius for a given black hole defines a sphere, from which escape is impossible, even for light. It is given by \[ R_{\mathrm{S}}=\frac{2 G M}{c^{2}} \] Show that this can be written in terms of the mass of the Sun as \[ R_{\mathrm{S}} \approx 2.95\left(\frac{M}{M_{\odot}}\right) \mathrm{km} . \] 1. Suppose that the Sun became a black hole. What would its Schwarzschild radius be? 2. What would the Schwarzschild radius be for Betelgeuse, whose mass is about 10 times the solar mass? Problem 6. Contrast the internal structures and properties of neutron stars with white dwarf and main sequence stars by: 1. Explaining the processes which balances the inward pull of gravity. 2. Estimating their densities using the following information. a) WHITE DWARFS: Mass is equal to \( M_{\odot} \) and is concentrated within a radius equal to that of earth. b) NEUTRON STARS: Mass equal to \( M_{\odot} \) and is concentrated within a radius of \( 10 \mathrm{~km} \).