Consider a high-mass star just prior to a supernova explosion, with a core of
diameter \(20 \mathrm{~km}\) and density \(4 \times 10^{17}\) \(\mathrm{kg} /
\mathrm{m}^{3}\). (a) Calculate the mass of the core. Give your answer in
kilograms and in solar masses. (b) Calculate the force of gravity on a 1-kg
object at the surface of the core. How many times larger is this than the
gravitational force on such an object at the surface of the Earth, which is
about 10 newtons? (c) Calculate the escape speed from the surface of the
star's core. Give your answer in \(\mathrm{m} / \mathrm{s}\) and as a fraction
of the speed of light. What does this tell you about how powerful a supernova
explosion must be in order to blow material away from the star's core?