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?

Stellar evolution refers to the process by which a star changes over the course of time. It is a fascinating journey that stars go through, starting from their birth in nebulae to their ultimate fate, which can include becoming a supernova. High-mass stars, significantly larger than our sun, have short but spectacular lifespans. They fuse heavier elements in their core and, once they exhaust their nuclear fuel, the core may collapse under its own gravitational force. This collapse can sometimes lead to a cataclysmic supernova explosion, which is one of the most energetic events in the universe.

During a supernova, the star's core contracts rapidly and then rebounds, ejecting its outer layers into space. This process redistributes elements essential for life, scattering them across the cosmos. High-mass stars that go supernova are crucial for recycling matter, contributing to the evolution of galaxies and the formation of new stars. Understanding stellar evolution, particularly the supernova phase, provides insight into how the elements on Earth were formed and how they continue to evolve in space.

Gravitational force is a fundamental interaction that pulls two masses toward each other. It's described by Newton's law of universal gravitation, which states that every point mass attracts every other point mass with a force along the line intersecting both points. The force is proportionate to the product of the two masses and inversely proportionate to the square of the distance between their centers.

In the context of a supernova, the gravitational force plays a crucial role. It is the gravitational collapse of the star's core that sets the stage for the supernova explosion. The mass of the core, which can be millions to billions of times more massive than the Earth, creates a gravitational pull that is immense. This gravitational pull is so strong that it influences the movement of objects even at the very edge of the star's influence and is critical in calculating the escape velocity needed for matter to break free from the star, especially during the forceful supernova event.

Escape velocity is the minimum speed needed for an object to 'break free' from the gravitational attraction of a massive body, without further propulsion. This concept is pivotal when examining the physics of a supernova explosion. Given the tremendous mass concentrated in the tiny volume of a supernova's core, the escape velocity is enormously high.

The calculation of escape velocity takes into account the mass of the celestial body and the distance from its center to the point of escape - in this case, the surface of the star's core. During a supernova explosion, the energy released must be enough to propel the star's matter at or above this escape velocity; otherwise, the material will fall back into the core. Material that reaches the escape velocity becomes part of the interstellar medium, travelling through space and potentially contributing to the formation of new stars and planets. The fact that supernovae can expel vast amounts of matter into space at speeds approaching or even exceeding the speed of light showcases their incredible power.