Virial Theorem

This lecture explains the Virial Theorem, which relates the kinetic energy to the potential energy of self-gravitating systems, such as globular clusters and stellar clusters. The theorem is demonstrated by showing that the time-averaged kinetic energy is equal to the time-averaged potential energy. The lecture also covers the application of the Virial Theorem in astrophysics, where it is used to determine the mass of objects based on their potential energy and to express kinetic energy in terms of temperature. The derivation of the Virial Theorem involves integrating the gravitational force to calculate the total potential energy of a spherical object. The theorem plays a crucial role in determining the masses of various astronomical objects by analyzing their velocities or velocity distributions.