Conservation of Energy.
a) The potential energy in the sun is the energy that would be liberated if it collasped. For a sphere of uniform density this is given by:
Where G is the universal constant, M is the mass of the sun, and R is the radius of the sun. Solve this set of integrals, find values for the constant and properties, and calculate the potential energy of the sun (astronomers usually do this calculation in ergs). This is actually an approximation. To see a more accurate derivation check out this page.
b) The thermal energy of the sun can be described by:
Where N is the number of particles, k is the Boltzmann factor, and T is the average temperature in the sun. This equation comes from assuming that hydrogen is an ideal gas and calculating its kinetic energy. Using 8E6 K for the average internal temperature of the sun and 2E57 for the number of particles, calculate the energy. Compare your answer with part A. Because of the approximation in the previous part, your answer may be off by a factor of 2.