a) Explain how we estimate the effective surface temperature of the Sun. A main sequence star has mass  kg and radius  m.Obtain an estimate of the average temperature throughout the star. 

Estimating the effective surface temperature of the Sun, or any other main sequence star, involves understanding the balance between the energy produced in its core through nuclear fusion and the energy radiated from its surface. One commonly used method to estimate the surface temperature is through the use of the Stefan-Boltzmann Law and the luminosity of the star.

The Stefan-Boltzmann Law relates the total power radiated by a blackbody to its temperature and surface area. It is expressed by the equation:

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