stellar temperatures and fluxes: (a) if a spherical star located at a distance d subtends a solid angle ω on the sky, and the flux from the star (integrated over all wavelengths) just above the earth's atmosphere is f(d), show that the flux at the star's photosphere (emitting surface) is π/(d)/q. (b) derive an expression for the surface temperature of a spherical star, in terms only of its at earth, and solid angle ω, its flux per unit wavelength fah) at one wavelength fundamental constants (e) the star betelgeuse has a measured angular diameter of 0.044 arcseconds, and a measured bolometric apparent magnitude of -1.00. use the sun's physical quantities, including its bolometric absolute magnitude from the constants sheet handout, to estimate the surface temperature of betelgeuse in k using the stefan-boltzmann law. (hint: write your equations in terms of ratios between betelgeuse and the sun.)