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AST 443 Ch - 20 Problems 5. The Sun will reside on the main sequence for 1010 years. If the luminosity of a main-sequence star is proportional to the fourth power of the star’s mass, what mass star is just now leaving the main sequence in a cluster that formed (a) 400 million years ago, (b) 2 billion years ago? 8. Calculate the average density of a red-giant core of 0.25 solar-mass and radius 15,000 km. Compare this with the average density of the giant’s envelope, if it has a 0.5 solar-mass and its radius is 0.5 A.U. Compare each with the central density of the Sun. 9. A 15-solar-mass blue supergiant with a surface temperature of 20,000 K becomes a red supergiant with the same total luminosity and a temperature of 4000 K. By what factor does its radius change?