10.21 Estimate the hydrogen-burning lifetimes of stars near the lower and upper ends of the main...

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10.21 Estimate the hydrogen-burning lifetimes of stars near the lower and upper ends of the main sequence. The lower end of the main sequence 2 occurs near 0.072 Mo, with log10 Te = 3.23 and log 10 (L/L) = -4.3. On the other hand, an 85 M star near the upper end of the main sequence has an effective temperature and luminosity of log10 Te = 4.705 and log 10 (L/L) = 6.006, respectively. Assume that the 0.072 Mo star is entirely convective so that, through convective mixing, all of its hydrogen, rather than just the inner 10%, becomes available for burning. In the case of the 85 Mo star, assume that 10% of the star's mass is available for hydrogen burning. Using the information given, calculate the radii of a 0.072 Mo star and a 85 M star. What is the ratio of their radii? Recall the expression that relates luminosity L, effective temperature Te and stellar radius R. 10.21 Estimate the hydrogen-burning lifetimes of stars near the lower and upper ends of the main sequence. The lower end of the main sequence 2 occurs near 0.072 Mo, with log10 Te = 3.23 and log 10 (L/L) = -4.3. On the other hand, an 85 M star near the upper end of the main sequence has an effective temperature and luminosity of log10 Te = 4.705 and log 10 (L/L) = 6.006, respectively. Assume that the 0.072 Mo star is entirely convective so that, through convective mixing, all of its hydrogen, rather than just the inner 10%, becomes available for burning. In the case of the 85 Mo star, assume that 10% of the star's mass is available for hydrogen burning. Using the information given, calculate the radii of a 0.072 Mo star and a 85 M star. What is the ratio of their radii? Recall the expression that relates luminosity L, effective temperature Te and stellar radius R.