A star remains on the main sequence, with essentially constant radius and surface temperature, as long as there is hydrogen in its core (the inner 10% of its mass) to burn. Consider two stars, representing the extremes of the main sequence. Star 1 is a main sequence M7 star, with a mass of 0.12 solar masses, a radius of 0.18 solar radii, and a surface temperature of 3000K. Star 2 is a main sequence O5 star, with a mass of 60 solar masses, a radius of 12 solar radii, and a surface temperature of 45,000K. Given each star's luminosity, you can determine the rate at which it is burning hydrogen into helium. Calculate the main sequence lifetime (ie, the time for the hydrogen in the core to be used up) for both stars, and express your answers in years. How do these results compare with the main sequence lifetime of the Sun? Do not use the approximate scaling between luminosity and mass of a star for this problem. Rather, calculate the luminosity for each star directly from the temperature and radius information given. You may assume that each star's luminosity is constant over its main sequence lifetime.