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.

option number c is the right answer.

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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