Find the approximate mass of the dark and luminous matter in the Milky Way galaxy. Assume the luminous matter is due to approximately 101110^{11} stars of average mass 1.5 times that of our Sun, and take the dark matter to be 10 times as massive as the luminous matter.
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Final Answer

ml=3.0×1041 kgm_l = 3.0\times 10^{41}\textrm{ kg}
md=3.0×1042 kgm_d = 3.0\times 10^{42}\textrm{ kg}

Solution video

OpenStax College Physics for AP® Courses, Chapter 34, Problem 2 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We are going to estimate the mass of the luminous matter in the Milky Way galaxy we are told there are about 10 to the 11 stars and 1.5 solar masses per star and we look at the appendix in the textbook to find how many kilograms are in a solar mass, which is the mass of the Sun. So there's 1.99 times 10 to the 30 kilograms per solar mass. So this gives us units of kilograms and there are 3.0 times 10 to the 41 kilograms of luminous matter. The amount of dark matter is estimated to be 10 times the amount of mass that is luminous so we go 10 times the answer for the luminous mass and that's 3.0 times 10 to the 42 kilograms.