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Question
If the dark matter in the Milky Way were composed entirely of MACHOs (evidence shows it is not), approximately how many would there have to be? Assume the average mass of a MACHO is 1/1000 that of the Sun, and that dark matter has a mass 10 times that of the luminous Milky Way galaxy with its $10^{11}$ stars of average mass 1.5 times the Sun’s mass.
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Final Answer
$1.5\times 10^{15}\textrm{ MACHO'S}$
Solution Video

OpenStax College Physics Solution, Chapter 34, Problem 27 (Problems & Exercises) (0:58)

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Video Transcript

This is College Physics Answers with Shaun Dychko. MACHO's are massive compressed halo objects that might account for some of the dark matter in the universe and we are gonna calculate how many of them there must be in the milky way if they were to account for all the dark matter in the milky way. So there's one MACHO for every one one-thousandth of a solar mass and we multiply that by there's ten dark matter masses for every one luminous mass and then multiply by 10 to the 11 stars in the milky way galaxy times an average mass of one and a half solar masses per star and things cancel here very nicely and we have I mean this is mass divided by mass. So we have 1.5 times 10 to the 15 MACHO's if they were to account for all of milky way's dark matter.

Solutions for problems in chapter 34