   Chapter 34, Problem 27PE

Chapter
Section
Textbook Problem

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 1011 stars of average mass 1.5 times the Sun’s mass.

To determine

The number of MACHOs in the dark matter.

Explanation

Formula used:

Formula to calculate the number of MACHOs in the dark matter,

N=mmMACHOs ...... (I)

Where,

• m is the total mass of the dark matter.
• N is total number of MACHOs in the dark matter.
• mMACHOs is the average mass of MACHOs.

Calculation:

According to the question, the average mass of a MACHO is 11000 of the mass of Sun.

mMACHOs=11000×ms

......... (II)

Where,

ms is mass of Sun.

Since, the dark matter has a mass 10 times of the mass of the luminous Milky Way galaxy. The luminous Milky Way galaxy has 1011 stars with average mass of 1.5 times the mass of Sun.

m=10×1011×1.5×ms

......... (III)

Substitute 10×1011×1

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