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BOAS
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Homework Statement
The Milky Way contains 100 billion stars. The present masses of stars in the Milky Way are distributed according to dN/dm ∝ m−2 , and that stars have masses between 0.1 M and 100 M
M = Solar mass
Determine the number of stars with masses greater than or equal to the Sun.
Homework Equations
The Attempt at a Solution
[itex]\frac{dN}{dm} ∝ m^{-2}[/itex]
[itex]\frac{dN}{dm} = k m^{-2}[/itex]
[itex]dN = k m^{-2} dm[/itex]
[itex]\int^{100 \times 10^{9}}_{0} dN = \int^{100M}_{0.1M} k m^{-2} dm[/itex]
N = 100 billion, but I'm just leaving it as N for now.
[itex]N = - \frac{K}{m}|^{100M}_{0.1M}[/itex]
[itex]N = \frac{999K}{100M}[/itex]
I am a bit confused about the physical meaning of this and where to go next...
Do I use this to find a numerical answer for K and then integrate again between 1 solar mass and 100 solar masses to find the number of stars in the milky way with greater or equal mass?
Thanks for any help you can give!