# Finding the number of stars in the milky way

1. May 2, 2015

### BOAS

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

$\frac{dN}{dm} ∝ m^{-2}$

$\frac{dN}{dm} = k m^{-2}$

$dN = k m^{-2} dm$

$\int^{100 \times 10^{9}}_{0} dN = \int^{100M}_{0.1M} k m^{-2} dm$

N = 100 billion, but i'm just leaving it as N for now.

$N = - \frac{K}{m}|^{100M}_{0.1M}$

$N = \frac{999K}{100M}$

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!

2. May 2, 2015

### phyzguy

Yes. You're on the right track. Just keep going.