Question

The distance from the Sun to the nearest star is about `4 x 10^16` m. The Milky Way galaxy is roughly a disk of diameter `~10^21` m and thickness `~10^19` m. How do you find the order of magnitude of the number of stars in the Milky Way?

Answer 1

Approximating the Milky Way as a disk and using the density in the solar neighborhood, there are about 100 billion stars in the Milky Way.

Explanation:

Since we are making an order of magnitude estimate, we will make a series of simplifying assumptions to get an answer that is roughly right.

Let's model the Milky Way galaxy as a disk.

The volume of a disk is:
`V=pi*r^2*h`

Plugging in our numbers (and assuming that `pi approx 3`)
`V=pi*(10^{21} m)^2*(10^{19}m)`
`V= 3 times 10^61 m^3`
Is the approximate volume of the Milky Way.

Now, all we need to do is find how many stars per cubic meter (`rho`) are in the Milky Way and we can find the total number of stars.

Let's look at the neighborhood around the Sun. We know that in a sphere with a radius of `4 times 10^{16}`m there is exactly one star (the Sun), after that you hit other stars. We can use that to estimate a rough density for the Milky Way.

`rho = n / V`

Using the volume of a sphere
`V = 4/3 pi r^{3}`
`rho = 1 / { 4/3 pi (4 times 10^{16} m)^3}`
`rho = 1/256 10^{-48}` stars / `m^{3}`

Going back to the density equation:
`rho = n / V`
`n = rho V`

Plugging in the density of the solar neighborhood and the volume of the Milky Way:

`n = (1/256 10^{-48} m^{-3}) * (3 times 10^61 m^3)`
`n = 3/256 10^{13}`
`n = 1 times 10^11` stars (or 100 billion stars)

Is this reasonable? Other estimates say that there are are 100-400 billion stars in the Milky Way. This is exactly what we found.