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?

1 Answer
Oct 29, 2017

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.