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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.

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.

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Answer 2

John Alexander

To find the order of magnitude of the number of stars in the Milky Way, we can use the volume of the Milky Way disk and the average volume occupied by each star. The volume of the Milky Way disk can be calculated by multiplying its diameter and thickness. Then, we divide this volume by the average volume occupied by each star (which can be approximated as the volume of a sphere with a radius equal to the distance from the Sun to the nearest star). This gives us an estimate of the number of stars in the Milky Way. Taking the order of magnitude of this estimate provides the order of magnitude of the number of stars in the Milky Way.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.