Question

Assume that the disk of the Milky Way has a radius of 20 kpc (20 thousand parsecs). It contains 100 billion stars, each with a radius similar to the Sun's, 6.96 x 1010 cm. What fraction of the galaxy's disk is covered by stars?

Answer 1

Answer on Question #62484 - Physics - Astronomy | Astrophysics

Question:

Assume that the disk of the Milky Way has a radius of 20 kpc (20 thousand parsecs). It contains 100 billion stars, each with a radius similar to the Sun's, $6.96 \times 10^{10}$ cm. What fraction of the galaxy's disk is covered by stars?

Solution:

First, let's express the Milky Way disk's area as $S_{MW} = \pi R_{MW}^2$.

Now, we express the disk's area for one star — $S_{star} = \pi R_{star}^2$.

Let $N$ is the total quantity of stars. Then we can calculate the fraction $(F)$ of the galaxy's disk covered by stars like this:

$$F = \frac{NS_{star}}{S_{MW}} = \frac{N\pi R_{star}^2}{\pi R_{MW}^2} = N\left(\frac{R_{star}}{R_{MW}}\right)^2.$$ $$N = 100 \cdot 10^9 = 10^{11}$$ $$R_{star} = 6.96 \cdot 10^{10} \text{ cm} = 6.96 \cdot 10^8 \text{ m}$$ $$R_{MW} = 20 \text{ kpc} = 20000 \cdot 3,0857 \cdot 10^{16} \text{ m} = 6.1714 \cdot 10^{20} \text{ m}$$ $$F = 10^{11} \cdot \left(\frac{6.96 \cdot 10^8}{6.1714 \cdot 10^{20}}\right)^2 = 10^{11} \cdot (1.13 \cdot 10^{-12})^2 = 10^{11} \cdot 1.28 \cdot 10^{-24} = 1.28 \cdot 10^{-13}.$$

Answer:

$$1.28 \cdot 10^{-13}$$

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