Question

A particular spiral galaxy can be approximated by a thin disk-like volume 62 Thousand Light Years in radius and 7 Hundred Light Years thick. If this Galaxy contains 1,078 Billion stars, estimate the average distance between the stars in this galaxy. Hint: calculate the average volume per star in cubic Light Years, and then estimate the approximate linear dimension across such a volume. (Indicate your answer to one decimal place.)

Answer 1

Answer:

Approximate linear dimension is 2 light years.

Explanation:

Radius of the spiral galaxy r = 62000 LY

Thickness of the galaxy h = 700 LY

Volume of the galaxy = πr²h

                                   = (3.14)(62000)²(700)

                                   = (3.14)(62)²(7)(10)⁸

                                   = 84568×10⁸

                                   = $8.45\times 10^{12}$ (LY)³

Since galaxy contains number of stars = 1078 billion stars ≈ $1.078\times 10^{12}$

Now volume covered by each star of the galaxy = $\frac{\text{Total volume of the galaxy}}{\text{Number of stars}}$

= $\frac{8.45\times 10^{12} }{1.078\times 10^{12}}$

= 7.839 Light Years

Now the linear dimension across the volume

= $(\text{Average volume per star})^{\frac{1}{3}}$

= $(7.839)^{\frac{1}{3}}$

= 1.99 LY

≈ 2 Light Years

Therefore, approximate linear dimension is 2 light years.