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

Approximate linear dimension is 2 light years.

Step-by-step 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* 10^(12)` (LY)³

Since galaxy contains number of stars = 1078 billion stars ≈
`1.078* 10^(12)`

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

=
`(8.45* 10^(12) )/(1.078* 10^(12))`

= 7.839 Light Years

Now the linear dimension across the volume

=
`(\text{Average volume per star})^{(1)/(3)}`

=
`(7.839)^{(1)/(3)}`

= 1.99 LY

≈ 2 Light Years

Therefore, approximate linear dimension is 2 light years.