Question

Suppose there are 100,000 signaling societies in our galaxy. What is the average distance between civilizations, assuming that civilizations are spread evenly throughout the galactic disk?"

Answer 1

The average distance is 999.936 light years.

Solution:

As per the question:

Ours is the Milky Way Galaxy with the diameter:

D = 1,00,000 ly

Radius, R =
`(D)/(2) = (1,00,000)/(2) = 50,000\ ly`

Now,

A =
`\pi R^(2) = 50,000^(2)\pi = 7.8539* 10^(9)\ ly^(2)`

The area to each civilization, A' is:

A' =
`(A)/(10000) = (7.8539* 10^(9))/(10000) = 7.8539* 10^(5)\ ly^(2)`

The radius of each area of civilization, r:

`A' = \pi r^(2)`

`r = \sqrt{(A')/(\pi)}`

`r = \sqrt{(7.8539* 10^(5))/(\pi)} = 499.968\ ly`

Thus the average separation distance between civilizations is given as:

2r =
`2* 499.968 = 999.936\ ly`