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

Answer:

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 = $\frac{D}{2} = \frac{1,00,000}{2} = 50,000\ ly$

Now,

A = $\pi R^{2} = 50,000^{2}\pi = 7.8539\times 10^{9}\ ly^{2}$

The area to each civilization, A' is:

A' = $\frac{A}{10000} = \frac{7.8539\times 10^{9}}{10000} = 7.8539\times 10^{5}\ ly^{2}$

The radius of each area of civilization, r:

$A' = \pi r^{2}$

$r = \sqrt{\frac{A'}{\pi}}$

$r = \sqrt{\frac{7.8539\times 10^{5}}{\pi}} = 499.968\ ly$

Thus the average separation distance between civilizations is given as:

2r = $2\times 499.968 = 999.936\ ly$