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 = [tex]\frac{D}{2} = \frac{1,00,000}{2} = 50,000\ ly[/tex]
Now,
A = [tex]\pi R^{2} = 50,000^{2}\pi = 7.8539\times 10^{9}\ ly^{2}[/tex]
The area to each civilization, A' is:
A' = [tex]\frac{A}{10000} = \frac{7.8539\times 10^{9}}{10000} = 7.8539\times 10^{5}\ ly^{2}[/tex]
The radius of each area of civilization, r:
[tex]A' = \pi r^{2}[/tex]
[tex]r = \sqrt{\frac{A'}{\pi}}[/tex]
[tex]r = \sqrt{\frac{7.8539\times 10^{5}}{\pi}} = 499.968\ ly[/tex]
Thus the average separation distance between civilizations is given as:
2r = [tex]2\times 499.968 = 999.936\ ly[/tex]
