Suppose there were 100 other civilizations in our Galaxy. If they are spread randomly within the Galaxy's volu

Question

Suppose there were 100 other civilizations in our Galaxy. If they are spread randomly within the Galaxy's volume, about how far away would the nearest one be? State your assumptions to get partial credit, at least, for your answer. Hint: supppose that 1% of the stars in the Galaxy had a civilization, so that there would be about 1 billion civilizations in the whole Galaxy. How far would the nearest one be, on average? You would have to find out to what distance to look such that the volume searched would contain about 100 stars.

Answer 1

About 300 light years. The Milky Way galaxy is about 100,000 light years wide. Assume it is a disk 100,000 light years in diameter and 10,000 light years thick. Calculate the volume, divide by 100 and take the cube root. I get 315 when I do that. If there a billion civilizations, then divide by a billion instead of 100 before taking the cube root. In that case, the nearest one should be closer than the nearest star. That is probably because the density of stars near the center of the galaxy is way higher than it is near Earth. I assumed stars were evenly distributed throughout the galaxy, which is not true but it makes the calculation easy. So in the real galaxy, the nearest of the 100 would probably be more distant that 300 light years, with most of the 100 being near the center of the galaxy. But probably that location is not safe, due to too much radiation and too many stars too close to each other disrupting planetary orbits and so on.

Answer 2

Your question is highly inconsistent.

First, you "suppose" 100 other civilizations in our galaxy. Yet you turn around and suppose "1%" of the galaxy's stars have a civilization and then specify 1 billion. Which is it?

Second, random does not necessarily mean uniform or even. In fact, most truly random distributions have clusters or groups. A simple example of a non-uniform random distribution would be the so-called Normal or Bell curve.

So here's what I think you meant to ask:

If the estimated 100X10^9 stars in our galaxy were uniformly distributed over its volume and 1% of those stars had one or more planets with civlized life, what would be the expected distance from Earth to the next closest civilized life?

Clearly, from the information given, the probability of civilization is P(s = c) = .01 (1%). So all we need to do is take an area around Earth that contains sufficient stars where E(s=c) = NP(s=c) = 1; where E(s=c) is the expected number of stars (s) with a civilization (c) and N is the number of stars in the area around the Earth. (I am discounting the thickness (volume) of the galaxy as it is quite flat compared to its diameter.)

N = an; where a is the area around Earth and n is the stellar density n = M/A; where M = 100X10^9 stars (the assumption) and A = pi R^2 = area of the Milky Way and R is its radius ~ 15 kparsecs ~ 50 X 10^3 light years

OK, now, back to E(s=c) = 1 = NP(s=c) = (Ma/A).01; so we have Ma/A = 100 = M(r^2/R^2) and r^2/R^2 = 100/M or r = 10R sqrt(1/M). Note that a/A = (pi r^2)/(pi R^2) = r^2/R^2; where a is the sample area around the Earth.

r is the radius of the area around Earth in which you can expect to find one other civilization, given P(s=c) = .01, R = 50X10^3 light years, and M = 100X 10^9 stars in the Milky Way. You can do the math to find r = 10R sqrt(1/M).

PS: Without checking the math, I got r ~ 15.8 light years

Answer 3

It depends on the technology you use to travel from point A to B. Distance is relative, and sometimes its faster to go to farther destinations.

You would have to factor the 'matter disturbances' across the membranes or hemispheres of the galaxy such that, these 'mountains' or clouds are accounted for. These are usually 'densely populated' areas that would make it harder for you to reach the target civilization. If you are to talk about purely rocket distance, then it would be (roughly) 1.5 kiloparsecs away and the time factor correspondent and associated with such a distance.

Answer 4

I think the nearest civilization in our galaxy is probably on the other side. The chances of there being two civilizations within a few thousand light years of each other when they were both at their peak is extremely remote.

Answer 5

Our galaxy is about 100,000 light years in diameter...multiplied by the value of Pi, that puts it at approx. 330,000 "square-light years" in area. If there were 100 civilisations evenly spread, then the nearest one would be about 3300 light years away.
1 billion is TOO HIGH...that would average out to less than half a light year away..and the nearest star is just over 4 light years away.