this is for holding javascript data
Matteo Cantiello edited Derive L.tex
about 10 years ago
Commit id: 262fa6161122550e2c2d7fedb761b9a6c76b8947
deletions | additions
diff --git a/Derive L.tex b/Derive L.tex
index 8f0eab6..f5ddcce 100644
--- a/Derive L.tex
+++ b/Derive L.tex
...
\section{A lesson from the sky?}
Let's define $n=\frac{N}{V}$ the number density of communicative civilizations in the Galaxy, where $N$ is the total number of such civilizations existing at any given time in the Milky Way and $V$ is the total galactic volume. Assuming an homogeneous distribution across the Galaxy, the average separation $r$ between two neighbour communicative civilization is $r\sim n^{-1/3}$. In order for two civilization to communicate, their separation needs necessarily to be smaller than their communicative phase lifetime $L$. This is assuming communication technology that is limited by the speed of light. We can then ask what would be the minimum value for $L$ such that communication can occur (we call this value $L_c$). That is we impose $r=L$. We then obtain $L\approx (N/V)^{-1/3}$. On the other hand our discussion of the Drake equation led to the conclusion that, roughly speaking, $N \sim L$
(But (but see
the\href{http://en.wikipedia.org/wiki/Rare_Earth_hypothesis}{rare the \href{http://en.wikipedia.org/wiki/Rare_Earth_hypothesis}{rare Earth hypothesis} for a different conclusion). And so we can further simplify and write
$L_c \sim \left(\frac{V}{L_c}\right)^{1/3}$ = V^{1/4}