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Now we can use equation \ref{Drake_simplified} to derive the minimum lifetime of the communicative phase in order for contact to occur  \begin{equation}  L_c \sim \left[\frac{V}{5\,f_l\, \left[\frac{V}{2\,f_l\,  f_i\, f_c}\right]^{1/4}. \end{equation}  On the other hand our discussion of the Drake equation led to the conclusion that, roughly speaking, $N \sim L$ (meaning the denominator in previous equation is $\sim$ 1) (but see the \href{http://en.wikipedia.org/wiki/Rare_Earth_hypothesis}{rare Earth hypothesis} for a different conclusion). Therefore we can further simplify and obtain