Drake Equation

         
               The Drake equation is closely related to the Fermi paradox in that Drake suggested that a large number of extraterrestrial civilizations would form, but that the lack of evidence of such civilizations (the Fermi paradox) suggests that technological civilizations tend to disappear rather quickly. This theory often stimulates an interest in identifying and publicizing ways in which humanity could destroy itself, and then counters with hopes of avoiding such destruction and eventually becoming a space-faring species. 

             A similar argument is The Great Filter, which notes that since there are no observed extraterrestrial civilizations, despite the vast number of stars, then some step in the process must be acting as a filter to reduce the final value. According to this view, either it is very hard for intelligent life to arise, or the lifetime of such civilizations must be relatively short.

            

The equation

The Drake equation states that:

 

where:

N = the number of civilizations in our galaxy with which communication might be possible; 

and

R^* = the average rate of star formation per year in our galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_ℓ = the fraction of the above that actually go on to develop life at some point

f_i = the fraction of the above that actually go on to develop intelligent life

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space.^[3]

 Alternative expression

The number of stars in the galaxy now, N^*, is related to the star formation rate R^* by

 

 

where T_g = the age of the galaxy. Assuming for simplicity that R^* is constant, then   and the Drake equation can be rewritten into an alternate form phrased in terms of the more easily observable value, N^*.

  "by environment clean generations"

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