Monday 1 July 2013

Drake Equation




This is the strangest but simplest equation I have seen, $$N=R^{*}*f_p*n_e*f_l*f_i*f_c*L$$

R* = the average number of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fl = the fraction of planets that could support life that actually develop life at some point
fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations)
fc = 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

the original values were like this:

R* = 1/year (1 stars formed per year, on the average over the life of the galaxy; this was regarded as conservative)
fp = 0.2-0.5 (one fifth to one half of all stars formed will have planets)
ne = 1-5 (stars with planets will have between 1 and 5 planets capable of developing life)
fℓ = 1 (100% of these planets will develop life)
fi = 1 (100% of which will develop intelligent life)
fc = 0.1-0.2 (10-20% of which will be able to communicate)
L = 1000-100,000,000 years (which will last somewhere between 1000 and 100,000,000 years)
So if we put in the values:
first medium:
$$N=1*0.3*4*1*1*0.15*10000$$
$$N=1800 civilizations$$

Then small:
$$N=1*0.2*1*1*1*0.1*1000$$
$$N=20civilizations$$

Then even smaller:
$$N=1*0.001*0.02*0.1*0.05*0.1*500$$
$$N=0.000005civilizations$$ we are alone

finally larger:
$$N=1*0.5*5*1*1*0.2*1000000$$
$$N=50000000civi...$$

Now for aproximation:
$$N=\frac{1800+20+0.000005+500000}{4}$$
$$N\approx125455$$civili....

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