Question

Search for Extraterrestrial Intelligence (SETI) up to this point the search for extra terrestrial intelligence has come up empty. The reasons why we have not observed other life is up for debate and the subject of the Fermi Paradox. A thought experiment centering on the existence of alien life is summarized by the: Drake Equation

? = ?? ∙ ?? ∙ ?? ∙ ?? ∙ ?? ∙ ?? ∙ ?

N – number of civilizations in our galaxy with which communication might be possible

Rs - average rate of star formation per year

fp - fraction of formed stars that have planets

ne - for stars with planets, average number of planets that can support life

fl - fraction of those planets that actually develop life

fi - fraction of planets bearing life on which intelligent, civilized life, has developed

fc - fraction of these civilizations that developed communications

L - length of time over which civilizations release detectable signals

The equation works its way through some of the necessary conditions for humans to contact alien life. Some values such as Rs are relatively understood for our galaxy, while others further down the list cannot be. For the bonus assignment, solve the Drake Equation by coming up with values for each term in the equation with a sentence or two explanation for your estimate. There are no hard and fast, right or wrong answers, just give some idea or thought behind the values you come up with.

What is your value for the number of civilizations in our galaxy we might communicate with?

Answer 1

for the drakes equation given
N = Rs* fp * ne * fl * fi * fc * L

where N is number of civilizations in our galaxy with which communication might be possible
Rs - average rate of star formation per year
fp - fraction of formed stars that have planets
ne - for stars with planets, average number of planets that can support life
fl - fraction of those planets that actually develop life
fi - fraction of planets bearing life on which intelligent, civilized life, has developed
fc - fraction of these civilizations that developed communications
L - length of time over which civilizations release detectable signals

now, from NASA estimates, current rate of star formation in our galaxy is about 0.68–1.45 M☉ of material per year.
To get the number of stars per year, this must account for the initial mass function (IMF) for stars, where the average new
star mass is about 0.5 M☉.[21] This gives a star formation rate of about 1.5–3 stars per year.
hence Rs = 2.25 stars per year

Recent analysis of microlensing surveys has found that fp may approach 1—that is,
stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.

Since all star-systems have planets, and for our own solar system we can see 1 planet supports life, and one other (mars) has conditions to support life. Hence on an average ne
can be taken around 2.5, considering how mars, earth and some satellites of these planets might be okay to support life

Since we have no sample size to approximate fl, from solar system we can assume that value of fl has to be lower than 1

percent of species which can develop into intelligent life will give us fi, but since on earth we can see that out of all the species only one has
developed fully intelligent, we can assume fi is very low, of the order of 0.1% or even less

out of all the intelligent species, not all will be able to communicate at a given time and shall take time to develop into an
intelligent civilisation that can broadcast communication signals, hence fc = 1% (approximately)

L will be length of time for which these civilisation release these signals, and from length of human civilisation this can be close to 10^6 years

hence using these values we get
N = 2.25*1*2.5*0.001*0.01*10^6 = 56.25 number of civilizations in our galaxy with which communication might be possible