### ASTR 220 - Collisions in Space Drake Equation Discussion Results

In an attempt to estimate the number of civilizations in the galaxy which might be capable of interstellar communication (e.g., with radio), astronomers often use Drake's equation. The Drake equation is a list of probabilities which result in the estimate of the number of stars with planets harboring such civilizations given the number of stars in the galaxy:
N = R**fp*ne*fl*fi* fc*L
Here
N = the number of communication capable civilizations
R* = the formation rate (number per year) of stars suitable for supporting life
fp = the fraction of those stars with planets
ne = the number of planets per star suitable for life
fl = the fraction of those planets which develop life
fi = the fraction of planets with life which develop intelligent life
fc = the fraction of intelligent species which develop technology (like radio telescopes) capable of interstellar communication (or at least of broadcasting "we exist!")
L = the average lifetime (in years) of such a technologically advanced civilization

Below is a table of the responses of the various discussion groups on Nov. 11, 1999:

 Group R* fp ne fl fi fc L N Klingons 10 10-4 3 1/5 1/10 1/500 250 3x10-5 Romulans 2 1/4 1 1/2 10-6 1/4 1000 6x10-5 Correlians 3 1/4 1/5 1/2 3/4 1/500 500,000 56 "4" 8 1/8 3 2/3 1/3 1/9 15,000 1111 Kzin 4 1/2 1 4/5 3/10 10-5 50,000 0.24 Cardassians 7 10-2 2 1/2 10-5 10-6 350 2x10-10 Q 2 1 10-2 1 1/2 10-3 104 0.1

Obviously, our estimates of the number of intelligent species currently residing in our galaxy with technological capacity comparable to or greater than our own varies wildly. That is simply because even our best guesses for each of the pieces in Drake's equation are still just guesses. A number larger than one indicates the number of civilizations currently estimated to exist in the galaxy among its hundreds of billions of stars. The most optimistic number we came up with today is 1000, which is still only 1 per hundred million stars - the proverbial needle in a haystack. The pessimistic numbers (those less than one) suggest that on average, there is no such civilization present in the galaxy. We qualify as one, so this implies that our civilization is a rare and transient phenomenon.

I find it progressively more difficult to estimate each term in Drake's equation. The fraction of intelligent species which develop technology and the lifetime of their civilizations I find particularly difficult. Even if a species is "intelligent," it is far from obvious to me that it is likely to develop the sort of technology necessary to send a signal across interstellar space. And the lifetime - well, I suspect that has an odd distribution. I suspect most species are likely to destroy themselves within a few generations of being able to do so (or at least knock themselves back to the stone age). If one is able to survive for dozens of generations, then it might find a stable state capable of lasting a very long time indeed. The "average" lifetime of such a distribution is not tremendously meaningful.

### ET

If we are interested in the possibility that we have been visited by aliens, we can modify the Drake equation to estimate the probability that this might happen. To do this, we simply multiply the above equation by two new terms:
ft = the fraction of technological civilizations which develop the ability to travel between stars
pe = the probability that such an interstellar-mobile species has visited Earth
The modified Drake equation now becomes:
N = R**fp*ne*fl*fi* fc*L*ft*pe
These new terms are difficult to estimate. The most likely answer for ft is binary: either zero (it is physically impossible) or one (those who make it this far in the Drake equation eventually figure out a way). The probability of visiting the Earth is low - we are just one planet out of 10 in our solar system, and our star just one of hundreds of billions. There are 6 billion humans right now; even if we each had our own personal star ship, we would each have to personally scour many dozens of star systems to have visited the entire galaxy. Of course, a civilization which endures a long time has a better chance of eventually coming here, so these issues are hard to separate. Nevertheless, I would think it very optimistic to adopt
ft = 1
pe = 10-6
Even our most optimistic estimate makes the prospects of meeting ET quite dim, especially within our own brief lifetimes.