April 5, 2020

The Drake Equation: A Primer.

Nothing fires the ol’ mental juices like the Search for Extraterrestrial Intelligence. Only recently has the very idea of alien life moved from the realm of science fiction to a possible science reality in our lifetimes.

But the question has always lingered; where are they? Is life in our galaxy common, or are we effectively alone? Either outcome would be extremely profound; a visit tomorrow or a distant message that couldn’t have been generated by a natural source (a transmission of prime numbers was used in the movie Contact) would tell us much about ourselves. Does all life need to be carbon based? Is water a prime requisite? If we never hear from anyone, can we ever be sure that life is absent?

In 1960, astronomer Frank Drake proposed an equation to address the issue, mostly to organize the first real systematic searches of the skies. Also known as the Green Bank Equation, it gives us something of a starting point to ask a very enigmatic question. Much has been said about its validity, both good and bad. Many, such as me, were first introduced to the Equation by the late great Carl Sagan during the documentary Cosmos.

The Drake equation itself is pretty straight forward, and heck, fun to play with! I invite you to manipulate its factors with friends over cocktails, as all good astro-nerds are prone to do. Only basic algebra is required, so math phobics fear not! It breaks down as follows;

N = R* × fp × ne × fl × fi × fc ×L

Now, that may seem like a lot, but keep in mind that these are basically just simple arithmetic factors. N is our goal, the number of intelligent civilizations in the galaxy that currently we might hope to converse with. Note that as we go through the factors left to right, we go from known to progressively unknown quantities.

R* is the yearly rate of star formation.

fp is the number of stars that have planets.

ne is the fraction of planets that are potentially habitable.

fl is the number of worlds that life does arise.

fi is the fraction of worlds with life that evolve intelligence.

fc is the fraction of intelligent life that bothers with the fuss of what we call civilization, i.e. space travel, radio telescopes, Ipods, and the like.

And finally, L is the real sticker. This is the average lifespan of any given intelligent, technical civilization. Do civilizations arise, only to quickly snuff themselves out? Even if we successfully avoid nuclear war, overpopulation, and global warming, our chances of survival may be only 50/50 in the next century or so. An extinction level event, such as a large cometary impact, could just as easily do us in. And we wouldn’t necessarily need to be wiped out to loose our precarious technical standing. Who knows how to build a radio telescope from scratch? Still, knowing something can be done is half of the battle; I suspect if we did meet aliens zipping around in warp drives, it would be enough to put us on the right track to imitate them in a generation or so.

Let’s look at some of these factors and see what science says about them….

The rate of star formation in our galaxy per Earth year has been pretty well pinned down at one newly formed star per year. Of course, it isn’t possible for astronomers to count every star in our own galaxy from our Earthly vantage point; instead, estimates are based on stellar population samples. As for the number of stars with planets, since the discovery of the first extra-solar planets in 1988, the numbers have swollen at a fast and furious pace. As I write this, the number of extra-solar planets may well have changed!  I would place a pretty safe bet that this factor is pretty close to 1, or at least 0.9.

The conjecture gets wilder from there; how many of those worlds are potentially habitable? When we look at our own solar system, we only know of one for sure; Earth. Other planets or moons, such as Mars or Europa, could have once been, or could suitable in the future for some forms of extreme-o’-philes that we know. Place this factor at maybe 2.

On how many of those planets does life actually evolve? Again, we only have an example of one to go by… if even simple microbial life was found elsewhere in the solar system, this factor would double. Also, it is interesting to note that as soon as conditions stabilized on the young Earth, life took hold. That would suggest that simple organisms are relatively easy to get started. Lets go with a factor of 0.5.

Now things get even trickier… how many of those worlds with life might we find intelligence? It’s also of note that for a major portion of the span of life on Earth, life was unicellar. The jump from microbe to mammal seems to be a tough one. However, once made, you seem to have Triceratops, house cats, Dolphins and Man all in short order. A very rough guess might be a coefficient of 0.1.

How many of those intelligent species bother with technology? On Earth, Dolphins, Chimpanzees, and even Border Collies might be deemed intelligent; so far, only man bothers to build radio telescopes. What makes our particular brand of intelligence unique isn’t entirely clear, even to us. A guess-timation (a technical term!) By a biased ape such as myself might be 0.3.

How long do such civilizations last? Our own has had interstellar communications technology for only a little over half a century. We are currently in a technological adolescence; there is no reason to suppose that our intelligence is necessarily an asset. Perhaps civilizations constantly arise some where in the cosmos everyday, only to promptly wipe themselves out by means of nuclear warfare, global warming, or some other threat we have yet to face. Perhaps the tendency of highly evolved civilizations is to become more inward looking, and they simply aren’t that interested in the stars. Maybe they are busy playing with the Internet and their alien Ipods, or have holo-decks ala Star Trek, and don’t care about reality that much… maybe such apathetic aliens are more fascinated by a twelve eyed, eight tentacled, multi-sexual Paris Hilton… anyway, we’ll assume that once in a while, an enlightened civilization learns to live with themselves and takes an interest in galactic politics on a geological timescale. This would even out those short sighted, flash in the pan civilizations that snuff themselves out within a century of achieving the means of doing so. Let’s put this figure at a conservative 1,000 Earth years.

Ok, now for the fun part. Let’s input those numbers and see what kind of Galactic Federation (or Empire, for those Asimov/Star Wars fans) is spit out. Incidentally, a nifty site allows anyone to play Galactic Civilizations Creator is available. Our equation is set up something like this;

And the semi-ultimate answer is; (drum roll…) 27! If you take the estimate of 300 billion stars in our galaxy, maybe 1 out of 11 billion has an intelligent civilization we would be interested in talking to. Of course, the estimated number of stars within 250 light years of Earth is about 260,000. It’s unlikely anybody is nearby.  It would be a boring conversation! Of course, these numbers are only semi-educated guesses… but the final life span number can be fun to fudge. If the number is something like 100 years, (…and we have yet to reach that mark!) The number drops to just below 3 (2.7, but we will not deal in 0.7 of a civilization!) and we are pretty effectively alone. Of course, L is frequently given to be 10,000, which makes the numbers jump to around 270. Still pretty sparse, but the beginnings of an extended galactic federation none the less.

Of course, several criticisms have arisen of the Drake Equation over the years. Pick a variable, and there are several legitimate beefs to be had…

  • - Star formation: most stars in our galaxy are highly active red dwarfs; these routinely produce flares that are deadly to our forms of life.
  • - Another point can be made with regards to star formation; it’s not by all means constant throughout the history of the galaxy. Also, many stars are locked up in metal poor, ancient globular clusters .
  • - Could our own galaxy harbor “habitable zones?” How common are these choice pieces of real estate?
  • - Numbers of planets: what about moons? In our own solar system, we have a pretty good hunch (yes scientists have hunches!) that Jupiter’s Moon Europa has an underground sea. Also, frigid Titan may be down right balmy and conducive to life billions of years from now, when the sun becomes a red giant. Sure, it’s a short phase, but who knows, once life takes hold?
  • - Are we biased towards life on Earth in any way? All of our previous experience warns us against our own hubris. Does life need water, or would liquid ammonia do? Does it need carbon, or would complex silicon molecules suffice for DNA? I can easily imagine that corrosive oxygen that we use in our metabolism might be poisonous to an alien life form.
  • - Are radio telescopes the only method of communication? Perhaps, as we become more efficient in modes of communication, the radio din we emit into space will cease. One could even hypothesize that this racket is the signature of an immature, inefficient civilization. In recent years, ideas of using pulsed lasers to communicate have also been introduced. Just think, little more than a century ago, Percival Lowell had hypothesized that we use giant mirrors to contact Martians… maybe we still have farther to go.
  • - Where are they? Is there a galactic Prime Directive in place, warning against interference, ala Star Trek? This idea is also known as the Zoo Hypothesis or the Fermi Paradox ; either they simply aren’t there, we can’t recognize them, they fear/avoid us, or we simply aren’t interesting to them (yet!) Maybe everybody is listening, and nobody is transmitting! Perhaps we have an “application pending…” in the Galactic Federation and are simply unaware yet!

Finally, do you want to join in? Yes, it is possible to search for E.T.s from your desk/laptop. SETI at Home (http://setiathome.berkeley.edu/) is the longest running “distributed programming” application out there; it runs as a screensaver while your computer is idle. Hey, it beats wasting electrons on flying toasters!


  1. [...] breaks down the Drake Equation, arriving at very different conclusions than we did recently here at Astroguyz. The author seems to be somewhat more optimistic about variables such as the number of worlds in [...]

  2. [...] in just the right epoch. Of course, the Drake Equation has been given treatment, as it has here at Astroguyz… the sentiment echoes a recent controversial book, Rare Earth, which posits that our [...]

  3. [...] This post was mentioned on Twitter by David Dickinson, Frank. Frank said: RT @Astroguyz Astroguyz Retro:The Drake Equation-A Primer. http://bit.ly/icuRfo A back of the envelope look at the famous equation. #… [...]

  4. [...] to believe that in our lifetimes, one of the key factors of the Drake Equation (fp: “What fraction of those stars have planets?”) Now has some hard observational data to back [...]

  5. [...] the emergence of life on Earth, and thoughts on the existence of extraterrestrial intelligence. The Drake equation famously laid out a road map to get the discussion started on just how many civilizations might be [...]

  6. [...] Main Sequence lives, only to swell into bloated Red Giants and perhaps engulfing the occasional civilization orbiting them. It’s sobering to think that billions of years from now, the only evidence to say [...]

  7. [...] this simple question has become a central tenet of the Search for Extraterrestrial Intelligence (SETI) over the past few [...]

  8. [...] for the purposes of this exercise, we’ll use the answer to Drake’s equation we spitbllaed some years ago (feel free to insert your own, you may be just as right) as 270 for the number of alien [...]

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