by E.H. Shepard from A. A. Milne's Winnie-the-Pooh books

The Drake Equation

Barbara Jo Mattson

The Drake equation gives a means of estimating the number of civilizations capable of communication that are in the Milky Way Galaxy.  Dr. Frank Drake devised the equation in 1961 while working on "Project Ozma", a search for artificial signals from two nearby stars.  People involved in the Search for ExtraTerrestrial Intelligence (SETI) use the equation today to show that their searches are not in vain.  

This page is not meant as an extensive introduction to the Drake Equation.  Rather, it was sparked by a recent question I received about extending the equation to the rest of the Universe.  I first cover, briefly, the components of the equation and what they mean.  At the end, I discuss the possibility of extending  the equation from the Milky Way to the rest of the Universe.  For further information and ways to extend the equation, see the Web Resources section at the bottom of this page.  

The Equation

The Drake Equation, as far as mathematical equations go, is quite simple.  It consists of a string of unknowns multiplied by each other - that's it, no integration, no differentiation, nothing more difficult that multiplication.  This means that the equation is accessible to pretty much everyone.  Here it is:
N = R* fp ne f l fi fc L

Where:

The Values

The equation looks simple enough, but several of the quantities are unknown, even with our "advanced" knowledge of astronomy.  In fact, the only quantity that we can currently say we know with any accuracy is the rate of star formation in the galaxy.  Current estimates of the star birth rate in the Milky Way range from about 3 to 10 per year.  However, the criteria that these stars be suitable means that they must be F, G or K stars, and these stars account for about 10% of the stars in the Galaxy.  That means that 0.3 to 1 suitable stars are born each year.

Astronomers are currently able to detect large planets around other stars, so the fraction of planets with stars may one day be an observable quantity.  However, currently only large planets can be detected, so the challenge is extrapolating the number of Earth like planets from the observed systems with large planets.  In the not-too-distant future, we may be able to detect smaller planets around nearby stars.  In fact, at least one project, Darwin , is underway to detect Earth sized planets around other stars, but it will take many years before this project gets off the ground (literally).  Once we've detected extra solar, Earth sized planets, we can make more accurate predictions about how many planets per system are capable of sustaining life.  For our own solar system, we would guess that three planets lie in about the right places and are of the right size to sustain life - Venus, Earth and Mars.

Detecting and predicting life on other planets is another order of magnitude (or more) more difficult than detecting Earth sized planets around distant stars.  We are currently having a hard enough time determining if life ever existed on Mars, our closest neighbor.  This means that all of the other variables in the Drake equation are subject to wild speculation.  Fortunately, any of the "f" values are constrained to be between 0 and 1 (since they are fractions), so there is a definite upper limit to those values.

Let's take a stab at some of these numbers.  Let N* = 1 (the most optimistic value given above), ne = 2 and L = 10,000 years (maybe a bit optimistic, since we've only been communicating for several decades).  Let's try a couple different things for the fractional numbers (fp, fl, fi, fc)

What does this mean?  Well, our Galaxy could be littered with intelligent, communicating civilizations, or we could be fairly unique.  Hopefully, future studies of extra solar planets will help to constrain the planetary numbers.  The "life" numbers, however, will likely be open to speculation for some time to come.

What About Other Galaxies?

Indeed, an estimate of the number of communicating civilizations in the Universe could be obtained by multiplying the Drake equation by another parameter, say Ng -- the number of galaxies in the Universe.  In reality, this parameter isn't quite that simple.  There are many kinds of galaxies in our Universe, and each different type would have a different star formation rate -- some galaxies produce many, many stars each year (galaxies currently undergoing "starbursts"), while some galaxies are nearly dormant.

The light travel time is a concern even with detecting signals from our own Galaxy.  Sure, there are many stars that are less than 10 light years away, so we could hope to communicate with them and get a response within our lifetime, but what if we detect a signal from a civilization on the other side of the Galaxy?  Our galaxy is 200,000 light years in diameter!  So, just because we detect a signal doesn't mean that we will be able to "communicate".  The light travel time becomes even more of an issue when considering signals from other galaxies.  Our nearest neighbor (not including our nearby companion and dwarf galaxies) is Andromeda, with is about 2,500,000 light years away.  If we were to detect a signal (which is unlikely, see the next paragraph) from there, the light would have been traveling for more than two and a half million years before reaching us!

The other consideration for looking for life outside our galaxy, is that the civilization in question would have to put out a whopping signal to make it reach across the space between galaxies.  As a signal races across space, it loses intensity as one divided by the distance squared (like gravity), so even a very strong signal will diminish over the vast distances between galaxies.
 
 

Web Resources

Created: 22 October 2001