The Alien Equation

Throughout history, humanity’s view of the universe has changed drastically. For a long time, people believed that the Earth was all there was, with a dome high above it that had pinpricks they called stars. Later, they believed the solar system was the extent of the universe. Then that view expanded to the galaxy as we realized the pinpricks were actually other suns. Now, we believe there is a universe beyond even what we can observe, with other galaxies than our own populating space. When our understanding of the universe allowed us to understand that other stars exist, there began to be questions of extraterrestrial life around other stars and whether we on earth could somehow communicate with it. In the 1960’s, a man named Frank Drake wrote a book exploring the chances of life on other planets that was intelligent and capable of communicating with Earth in our galaxy. The book lead to an equation that expresses this chance numerically:

N = R * f(g) * f(p) * n(e) * f(l) * f(i) * f(c) * L

This equation has many terms that are not able to be calculated exactly, but they do lay extremely good groundwork for an estimate of intelligent, communicative life. This equation got experts talking about what they thought the odds for life in the universe could be and helped encourage the search for extraterrestrial life. This equation is also really easy to use to develop your own guess on the chances of extraterrestrial life. Breaking down this equation, there are three categories the values can be put into based on what factors they relate to. 


Astronomically Based Values

The first three values in the equation are values that are gained from observing the galaxy. They are astrophysical values that, with our current scientific capabilities, are reasonable to calculate somewhat accurately. The first value, R, is the rate of star formation in the galaxy. It can alternatively be the number of stars estimated to be in the galaxy. It is the starting point of the equation, as most of the other terms are fractions that whittle this value smaller and smaller as the criteria gets more specific. The current estimate of stars in the galaxy is between 100 and 400 billion stars. The second value, f(g), is an estimate of how many stars in the galaxy are suitable for hosting planets with life. Stars that can host planets with life must be long living and steady stars and they cannot have large fluctuations in temperatures and intensity. This value is currently estimated to be between 5 and 10 percent, meaning .05 to .1 for use in the equation The third value, f(p), is a measure of how many of those suitable stars actually have planetary systems. For example, stars that are in binary systems are thought to very rarely host planetary systems. This value is often estimated at about .5, as about 50% of star systems are binaries or multistar systems and the other 50% are single stars. 


Biologically Based Values

The next three values of the Drake equation are based on biological factors with life. The first one, n(e), is how many planets per star system are suitable for life. This mainly means how many planets are in the habitable zone of a star. The habitable zone is the distance from a star where planets can have water in all three phases, solid, liquid, and gas. The value to plug into the question can be found by taking your estimate of the number of planets in the habitable zone and dividing it by the estimated total number of planets in the system. For a system like our solar system, this would be .125. The next value, f(l), is the fraction of planets in the habitable zone that will actually have life form. This is where the values in the equation begin to vary greatly from person to person. Some people argue that if life can form it will and put this value at 1. Others argue that life is extremely rare to happen, putting the value closer to .001, or even smaller. Since we have so little understanding of how life started on Earth, it is hard to estimate its rarity in other places.  The final value, f(i), is the fraction of cases in which life develops intelligence. Once again, this is a controversial value to choose. Currently, we don’t know if life always evolves to intelligence. It can be argued that we did, so why wouldn’t other planets? However there have also been millions of species on our planet, and only one has evolved to our level of intelligence: humans. With those odds, intelligence seems rare. 


Sociological Based Values

The last two values of the Drake equation are sociological factors. The first one, f(c), is the number of intelligent races that have the technological capability and desire to try and communicate with other species. An example of this coming into play may be with an intelligent species that lives underwater. It would be difficult, if not impossible, for them to invent electronic devices like ours, and things like radio telescopes to communicate with might never be designed by them. Experts tend to estimate this as a fairly large value because it is thought by many that upon developing intelligence, a species will continually improve their technology. This is believed to always lead to communication technology in the process. The exception to this are species that face rare environmental factors that dissuade the invention of specific types of technologies, such as the underwater species example. The last value, L, is the lifetime of a civilization. This is as simple as it sounds. This value is necessary because we live so far from other planets that it would take a very long time to communicate with them. The very long time it takes to send a message means there needs to be long standing civilizations to continue any conversations, otherwise they would not be able to truly communicate with us. This value is often estimated to be between 1,000 and 100,000,000 years. 


Concluding Thoughts

Current estimates of the value calculated from the Drake equation range from as low as .00000000000091 to 15,600,000 planets that host intelligent, communicative life. The value can be much larger or lower than this as well, but there is no “correct” answer. You can find your own solution by plugging in values that you think are true. All you have to do is start with the number of stars in the galaxy and fill in what fractions you believe fit for the other values, and choose a lifetime to use. If your answer is greater than 1, your chosen parameters suggest that life exists elsewhere in our galaxy. However, if your answer is less than 1, your parameters suggest that we are likely alone in the galaxy. As long as you can give a reason for the values you chose, you have created your own theory for life in the universe.

Burchell, M. (2006). W(h)ither the Drake equation? International Journal of Astrobiology, 5(3), 243-250. doi:10.1017/S1473550406003107

Drake, F.; Sobel, D. (1992). Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence. Delta. pp. 55–62. ISBN 0-385-31122-2.

Alyssa is a first year physics major at Georgia Tech. She is planning to go into astrophysics or astronomy and loves giving tours of the night sky. She also enjoys horseback riding, painting, and playing board games.