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30.4 The search for extraterrestrial intelligence  (Page 6/27)

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Watch the TED talk Jill Tarter gave on the fascination of the search for intelligence.

The drake equation

At the first scientific meeting devoted to SETI, Frank Drake wrote an equation on the blackboard that took the difficult question of estimating the number of civilizations in the Galaxy and broke it down into a series of smaller, more manageable questions. Ever since then, both astronomers and students have used this Drake equation    as a means of approaching the most challenging question: How likely is it that we are alone? Since this is at present an unanswerable question, astronomer Jill Tarter has called the Drake equation a “way of organizing our ignorance.” (See [link] .)

Drake equation.

Photograph of a plaque commemorating the origins of the Drake equation.
A plaque at the National Radio Astronomy Observatory commemorates the conference where the equation was first discussed. (credit: NRAO/NSF/AUI)

The form of the Drake equation is very simple. To estimate the number of communicating civilizations that currently exist in the Galaxy (we will define these terms more carefully in a moment), we multiply the rate of formation of such civilizations (number per year) by their average lifetime (in years). In symbols,

N = R total × L

To make this formula easier to use (and more interesting), however, Drake separated the rate of formation R total into a series of probabilities:

R total = R star × f p × f e × f l × f i × f c

R star is the rate of formation of stars like the Sun in our Galaxy, which is about 10 stars per year. Each of the other terms is a fraction or probability (less than or equal to 1.0), and the product of all these probabilities is itself the total probability that each star will have an intelligent, technological, communicating civilization that we might want to talk to. We have:

  • f p = the fraction of these stars with planets
  • f e = the fraction of the planetary systems that include habitable planets
  • f l = the fraction of habitable planets that actually support life
  • f i = the fraction of inhabited planets that develop advanced intelligence
  • f c = the fraction of these intelligent civilizations that develop science and the technology to build radio telescopes and transmitters

Each of these factors can be discussed and perhaps evaluated, but we must guess at many of the values. In particular, we don’t know how to calculate the probability of something that happened once on Earth but has not been observed elsewhere—and these include the development of life, of intelligent life, and of technological life (the last three factors in the equation). One important advance in estimating the terms of the Drake equation comes from the recent discovery of exoplanets. When the Drake equation was first written, no one had any idea whether planets and planetary systems were common. Now we know they are—another example of the Copernican principle.

Solution

Even if we don’t know the answers, we can make some guesses and calculate the resulting number N . Let’s start with the optimism implicit in the Copernican principle and set the last three terms equal to 1.0. If R is 10 stars/year and if we measure the average lifetime of a technological civilization in years, the units of years cancel. If we also assume that f p is 0.1, and f e is 1.0, the equation becomes
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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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