Drake equation

From Wikipedia, the free encyclopedia
Jump to: navigation, search



The equation was written in 1961 by Frank Drake not for purposes of quantifying the number of civilizations,[1] but as a way to stimulate scientific dialogue at a meeting on the search for extraterrestrial intelligence (SETI). The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life.[1] Criticism of the Drake equation follows from the fact that several of its terms are conjectural, the net result being that the error associated with any derived value is very large such that the equation cannot be used to draw firm conclusions. A consistent reply to these critiques is that the formalism was intended to stimulate dialogue, indeed, that this was Drake's original intent.



Two months later, Harvard University astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution."[4]

Seven months after Cocconi and Morrison published their article, Drake made the first systematic search for signals from extraterrestrial intelligent beings. Using the 25 meter dish of the National Radio Astronomy Observatory in Green Bank, West Virginia, Drake monitored two nearby Sun-like stars: Epsilon Eridani and Tau Ceti. In this project, which he called Project Ozma, he slowly scanned frequencies close to the 21 cm wavelength for six hours a day from April to July 1960.[3] The project was well designed, inexpensive, and simple by today's standards. It was also unsuccessful.



The ten attendees were conference organizer J. Peter Pearman, Frank Drake, Philip Morrison, businessman and radio amateur Dana Atchley, chemist Melvin Calvin, astronomer Su-Shu Huang, neuroscientist John C. Lilly, inventor Barney Oliver, astronomer Carl Sagan and radio-astronomer Otto Struve.[6] These participants dubbed themselves "The Order of the Dolphin" (because of Lilly's work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.[7][8]


The Drake equation is:





R* = the average rate of star formation in our galaxy
fp = the fraction of those stars that have planets
L = the length of time for which such civilizations release detectable signals into space[9][10]


The Allen Telescope Array for SETI

Drake equation is best understood not as an equation in the strictly mathematical sense.[11][9][12] The last four parameters, f_{\ell}, f_i, f_c, and  L , are not known and are very hard to estimate, with values ranging over many orders of magnitude (see criticism). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere,[1][11] and gives the question of life elsewhere a basis for scientific analysis. The Drake equation is a statement that stimulates intellectual curiosity about the universe around us, for helping us to understand that life as we know it is the end product of a natural, cosmic evolution, and for helping us realize how much we are a part of that universe.[10] What the equation and the search for life has done is focus science on some of the other questions about life in the universe, specifically abiogenesis, the development of multi-cellular life and the development of intelligence itself.[13]



As many observers have pointed out, the Drake equation is a very simple model that does not include potentially relevant parameters,[15] and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms.[16]




Reappearance factor



METI factor



Biogenic gases


The Seager equation looks like this:[19][a] {\displaystyle N = N_**F_Q*F_\text{HZ}*F_O*F_L*F_S} Where:

N = the number of planets with detectable signs of life
N* = the number of stars observed
FQ = the fraction of stars that are quiet
FO = the fraction of those planets that can be observed
FL = the fraction that have life
FS = the fraction on which life produces a detectable signature gas

Seager stresses, “We’re not throwing out the Drake Equation, which is really a different topic,” explaining, “Since Drake came up with the equation, we have discovered thousands of exoplanets. We as a community have had our views revolutionized as to what could possibly be out there. And now we have a real question on our hands, one that’s not related to intelligent life: Can we detect any signs of life in any way in the very near future?”[20]


Original estimates[edit]

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:[21][22]



Current estimates[edit]


Rate of star creation in our galaxy, R*[edit]


Fraction of those stars that have planets, fp[edit]


Average number of planets per star having planets that might support life, ne[edit]

Here it is understood that satellites might also serve as good candidates.[citation needed]
In November 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy.[26][27] 11 billion of these estimated planets may be orbiting sun-like stars.[28] Since there are about 100 billion stars in the galaxy, this implies fp*ne is roughly 0.4. The nearest planet in the habitable zone may be as little as 12 light-years away, according to the scientists.[26][27]
Even if planets are in the habitable zone, however, the number of planets with the right proportion of elements is difficult to estimate.[29] Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about 10% of star systems in the Milky Way galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable for a sufficient time.[30]
The discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called hot Jupiters may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets.
In addition, most stars in our galaxy are red dwarfs, which flare violently, mostly in X-rays, a property not conducive to life as we know it.[citation needed] Simulations also suggest that these bursts erode planetary atmosphere.[31]
The authors of the rare Earth hypothesis propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a hot Jupiter; and a planet with plate tectonics, a large moon that creates tidal pools, and moderate axial tilt to generate seasonal variation.[33]

Fraction of the above that actually go on to develop life, fl[edit]


Fraction of the above that develops intelligent life, fi[edit]

This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr, point out that of the billions of species that have existed on Earth, only one has become intelligent and from this, infer a tiny value for fi.[36] Those who favor higher values note the generally increasing complexity of life and conclude that the eventual appearance of intelligence might be imperative,[37][38] implying an fi approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable. (See Criticism).

Fraction of the above revealing their existence via signal release into space, fc[edit]

Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals.[according to whom?][citation needed]

Lifetime of such a civilization wherein it communicates its signals into space, L[edit]

Inserting these current estimates into the original equation, using a value of 0.1 wherever the text says someone has proposed an unspecified "low value," results in the range of N being from a low of 2 to a high of 280,000,000.[citation needed][original research?] As study of the concepts has gone on, the range has increased at both the minimum and maximum ends.[citation needed]

Range of results[edit]

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions. One point of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero.[43] Beyond this, however, the values one may attribute to each factor in this equation tell more about a person's beliefs than about scientific facts.[44][dubious ][better source needed]

Using lowest values in the above estimates,[citation needed] and assuming the rare Earth hypothesis implies ne*fl = 10−11,[citation needed] one can calculate N:

R* = 7/year,[23] fp = 0.4,[45][better source needed] ne*fl = 10−11, fi = 10−9,[36] fc = 0.1, and L = 304 years[40]

Use of these parameters gives:


i.e., suggesting that we are probably alone in this galaxy, and likely the observable universe.

On the other hand, with larger values for each of the parameters above, values of N can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:

R* = 7/year,[23] fp = 1,[24] ne = 0.2,[46][47] fl = 0.13,[48] fi = 1,[37] fc = 0.2[Drake, above], and L = 109 years[41]

Use of these parameters gives:

N = 7 × 1 × 0.2 × 0.13 × 1 × 0.2 × 109 = 36.4 million.[citation needed][original research?]

This result's 26 order of magnitude higher estimate that the foregoing provides motivation for funding and executing SETI research.[citation needed]





Fermi paradox[edit]

Main article: Fermi paradox


A large number of explanations have been proposed to explain this lack of contact; a recent book elaborated on 50 different explanations.[55] In terms of the Drake Equation, the explanations can be divided into three classes:


In fiction and popular culture[edit]

  • The equation was cited by Gene Roddenberry as supporting the multiplicity of inhabited planets shown in Star Trek, the television show he created. However, Roddenberry did not have the equation with him, and he was forced to "invent" it for his original proposal.[58] The invented equation created by Roddenberry is:

See also[edit]


  1. ^ The rendering of the equation here is slightly modified for clarity of presentation from the rendering in the cited source.[19]


  1. ^ a b c "Chapter 3 — Philosophy: "Solving the Drake Equation". SETI League. December 2002. Retrieved 2013-04-10. 
  4. ^ newspaper, staff (8 November 1959). "Life On Other Planets?". Sydney Morning Herald. Retrieved 2015-10-02. 
  7. ^ "Drake Equation Plaque". Retrieved 2013-08-13. 
  10. ^ a b "What do we need to know about to discover life in space?". SETI Institute. Retrieved 2013-04-16. 
  11. ^ a b c Burchell, M.J. (2006). "W(h)ither the Drake equation?". International Journal of Astrobiology 5 (3): 243–250. Bibcode:2006IJAsB...5..243B. doi:10.1017/S1473550406003107. 
  19. ^ a b c The Drake Equation Revisited: Interview with Planet Hunter Sara Seager Devin Powell, Astrobiology Magazine 4 September 2013.
  20. ^ "A New Equation Reveals Our Exact Odds of Finding Alien Life". io9.com. 
  31. ^ "Red Dwarf Stars Could Leave Habitable Earth-Like Planets Vulnerable to Radiation". SciTech Daily. Retrieved 22 September 2015. 
  33. ^ Ward, Peter D.; Brownlee, Donald (2000). Rare Earth: Why Complex Life is Uncommon in the Universe. Copernicus Books (Springer Verlag). ISBN 0-387-98701-0. 
  36. ^ a b "Ernst Mayr on SETI". The Planetary Society. 
  41. ^ a b Grinspoon, D. (2004). Lonely Planets. 
  43. ^ [better source needed] Dean, T. (10 August 2009). "A review of the Drake Equation". Cosmos Magazine. Retrieved 2013-04-16. 
  59. ^ Crichton, Michael (2012). Sphere. Knopf Doubleday Publishing Group. p. &q=drake+equation 28. ISBN 978-0-307-81648-1. 
  61. ^ "Seyton Discography at Discogs". 

Further reading[edit]

  • Morton, Oliver (2002). "A Mirror in the Sky". In Graham Formelo. It Must Be Beautiful. Granta Books. ISBN 1-86207-555-7. 
  • Rood, Robert T.; James S. Trefil (1981). Are We Alone? The Possibility of Extraterrestrial Civilizations. New York: Scribner. ISBN 0684178427. 
  • Douglas A. Vakoch, et al.: The Drake equation - estimating the prevalence of extraterrestrial life through the ages. Cambridge University Press, Cambridge 2015, ISBN 978-1-10-707365-4.

External links[edit]