Drake equation

From Academic Kids

The Drake equation (also known as the Green Bank equation) is a famous result in the speculative fields of xenobiology, astrosociobiology and the search for extraterrestrial intelligence.

This equation was devised by Dr. Frank Drake in the 1960s in an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. The main purpose of the equation is to allow scientists to quantify the uncertainty of the factors which determine the number of extraterrestrial civilizations.

The Drake equation is closely related to the Fermi paradox. It was cited by Gene Roddenberry as supporting the multiplicity of starfaring civilizations shown in Star Trek, the television show he created.

The Drake equation states that:

<math>N = R^{*} ~ \times ~ f_{p} ~ \times ~ n_{e} ~ \times ~ f_{l} ~ \times ~ f_{i} ~ \times ~ f_{c} ~ \times ~ L<math>


N is the number of extraterrestrial civilizations in our galaxy with which we might expect to be able to communicate


R* is the rate of star formation in our galaxy
fp is the fraction of those stars which have planets
ne is average number of planets which can potentially support life per star that has planets
fl is the fraction of the above which actually go on to develop life
fi is the fraction of the above which actually go on to develop intelligent life
fc is the fraction of the above which are willing and able to communicate
L is the expected lifetime of such a civilization

Historical estimates of the Drake equation parameters

Considerable disagreement on the values of most of these parameters exists, but the values used by Drake and his colleagues in 1961 were:

  • R* = 10/year,
  • fp = 0.5,
  • ne = 2,
  • fl = 1,
  • fi = fc = 0.01,
  • and L = 10 years.

The value of R* is the least disputed. fp is more uncertain, but is still much firmer than the values following. Confidence in ne was once higher, but the discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the creation of their stellar systems. In addition, most stars in our galaxy are red dwarfs, which have little of the ultraviolet radiation that has contributed to the evolution of life on Earth. Instead they flare violently, mostly in X-rays - a property not conducive to life as we know it (simulations also suggest that these bursts erode planetary atmospheres). The possibility of life on moons of gas giants (e.g. Jupiter's satellite Europa) adds further uncertainty to this figure.

What evidence is currently visible to humanity suggests that fl is very high; life on Earth appears to have begun almost immediately after conditions arrived in which it was possible, suggesting that abiogenesis is relatively "easy" once conditions are right. But this evidence is limited in scope, and so this term remains in considerable dispute. One piece of data which would have major impact on this term is the controversy over whether there is evidence of life on Mars. The conclusion that life on Mars developed independently from life on Earth would argue for a high value for this term.

fi, fc, and L are obviously little more than guesses. fi has been affected by discoveries that the solar system's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for hundreds of millions of years (evading radiation from novae). Also, Earth's very large, unusual moon appears to aid retention of hydrogen by breaking up the crust, inducing a magnetosphere by tidal heating and stirring, and stabilizing the planet's axis of rotation. In addition while it appears that life developed soon after the formation of Earth, the Cambrian explosion in which a large variety of multicellular life forms came into being occurred considerable amounts of time after the formation of Earth, which suggests the possibility that special conditions were necessary for this to occur. In addition some scenarios such as the Snowball Earth or research into the extinction events have raised the possibility that life on Earth is relatively fragile. Again, the controversy over life on Mars is relevant since a discovery that life did form on Mars but ceased to exist would affect estimates of these terms.

The well-known astronomer Carl Sagan speculated that all of the terms, except for the lifetime of a civilization, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation was a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of nuclear warfare.

(Note, however, that in the year 2001 a value of 50 for L can be used with exactly the same degree of confidence that Drake had in using 10 in the year 1961.)

The remarkable thing about the Drake equation is that by plugging in apparently fairly plausible values for each of the parameters above, the resultant expectant value of N is generally often >> 1. This has provided considerable motivation for the SETI movement. However, this conflicts with the currently observed value of N = 1 - one observed civilization in the entire universe. Other assumptions give values of N that are << 1, in accord with the observable evidence.

This conflict is often called the Fermi paradox, after Enrico Fermi who first publicised the subject, and suggests that our understanding of what is a "conservative" value for some of the parameters may be overly optimistic or that some other factor is involved to suppress the development of intelligent space-faring life.

Other assumptions give values of N that are << 1, but some observers believe this is still compatible with observations due to the anthropic principle: no matter how low the probability that any given galaxy will have intelligent life in it, the galaxy that we are in must have at least one intelligent species by definition. There could be hundreds of galaxies in our galactic cluster with no intelligent life whatsoever, but of course we would not be present in those galaxies to observe this fact.

Some computations of the Drake equation, given different assumptions:

R* = 10/year, fp = 0.5, ne = 2, fl = 1, fi = fc = 0.01, and L = 50 years
N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 50 = 0.05

Alternatively, making some more optimistic assumptions, and assuming that 10% of civilizations become willing and able to communicate, and then spread through their local star systems for 100,000 years (a very short period in geologic time):

R* = 20/year, fp = 0.1, ne = 0.5, fl = 1, fi = 0.5, fc = 0.1, and L = 100,000 years
N = 20 × 0.1 × 0.5 × 1 × 0.5 × 0.1 × 100000 = 5000

Current estimates of the Drake equation parameters

This section attempts to list best current estimates for the parameters of the Drake equation. Please list new estimates for these values here, giving the rationale behind the estimate and a citation to their source.

R*, the rate of star creation in our galaxy

Estimated by Drake as 10/year

fp, the fraction of those stars which have planets

Estimated by Drake as 0.5

ne, the average number of planets which can potentially support life per star that has planets

Estimated by Drake as 2

fl, the fraction of the above which actually go on to develop life

Estimated by Drake as 1
In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales and the Australian Centre for Astrobiology) estimated fl as > 0.33 using a statistical argument based on the length of time life took to evolve on Earth. Lineweaver has also determined that about 10% of star systems in the Galaxy are hospitable to life, by having heavy elements, being far from supernovas and being stable themselves for sufficient time. [1] (

fi, the fraction of the above which actually go on to develop intelligent life

Estimated by Drake as 0.01. Solar systems in galactic orbits with radiation exposure as low as Earth's solar system are more than 100,000 times rarer, however.

fc, the fraction of the above which are willing and able to communicate

Estimated by Drake as 0.01

L, the expected lifetime of such a civilization

Estimated by Drake as 10 years.
The value of L can be estimated from the lifetime of our current civilization from the advent of radio astronomy in 1938 (dated from Grote Reber's parabolic dish radio telescope) to the current date. In 2005, this gives an L of 67 years.
In an article in Scientific American, Michael Shermer estimated L as 420 years, based on compiling the durations of sixty historical civilizations. Using twenty-eight civilizations more recent than the Roman Empire he calculates a figure of 304 years for "modern" civilizations. Note, however, that the fall of most of these civilizations did not destroy their technology, and they were succeeded by later civilizations which carried on those technologies, so Shermer's estimates should be regarded as pessimistic.

The equation based on current lower estimates, therefore, is thus:

R* = 10/year, fp = 0.5, ne = 2, fl = 0.33, fi = 1×10-7, fc = 0.01, and L = 67 years
N = 10 × 0.5 × 2 × 0.33 × 1×10-7 × 0.01 × 67 = 2.211×10-7 = 0.0000002211

See also

External links


  • Charles H. Lineweaver and Tamara M. Davis, Does the Rapid Appearance of Life on Earth Suggest that Life is Common in the Universe?, arXiv:astro-ph/0205014 v1 2 May 2002
  • Michael Shermer, Why ET Hasn't Called, Scientific American, August 2002, page 21da:Drakes ligning

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