The Drake equation (sometimes called the "Green Bank equation", the "Green Bank Formula" or–erroneously–the "Sagan equation") is an equation to calculate the potential number of extraterrestrial civilizations in our galaxy, the Milky Way. It is used in the fields of exobiology and the search for extraterrestrial intelligence (SETI).
This equation was devised by Frank Drake in 1961, in an attempt to estimate the number of extraterrestrial civilizations in the Milky Way with which we might come into contact.
History
Drake formulated his equation in 1961 in preparation for the Green Bank meeting. This meeting, held at Green Bank, West Virginia, established SETI as a scientific discipline. The meeting's participants became known as the "Order of the Dolphin," and included astronomers, physicists, biologists, social scientists, and industry leaders who came together to discuss the possibility of detecting intelligent life outside of the planet Earth.
The Green Bank meeting was the first gathering to use the formula that came to be known as the "Drake Equation." This explains why the equation is also known by its other names with the "Green Bank" designation. When Drake came up with this formula, he had no notion that it would become a staple of SETI theorists for decades to come. In fact, he thought of it as an organizational tool — a way to order the different issues to be discussed at the Green Bank conference, and bring them to bear on the central question of intelligent life in the universe. Carl Sagan, a great proponent of SETI, quoted the formula often and as a result the formula is often mislabeled as "The Sagan Equation." The Green Bank Meeting was commemorated by a plaque.
The Drake equation is closely related to the Fermi paradox in that Drake suggested that a large number of extraterrestrial civilizations would form, but that the lack of evidence of such civilizations (the Fermi paradox) suggests that technological civilizations tend to disappear rather quickly. This theory often stimulates an interest in identifying and publicizing ways in which humanity could destroy itself, and then counters with hopes of avoiding such destruction and eventually becoming a space-faring species. A similar argument is The Great Filter, which notes that since there are no observed extraterrestrial civilizations, despite the vast number of stars, then some step in the process must be acting as a filter to reduce the final value. According to this view, either it is very hard for intelligent life to arise, or the lifetime of such civilizations must be relatively short.
The grand question of the number of communicating civilizations in our galaxy could, in Drake's view, be reduced to seven smaller issues with his equation.
The equation
The Drake equation states that:
where:
and
Alternative expression
The number of stars in the galaxy now, N * , is related to the star formation rate R * by
where T g = the age of the galaxy. Assuming for simplicity that R * is constant, then
and the Drake equation can be rewritten into an alternate form phrased in terms of the more easily observable value, N * .
R factor
One can question why the number of civilizations should be proportional to the star formation rate, though this makes technical sense. (The product of all the terms except L tells how many new communicating civilizations are born each year. Then you multiply by the lifetime to get the expected number. For example, if an average of 0.01 new civilizations are born each year, and they each last 500 years on the average, then on the average 5 will exist at any time.) The original Drake Equation can be extended to a more realistic model, where the equation uses not the number of stars that are forming now, but those that were forming several billion years ago. The alternate formulation, in terms of the number of stars in the galaxy, is easier to explain and understand, but implicitly assumes the star formation rate is constant over the life of the galaxy.
Expansions
Additional factors that have been described for the Drake equation include:
With these factors in mind, the Drake equation states:
Reappearance number
The equation may furthermore be multiplied by how many times an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime after, for example, 10,000 years, life may still prevail on the planet for billions of years, availing for the next civilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if n r is the average number of times a new civilization re appears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be (1+ n r ), which is the actual reappearance factor added to the equation.
The factor depends on what generally is the cause of civilization extinction. If it is generally by temporary inhabitability, for example a nuclear winter, then n r may be relatively high. On the other hand, if it is generally by permanent inhabitability, such as stellar evolution, then n r may be almost zero.
In the case of total life extinction, a similar factor may be applicable for f ℓ , that is, how many times life may appear on a planet where it has appeared once.
METI factor
Alexander Zaitsev said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans, although being in a communicative phase, are not a communicative civilization; we do not practice such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (Messaging to Extra-Terrestrial Intelligence) to the classical Drake Equation. The factor is defined as "The fraction of communicative civilizations with clear and non-paranoid planetary consciousness", or alternatively expressed, the fraction of communicative civilizations that actually engage in deliberate interstellar transmission.
Historical estimates of the 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 (10 stars formed per year, on the average over the life of the galaxy)
- f p = 0.5 (half of all stars formed will have planets)
- n e = 2 (stars with planets will have 2 planets capable of supporting life)
- f l = 1 (100% of these planets will develop life)
- f i = 0.01 (1% of which will be intelligent life)
- f c = 0.01 (1% of which will be able to communicate)
- L = 10,000 years (which will last 10,000 years).
Drake's values give N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 10,000 = 10.
The value of R * is determined from considerable astronomical data, and is the least disputed term of the equation; f p is less certain, but is still much firmer than the values following. Confidence in n e 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 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 (such as Jupiter's moon Europa, or Saturn's moon Titan) adds further uncertainty to this figure.
Geological evidence from the Earth suggests that f l may be very high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that abiogenesis may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains anthropic bias, as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). Also countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. In addition, from a classical hypothesis testing standpoint, there are zero degrees of freedom, permitting no valid estimates to be made.
One piece of data that would have major impact on f l is the discovery of life on Mars or another planet or moon. If life were to be found on Mars that developed independently from life on Earth it would imply a higher value for f l . While this would improve the degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.
Similar arguments of bias can be
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