# Drake equation

The Drake equation is used to estimate the number of technical, intelligent civilizations in our galaxy , the Milky Way . It was developed by Frank Drake , a US astrophysicist , and presented in November 1961 at a conference in Green Bank , USA; it is therefore also known as the Green Bank formula or SETI equation . The formula is often used in considerations related to finding extraterrestrial life . The equation is a product of which most of the factors are unknown. While Drake's original calculations were very optimistic about the possibility of extraterrestrial life, the latest solutions to a modification of the equation to include probability distributions from Sandberg, Drexler and Ord (2018) come to sobering results and place only a low probability of extraterrestrial life within and near outside the Milky Way.

## Preview

Life based on sulfur and silicon is not taken into account in the equation, since it cannot be precisely foreseen whether and under what conditions such life can arise. Drake's considerations relate to life that develops under certain conditions with regard to the proportions of nitrogen , carbon and other factors of uncertainty. The human species is considered proof that it can work. According to this theory, the system and the planet on which such life is to develop must meet certain astronomical and physical-chemical requirements:

The central star must have a suitable circumstellar habitable zone . This is the case for stars of the spectral classes F to M and the luminosity class V. So that on the one hand planets with suitable chemistry can form and on the other hand these planets are protected from all too frequent cosmic catastrophes such as supernova explosions, the system must be in the galactic habitable zone. In addition, the planet must form before the end of the cosmic habitable age (which will, however, last 10 to 20 billion years) so that there are still enough radioactive elements available to enable plate tectonics on the planet, which are beneficial for various reasons affects the formation of life and evolutionary processes.

In addition to these generally recognized conditions, there are some limitations that astrobiology considers likely due to the development of our earth, but which are not recognized as absolutely necessary. For example, it is assumed that the axis of rotation should not be tilted too much so that there are no large seasonal differences. A moon of the right size stabilizes the inclination of the axis of rotation and thus the climate , but a planet with a high or even chaotic axis inclination can also be habitable.

## equation

${\ displaystyle N}$ indicates the possible number of extraterrestrial civilizations in our galaxy that would be able and willing to communicate.

${\ displaystyle N}$ can be estimated as follows:

${\ displaystyle N = R _ {*} \ cdot f_ {p} \ cdot n_ {e} \ cdot f_ {l} \ cdot f_ {i} \ cdot f_ {c} \ cdot L \! \,}$

### The factors in detail

${\ displaystyle \ mathbf {R _ {*}}}$- Average star formation rate per year in our galaxy

The mean star formation rate can be estimated relatively well through empirical observations such as the Hubble Space Telescope and is estimated between 4 and 19.

When looking at it, however, it should be noted that a medium-sized star is required. Stars that are larger and more luminous than the sun ( spectral class type G) use up their energy in less than a billion years, so that there is not enough time for the development of life on planets orbiting such a star. It is therefore searched for stars that are comparable to our sun, since it is assumed that the development of life like on earth takes about a billion years. About 7% of all stars are of type G.

Stars that are smaller than the Sun have other significant disadvantages. About 70% of the stars are faint red dwarfs . Although these stars have a lifespan that can be a thousand times that of the sun, their luminosity as well as their mass and gravitational force are much lower, which means that the habitable zone is very close to the central star , where planets are exposed to strong tidal forces . The tidal friction can be so strong that there is a bound rotation between the star and the planet , with one half of the planet constantly facing the star and hot, while the other half would be in constant night. Additionally, red dwarfs are much more active than sun-like stars. Strong magnetic activity leads to more prominences and stronger cosmic rays, which is detrimental to the development of life. And finally, red dwarfs mainly emit in the infrared range of light, which means that the light that is visible to humans and most animals would be missing on planets of this star system and that plants would not be able to photosynthesize.

Furthermore, roughly every second formation is a double or multiple star system. These are two or more stars that orbit each other, more precisely rotate around their common center of gravity . Physical simulations have shown that planets in such systems have an extremely unstable orbit and sooner or later crash into one of the suns or are completely thrown out of the system ( three- and multi-body problem ). An exception are planets that are so far away from their suns that the gravitational pull of the two stars acts like that of a single star and the planet has a more stable orbit (two-body problem). The probability that a multiple star system will have planets for a long time has long been considered very low, but planetary companions around several double stars have now been found.

${\ displaystyle \ mathbf {f_ {p}}}$- Proportion of stars with a planetary system

How many stars in our galaxy have a planetary system? Observations show that roughly half of all stars can have planetary systems like our sun. Since 1995, more than 4100 extrasolar planets have been discovered with very sensitive detectors by measuring the radial speed of stars and observing planetary transits (as of January 2020). With increasing accuracy of the instruments, new methods and better resolving telescopes , even more precise measurements will be possible. In particular, the mission of the Kepler space telescope has multiplied the number of smaller planets discovered. Before that, it was mainly possible to find extrasolar planets that are very massive (several masses of Jupiter) and / or very close to their star. In both cases, the living conditions are likely to be very inhospitable.

${\ displaystyle \ mathbf {n_ {e}}}$- average number of planets (per star) within the ecosphere

The ecosphere is the area in the planetary system in which the physical conditions do not exclude the emergence of life from the outset. Depending on the size of the sun, a planet must not be too close and not too far away from its star. If it is too far away, it is too cold; if it is too close, it is too hot and the solar wind blows the atmosphere away. In our solar system, Venus , Mars and Earth are in the ecosphere. In 2007, two exoplanets were discovered for the first time that could be in the habitable zone: HD 209458 b , and the planet Gliese 581 c , which its discoverers described as being Earth-like . Whether the conditions there are really friendly to life is controversial among scientists.

Statistical analyzes of the data from the Kepler telescope indicate that in the Milky Way there are several billion earth-sized planets in the ecosphere around sun-like stars.

${\ displaystyle \ mathbf {f_ {l}}}$- Share in planets with life

On how many planets in the ecosphere does life arise? There are no scientifically verifiable numbers for this factor, because so far there is only the example of our solar system. In the future, it is expected that more sensitive telescopes will also be able to search for traces of life on exoplanets, for example oxygen in the atmosphere.

${\ displaystyle \ mathbf {f_ {i}}}$- Proportion of planets with intelligent life

If life evolves on a planet it need not evolve into intelligent life. There are no scientifically verifiable figures for this factor either. Only our solar system can be used as an example. This also raises the question of how intelligence is defined.

${\ displaystyle \ mathbf {f_ {c}}}$- Share of planets with an interest in interstellar communication

How many of the intelligent civilizations are interested in communicating with other individuals? Because we can only find you if you are interested in communication. It is believed that extraterrestrial intelligent beings also go in search of life.

${\ displaystyle \ mathbf {L}}$- Lifespan of a technical civilization in years

A technical civilization is a civilization that is able to receive a radio signal from space and send a signal into space. Life on planets is threatened by external and internal factors. Complete destruction can be triggered by events that have led to mass extinctions several times in the history of the earth. These include drastic climate changes such as B. by massive volcanic eruptions and impacts by comets or minor planets . The self-destruction of a technical civilization and the destruction of a technically intelligent civilization by another species such as z. B. a virus.

Since the lifespan of stars is limited, the lifespan of a civilization in the respective solar system is also limited. Civilizations outside of solar systems should have switched to sufficient solar-independent energy sources.

## Uncertainties

The uncertainties of the individual factors are decisive for the informative value of the Drake equation. For the last four factors in particular, there are at best very wide-ranging assumptions about the correct value. This makes the total number of intelligent civilizations estimated from the product of uncertain factors extremely inaccurate.

The Drake equation only relates to our galaxy , the Milky Way , which is a barred spiral galaxy . This barred spiral type correspond approximately to the in 03.02 according to present knowledge universe contained galaxies . Assuming that the universe observable today contains around 50–100 billion galaxies of a similar type, the value from the Drake equation for the entire universe would have to be multiplied by a corresponding factor. Although this increases the estimated total number of possible civilizations quite considerably, it still remains extremely inaccurate due to insufficient data from other galaxies. The estimated values ​​are also based on the extrapolation of merely assumed similarities of the initial data in all galaxies.

The Drake equation refers explicitly not only to the theoretically possible number of civilizations, but to the practical possibility of contacts. Since the next galaxy, the Andromeda Nebula , is 2.5 million light-years away, these and all others are not considered for practical contact.

## Criticism, discussion and extensions

The biologist Ernst Mayr has pointed out that of the approximately 50 billion species that the earth has produced, only one is that has developed intelligence.

Michael Schmidt-Salomon believes that, analogous to biological selection processes, a similar one would take place on the cosmic level, and that only those planets will receive higher forms of life in the long term that produce species that can protect biodiversity from external threats such as impact events from mass extinction . This ability is currently being pursued on Earth through planetary defense research programs such as NEOShield .

In 1983 David Brin proposed an extended Drake equation.

In 2010 the astronomer and technical director of the IAA Claudio Maccone published a more complex version of the equation, the statistical Drake equation.

The astrophysicist Martin Elvis adapted the Drake equation in 2013 in order to be able to make initial estimates about a possible number of asteroids that could be considered for space mining .

## Models

At the Green Bank conference mentioned above, three models were presented for the Drake equation.

1. Conservative model: a civilization in our Milky Way galaxy.
2. Optimistic model: 100 civilizations in our Milky Way, 5000 light-years mean distance between two transmitting civilizations.
3. Enthusiastic model: 4,000,000 civilizations in our Milky Way, 150 light years mean distance between two transmitting civilizations.

Although this information cannot be refuted in view of the enormous uncertainties described, various later sources assume significantly lower values ​​for the second and third model. On the one hand, the ecosphere becomes significantly narrower if one already includes the fundamental possibility of more complex life. On the other hand, the above models assume that there is a high probability that life will emerge at some point if the conditions are favorable over a long period of time.

The American astronomer and exobiologist Carl Sagan estimated the number of civilizations at ten.

## literature

• Amir D. Aczel: Probability 1. Why there must be intelligent life in space , rororo nonfiction. Rowohlt Taschenbuch Verlag, Reinbek 2001. ISBN 3-499-60931-2
• Frank Drake, Dava Sobel : Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence , Delacorte Pr., New York 1992, ISBN 0-385-30532-X
• Hansjürg Geiger: Astrobiology , vdf Hochschulverlag AG at the ETH Zurich (2009), ISBN 978-3-8252-3275-7
• Robert T. Rood, James S. Trefil: Are We Alone? The Possibility of Extraterrestrial Civilizations , Scribner, New York 1981, ISBN 0-684-16826-X
• Claudio Maccone: The Statistical Drake Equation. Acta Astronautica, Vol. 67, Issues 11-12, December 2010, pp. 1366-138, doi: 10.1016 / j.actaastro.2010.05.003
• Douglas A. Vakoch, et al .: The Drake equation - estimating the prevalence of extraterrestrial life through the ages. Cambridge University Press, Cambridge 2015, ISBN 978-1-107-07365-4 .

## Individual evidence

1. Sebastian von Hoerner : Are we alone? - SETI and life in space. Beck, Munich 2003, ISBN 3-406-49431-5 , pp. 151-152
2. ^ Michael AG Michaud: Contact with Alien Civilizations - Our Hopes and Fears about Encountering Extraterrestrials. Copernicus Books, New York 2007, ISBN 0-387-28598-9 , pp. 55-57.
3. Drake Equation daviddarling.info (accessed January 22, 2010)
4. ^ Mark J. Burchell: W (h) ither the Drake equation ?. International Journal of Astrobiology, vol. 5, Issue 3, pp. 243-250, September 2006, doi: 10.1017 / S1473550406003107
5. Anders Sandberg, Eric Drexler, Toby Ord (2018) Dissolving the Fermi Paradox, https://arxiv.org/abs/1806.02404
6. ^ Lammer et al .: What makes a planet habitable? . In: The Astronomy and Astrophysics Review . 17, 2009, pp. 181-249. bibcode : 2009A & ARv..17..181L .
7. ^ Williams & James F. Kasting : Habitable Planets with High Obliquities . In: Icarus . 129, 1997, pp. 254-267. bibcode : 1997Icar..129..254W .
8. ^ Frank White: The Seti Factor - How the Search for Extraterrestrial Intelligence Is Changing Our View of the Universe and Ourselves. Walker & Company, New York 1990, ISBN 978-0-8027-1105-2 . P. 77: N = "Number of Extraterrestrial Civilizations Able and Willing to Communicate".
9. The Drake Equation Revisited: Part I. (No longer available online.) Astrobiology Magazine, archived from the original on Aug. 7, 2011 ; Retrieved March 22, 2013 .
10. ^ AP Hatzes et al .: A Planetary Companion to Cephei${\ displaystyle \ gamma}$ , Astrophys. J., Volume 599 (2003), page 1383
11. Jerome Orosz et al .: Kepler-47: A Transiting Circumbinary Multiplanet System . In: Science . tape 337 , 2012, p. 1511–1514 , doi : 10.1126 / science.1228380 , arxiv : 1208.5489 .
12. Amina Khan: Milky Way may host billions of Earth-size planets. November 4, 2013, accessed November 10, 2013 .
13. Zsolt Hetesi: Energy use, entropy and extra-terrestrial civilizations. Journal of Physics, Vol. 218, Issue 1, pp. 012016, 03/2010, doi: 10.1088 / 1742-6596 / 218/1/012016
14. ^ Frank White: The Seti Factor - How the Search for Extraterrestrial Intelligence Is Changing Our View of the Universe and Ourselves. Walker & Company, New York 1990, ISBN 978-0-8027-1105-2 . P. 77: N = "Number of Extraterrestrial Civilizations Able and Willing to Communicate".
15. Michael Schmidt-Salomon : Hope human. A better world is possible. , Piper Verlag, Munich 2014, pp. 307–309.
16. ^ Brian MacConnell: Beyond contact - a guide to SETI and communicating with Alien civilizations. O'Reilly, Beijing 2001, ISBN 0-596-00037-5 , Brin's equation pp. 68ff. @google books  ( page no longer available , search in web archivesInfo: The link was automatically marked as broken. Please check the link according to the instructions and then remove this notice.
17. ^ GD Brin: The Great Silence - the Controversy Concerning Extraterrestrial Intelligent Life , bibcode : 1983QJRAS..24..283B
18. At Last, How Many Alien Civilizations Are There? astrobio.net
19. Claudio Maccone: Mathematical SETI - statistics, signal processing, space missions. Springer, Berlin 2012, ISBN 978-3-642-27436-7 , The statistical Drake equation, pp. 3-72
20. ^ Alien-hunting equation revamped for mining asteroids newscientist.com, accessed December 11, 2013
21. https://www.youtube.com/watch?v=MlikCebQSlY Carl Sagan - Cosmos - Drake Equation