Drake equation

The Drake equation is an equation to estimate the number of civilizations in our galaxy, the Milky Way, likely to have detectable radio emissions. It was conceived in 1961 by radio astronomer Frank Drake (b. 1930/02.09.2022), president of the SETI institute, while working at the National Radio Astronomy Observatory in Green Byunk, West Virginia [USA].

The Drake equation identifies specific factors believed to play an important role in the development of civilizations. Although there are currently not enough data to solve the equation, the scientific community has accepted its relevance as a first theoretical approach to the problem, and various scientists have used it as a tool to propose different hypotheses.

Our Sun is just a lone star in the abundance of 7×10²² stars in the observable universe. The Milky Way is just one of the 2,000,000,000,000 [two trillion] galaxies in the universe.

Drake Equation Details

The equation is as follows:

N=R↓ ↓ ⋅ ⋅ fp⋅ ⋅ ne⋅ ⋅ fl⋅ ⋅ fi⋅ ⋅ fc⋅ ⋅ L{displaystyle N=R^{*}~cdot ~f_{p}~cdot ~n_{e}~cdot ~f_{l}~cdot ~f_{i}~cdot ~f_{cdot}~cdot ~~

Symbol	Name
N{displaystyle N}	Number of civilizations that could communicate in our galaxy, the Milky Way
R↓ ↓ {displaystyle R^{*}	Annual "adequate" star formation rhythm in the galaxy
fp{displaystyle f_{p}}	Fraction of stars that have planets in their orbit
ne{displaystyle n_{e}	Number of these planets orbiting within the star's inhabitability zone (or orbits whose distance to the star is not as close as to being too hot, not as far away as to be too cold to be able to shelter life)
fl{displaystyle f_{l}}	Fraction of these planets within the zone of inhabitability in which life has developed
fi{displaystyle f_{i}	Fraction of those planets in which intelligent life has developed
fc{displaystyle f_{c}	Fraction of those planets where intelligent life has developed technology and attempts to communicate
L{displaystyle L}	Lapso, measured in years, during which intelligent and communicative civilization may exist

Initial estimate

In 1961, Drake and his team assigned the following values to each parameter:

N=10× × 0.5× × 2× × 1× × 0.01× × 0.01× × 10,000{displaystyle N=10times 0.5times 2times 1times 0.01times 0.01times 10,000}

Value	Description
R↓ ↓ =10{displaystyle R^{*}=10}	10 stars are formed every year
fp=0.5{displaystyle f_{p}=0.5}	Half of those stars have planets
ne=2{displaystyle n_{e}=2}	Each of those stars contains two habitable planets
fl=1{displaystyle f_{l}=1}	100% of these planets develop life
fi=0.01{displaystyle f_{i}=0.01}	Only 1 % would harbor intelligent life
fc=0.01{displaystyle f_{c}=0.01}	Only 1 % of such intelligent life can be communicated
L=10000{displaystyle L=10000}	Every civilization would last 10,000 years by transmitting signs

N=10{displaystyle N=10} possible detectable civilizations.

Other estimates

Since Drake published the above values given to each parameter many people have had considerable disagreement.

Approaches

R↓ ↓ {displaystyle {boldsymbol {R^{ast}}}}} = "adequate" star formation rhythm in the galaxy (stars per year).

According to the latest data from NASA and the European Space Agency, the rate of galactic production is seven stars per year. In the understanding that they are suitable stars type K and G, and if of the total stars 12.1 % are type K stars and 7.6 % are type G stars like the Sun, then only 19.7 % of those seven stars that are born each year are favorable, therefore only 1,3790 of those seven annual stars is truly apt.

fp{displaystyle {boldsymbol {f_{p}}}}} = Fraction of stars that have planets in their orbit.

Modern researchers from the European Southern Observatory dedicated to the search for planets argue that approximately one in three stars of type G could contain planets.

The percentage of planets in orange stars or red dwarfs is not counted in the estimate.

ne{displaystyle {boldsymbol {n_{e}}}} = Number of these planets inside the star echoosphere.

The number of planets orbiting within the echoosphere or living area with non-excentric orbit is estimated at around one in two hundred, based on the only discovery thereto, Gliese 581 d (around a red dwarf star).

Possible satellites of massive exoplanets are not counted in this estimate. It can also be expected that the current technological limitations to detect Earth-sized planets are significantly altering the data.

fl{displaystyle {boldsymbol {f_{l}}}}} = Fraction of these planets within the echoosphere in which life has developed.

In 2002, Charles H. Lineweaver and Tamara M. Davis (from the University of the South of New Wales and the Australian Center for Astrobiology) estimated that thirteen of every one hundred planets within the echoosphere that have lived around 1000 million years can develop life. The estimate does not have planets that have lived less than that time within a stable echoosphere.

fi{displaystyle {boldsymbol {f_{i}}}}} = Fraction of those planets where intelligent life has developed.

The amount of opportunities for intelligent life to develop on these stable planets can be extrapolated from the fraction of time represented by intelligent life on Earth, in relation to time elapsed since the emergence of unicelular life. That is, of the 3700 million years of life on the planet alone in the last 200 000 years has existed Homo sapiens.

fc{displaystyle {boldsymbol {f_{c}}}}} = Fraction of those planets where intelligent life has developed a technology and tries to communicate.

According to Drake's initial estimate, the possibility of developing technology capable of broadcasting radiofrequency signals is one in a hundred. This adopted value, however, is a simple conjecture. Another alternative has been suggested to estimate the number of opportunities for intelligent life to broadcast radio frequencies, which would consist of extrapolating the amount of time that humanity can last by transmitting radio signals in relation to the time that has elapsed since its inception (about 200,000 years ago). The length of time that industrial civilization can last by emitting radio signals could be based on the data provided in the L parameter.

L{displaystyle {boldsymbol {L}}} = The span of time that intelligent and communicative civilization can exist (years).

Life expectancy calculated in a magazine article Scientific American made by Michael Shermer was 420 years on average, based on the observation of 60 ancient human civilizations that consistently used pre-industrial technology. According to Olduvai's theory the time of life of the current industrial civilization will be 100 years (1930-2030) coinciding more or less in its appearance with the beginning of radio broadcasts (1938).

Answers

Equation:

• N=R⋅ ⋅ fp⋅ ⋅ ne⋅ ⋅ fl⋅ ⋅ fi⋅ ⋅ fc⋅ ⋅ L{displaystyle N=Rcdot f_{p}cdot n_{e}cdot f_{l}cdot f_{i}cdot f_{c}cdot L}

Estimate made by Drake:

• N=10× × 0.5× × 2× × 1× × 0.01× × 0.01× × 10,000{displaystyle N=10times 0.5times 2times 1times 0.01times 0.01times 10,000}
• N=10{displaystyle N=10} possible detectable civilizations.

Estimate made by counting Michael Shermer's civilization duration estimate with Drake's f_c parameter:

• N=1.379{displaystyle N=1.379} × × 0.333{displaystyle times 0.333} × × 0.005{displaystyle times 0.005} × × 0.13{displaystyle times 0.13} × × 0.000054{displaystyle times 0.000054} × × 0.01× × 420{displaystyle times 0.01times 420}
• N=0.0000000676963{displaystyle N=0.0000676963} possible detectable civilizations.

Estimate made by counting the duration estimate of a civilization made by Michael Shermer

• N=1.379{displaystyle N=1.379} × × 0.333{displaystyle times 0.333} × × 0.005{displaystyle times 0.005} × × 0.13{displaystyle times 0.13} ⋅ ⋅ 0.000054{displaystyle cdot 0.000054} × × 0.0021{displaystyle times 0.0021}× × 420{displaystyle times 420}
• N=0.0000000142162{displaystyle N=0.0000000142162} possible detectable civilizations.
• A civilization detected every 70 342 300 years in the Milky Way.
• A civilization detected annually within a group of 70 342 300 galaxies of the size of the Milky Way.
• Taking as a data recent estimates of the number of stars in the universe there must be 4975 civilizations emitting radio signals throughout the observable universe.

Estimate made by counting the duration estimate of the current industrial civilization by Olduvai's theory with Drake's f_c parameter:

• N=1.379{displaystyle N=1.379} × × 0.333{displaystyle times 0.333} × × 0.005{displaystyle times 0.005} × × 0.13{displaystyle times 0.13} × × 0.000054{displaystyle times 0.000054} × × 0.01× × 100{displaystyle times 0.01times 100}
• N=0.0000000161182{displaystyle N=0.00000161182} possible civilizations detected a year.

Estimate made by counting the duration estimate of the current industrial civilization by Olduvai's theory:

• N=1.379{displaystyle N=1.379} × × 0.333{displaystyle times 0.333} × × 0.005{displaystyle times 0.005} × × 0.13{displaystyle times 0.13} × × 0.000054{displaystyle times 0.000054}× × 0.0005{displaystyle times 0.0005}× × 100{displaystyle times 100}
• N=0.000000805908{displaystyle N=0,0000805908} possible civilizations detected a year.
• A civilization detected every 1 240 836 423 years in the Milky Way.
• A civilization detected annually within a group of 1 240 836 423 galaxies the size of the Milky Way.
• Taking as a data recent estimates of the number of stars in the universe there must be 282 civilizations emitting radio signals throughout the observable universe.
• Each of these civilizations has a separation of two billion light years from another.
• Approximately 110 of these civilizations live around a G-star.
• In the last 7 500 million years in the Milky Way there have only been two to three civilizations with technology very similar to ours around a G-type star.
• In the last 7500 million years in the observable universe there have been 819 billion civilizations with technology very similar to ours around a G-type star.

Speculations on the evolution of the equation

Due to a lack of evidence, as technology evolves, many parameters of the equation may vary dramatically. Various changes have been theorized:

In favor of more abundant life.

• It has not been well diluted if the echoes of planets in orange dwarf stars or red dwarfs could be stable improving the figure around R in case they were suitable.
• The estimate does not count possible satellites of mass exoplanets by improving the figure around f_p.
• Failure to use better technology to detect earth-sized rocky planets would improve the figure around n_e.
• Another lacking criterion is the important fact of what should be taken by definition of life, there could be life around replicators other than DNA or RNA in very different physical situations.

Against more abundant life

• The estimate does not have planets that have lived less than 1000 million years in a stable echoosphere as a life-generating criterion, and can change the figure around f_l.
• Drake's estimates from the outset do not have that fraction of planets with life-friendly chemical elements, such as water or coal source and so many other requirements, but may be implied around f_l.
• There are no parameters that can define aspects mentioned in the rare Earth hypothesis as:
  • The location of the sun on the galactic disk.
  • The Jovian effect (produced by Jupiter), which serves as a protective shield.
  • The lunar effect, which stabilizes the axis of terrestrial rotation.
  • The effect of the tectonic of terrestrial plates, which serve as thermostat.
  • The effect of the Earth's core, protecting the atmosphere of the solar wind.
  • Vulcanism that renews chemical elements and provides metals to the atmosphere and surface of the planets.

Element of unpredictable effect:

• The rhythms and times of historical events and patterns of population growth might not be the same as that of human history. Change the figure around f_c and L.

Criticism of the Drake equation

From a scientific point of view, the interest of the Drake Equation lies in the formulation of the equation itself, while on the contrary it makes no sense to try to obtain any numerical solution of it, given the enormous lack of knowledge about many of them. its parameters. Calculations by different scientists have yielded values as relatively disparate as a single civilization, or ten million.

It has also been postulated that the equation might be overly simplistic and incomplete. A team of astrobiologists has suggested including energy aspects, as well as the inclusion of icy planetesimals as new variables in the equation. One would have to take into account satellites like Europa that could contain huge oceans of liquid water.

Equation Modifications

Rather than just assuming that aliens use radio frequency technologies, Sara Seager has proposed an equation that focuses on the simple presence of any form of alien life. Her equation can be used to estimate how many planets with signs of life may be found in the next few years. This equation was presented in early 2013 and looks like this:

N = N* FQ FHZ FO FL FS

N = Number of Planets with detectable signs of life.

N* = The number of observable stars

FQ = The fraction of those stars that are in a stable phase of their existence.

FHZ = The fraction of those stars with rocky planets located in the habitable zone.

FO = The fraction of those planets that can be detected.

FL = The fraction of planets that contain life.

FS = The fraction of living organisms that can produce a characteristic gas signal, indicating some metabolic activity.

Considering only 'M' type stars, the most common stars in our neighborhood that are small and less luminous than the Sun. Seager calculated by estimating values for each of the variables, that at least two planets with life could be discovered in the next decade.

In the Drake equation modified by Luis Dévora, new factors are added, such as the possibility of existence of post-biological life (artificial intelligence), other universes and hidden dimensions to human sensory perception. The formulation is as follows:

N = E* Fz Df* Uf*

E*= (Fu·R·Fp·Np·Fi·Fc·L)
Df*= D·(1+Fz)
Uf*= U·(Rm·Fu)

N = Number of civilizations that could be detected.

Fu = Fraction of time of the universe where the conditions for life are given (The fraction of time is equivalent to T/13800 million years, where T is the time that the universe takes with conditions fit for life.

R = Average annual rate of formation of stars suitable for life during that period.

Fp = Fraction of those stars that have planets and satellites in their orbit.

Np = Number of planets and satellites in each of those stars where biological and post-biological life (artificial intelligence) is possible

Fi = Fraction of those planets and satellites where intelligent biological or post-biological life has developed.

Fc = Fraction of those planets and satellites where intelligent life wants to communicate. If an intelligent civilization wants to hide its signals, we will not be able to contact it

L = Years an intelligent civilization can exist.

Fz = Fraction of the universe whose distance does not exceed half the years that a civilization can exist, is the contact zone. This zone depends on the location of the civilization in the universe. The distance cannot exceed half the years that a civilization can exist. If a civilization exists for 1000 years, it will take a maximum of 500 years to send a signal to a supposed civilization located at that distance in light years and another 500 years to receive the response.

D = Dimensions perceived by civilization (Value 4: 5D space + time, Value 2: 4D space + time, Value 1: 3D space + time, Value 0.5 2D space + time).

1 + Fz = Fraction of the universe whose distance does not exceed half the years that a civilization can exist. The civilization must perceive more than three spatial dimensions to apply this parameter. The integer 1 is added to this result because we use as a reference the value given to the 3D space + the time perceived by the human being. In the event that civilization does not perceive more dimensions than the three spatial dimensions, the value of Fz will be 0. The formula is formulated in such a way that if there are only three dimensions + 1 temporal, its value is multiplied by 1 and therefore the number of civilizations is the same. In case of perceiving four dimensions + 1 temporal, the number of civilizations that we can find increases within the contact zone. On the other hand, if a civilization can only perceive in two dimensions, the number of civilizations it can find is considerably reduced.

U = Number of perceived universes.

Rm = Average result of E, of all perceived universes

Fu = Fraction of the perceived extra universes that are inside the contact zone. This parameter also depends on the "contact zone" where the new universes are visible.