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SETI: The Drake Equation

In the [link:diploma-10|previous lecture], we looked at two of the upcoming missions aimed at searching for extrasolar life: NASA's Kepler and ESA's Darwin. In this lecture and the subsequent lectures, we examine the more-speculative side of the search for life: the search for extraterrestrial intelligence (SETI). This lecture focuses on the Drake Equation, a useful tool in this endeavour.

  1. Background
  2. The Drake Equation : Introduction
  3. The Drake Equation : R*
  4. The Drake Equation : fp
  5. The Drake Equation : ne
  6. The Drake Equation : fl
  7. The Drake Equation : fi
  8. The Drake Equation : fc
  9. The Drake Equation : L
  10. The Drake Equation : Putting it all together
  11. The Drake Equation : Limitations


So far, we have considered extrasolar life to be passive: it is something which sits there, waiting for us to discover it through our own endeavours. However, suppose that some extrasolar life is sentient, intelligent, and technologically advanced. Then, this life may be making attempts to signal its presence, and to contact other lifeforms in the Milky Way galaxy.

In fact, this signaling might not be deliberate. The case of Earth itself can be used as an example. Beginning with the first radio transmission by Marconi, in 1897, a sphere of artificial electromagnetic radiation has been expanding outwards from the Earth at the speed of light. This sphere now has a radius of over 100 light years; if detected by an extraterrestrial intelligence, it could be used to deduce the existence of intelligent life in our Solar System.

The Drake Equation : Introduction

Before we go about deciding how to detect the signals of an extraterrestrial civilization, we must first establish how many of these civilizations we expect to exist in our galaxy, whose presence we might be able to detect. To assist in this task, Frank Drake developed a now-famous equation, which estimates the number of communicating (deliberate or otherwise) extraterrestrial civilizations which exist in the Galaxy at any one point in time.

The Drake Equation may be written as the product of a number of terms:

N = R* fp ne fl fi fc L'''

Here, the terms have the following meanings:

The number of civilizations in Galaxy whose

electromagnetic emissions are detectable.

The rate of formation of stars suitable for the development of

intelligent life, in stars per year.

The fraction of those stars with planetary systems.
The number of planets, per solar system, with an environment

suitable for life.

The fraction of suitable planets on which life actually


The fraction of life bearing planets on which intelligent life


The fraction of civilizations that develop a technology that

releases detectable signs of their existence into space.

The length of time such civilizations release detectable signals

into space, in years.

A couple of important points concerning the Drake Equation should be made. Firstly, the symbols used in the equation are not universal; different people use different sets of symbols, although their general meaning remains the same. Secondly, the Drake Equation is not the only possible equation which can be used to estimate N; alternative formulas could be developed. However, the Drake Equation remains the most popular tool to estimate our chances of detecting extraterrestrial intelligence.

In the following sections, we will look at how we might estimate each term in the Drake Equation.

The Drake Equation : R*

Estimation of R* relies on our knowledge of star formation. Although this area is still the subject of much work, we have a pretty complete knowledge of the rate at which stars form. In the case of solar-type stars, which are not too hot and not too cold to harbour a solar system suitable for life to develop, the rate of star formation comes out at about 1 per year.

The Orion Nebula, a region of star formation

The Orion Nebula, a region of star formation

The Drake Equation : fp

As discussed in Lecture 1, the planets in our own Solar System formed as a natural consequence of the birth of the Sun. Based on the fact that planets are regularly being found around other stars, many astronomers believe that the formation of planets around single solar-type stars is inevitable. Therefore, a good estimate for fp is 1.

The formation of a solar system

The formation of a solar system

The Drake Equation : ne

When it comes to estimating ne, and the remaining terms in the Drake Equation, our knowledge is much less certain than it was for R* and fp. To date, no terrestrial extrasolar planets have been detected. However, this is primarily due to the limitations of our own detection technology; the situation can be expected to change with the launch of the Kepler mission in 2006 (see [link:diploma-1|Lecture 1]). Until then, if we take our own Solar System as representative of all extrasolar systems, then we might estimate ne as 0.25, reflecting the fact that out of our four terrestrial planets, only one (the Earth) is situated within the habitable zone.

Planet Earth, the only habitable planet of our Solar System

Planet Earth, the only habitable planet of our Solar System

The Drake Equation : fl

To estimate fl we can rely on our knowledge of how life developed on Earth (see [link:diploma-4|Lecture 4]). With the discovery of all the different types of extremophile which are found on Earth (see [link:diploma-6|Lecture 6]), it appears life can develop in pretty hostile environments, so long as the essential conditions are fulfilled: liquid water, organic compounds and a source of energy. Therefore, we can estimate fl as 1, indicating that we expect life to develop on all terrestrial planets situated within a habitable zone.

frameCyanobacteria, one of the first oxygenic photosynthesizers to develop on Earth

The Drake Equation : fi

Estimation of fi is difficult. Anthropologists still argue about the reasons why one particular branch of the ape family went down an evolutionary pathway which led to the ultimate development of modern-day humanity, the only-known example of intelligent, sentient lifeforms. It is still not clear whether this development is inevitable or merely a product of chance. However, given that there are other terrestrial species (such as dolphins and chimpanzees) which could develop into sentient beings in the future, some scientists conclude that if life develops, then intelligent life will also develop. Therefore, we can estimate fi as 1.

Early human life on Earth

Early human life on Earth

The Drake Equation : fc

If sentient lifeforms develop, it seems inevitable that they will progress toward a technological level where they broadcasts signals of its existence out into the Galaxy. However, we should recognize that there is a sociological factor involved here. Do the lifeforms deliberately broadcast signals indicating their presence? Or does this process occur inadvertently, as is the case with Earth? Or do the lifeforms take deliberate measures to hide their existence, by shielding their electromagnetic transmissions?

Marconi, the first person on Earth to transmit radio signals

Marconi, the first person on Earth to transmit radio signals

These questions are very difficult to answer: if we do not know what these lifeforms look like, how can we possibly guess at how they might think? With the absence of any knowledge whatsoever in this area, we can only make estimations based on our knowledge of ourselves: humanity as a species has broadcast its existence both inadvertently and deliberately. On this basis, we can estimate fc as 1.

The Drake Equation : L

As with fc, estimation of L requires us to make conjectures about the sociological factors at work in an extraterrestrial civilization. In the case of the Earth, the population has grown exponentially over the past two centuries; but so has the chance that we might destroy ourselves through man-made catastrophes. Present-day threats to humanity include nuclear war (e.g., the situation with Iraq and North Korea), disease (e.g., HIV/AIDS and the new flu-like epidemic spreading from the Far East), and environmental disaster (e.g., global warming).

The mushroom cloud produced by the detonation of a hydrogen bomb

The mushroom cloud produced by the detonation of a hydrogen bomb

With all of these threats to our existence, it is not certain whether humanity will survive to the turn of the next century. If we take a pessimistic view that we will destroy ourselves by then, then the amount of time our technological civilization will have existed will be a mere two centuries: from the start of the industrial revolution until somewhere in the 21st century. On this basis, we can estimate L as 200 years.

The Drake Equation : Putting it all together

Based on the above estimates of each term in the Drake Equation, the expected number N of civilizations in the Galaxy which are currently producing electromagnetic signals is 50. Taking the radius of the galactic disk as 15 kiloparsecs, and assuming that stars are spread evenly throughout this disk, then on average we can expect to find one communicating civilization in each 14 square kiloparsecs of the disk (i.e., in each 120 by 120 parsec region).

Therefore, the nearest communicating civilization can be expected to be around 120 parsecs away. One of the topics we will address in the next lecture is how we are addressing the technological challenge of detecting and/or communicating with such a neighbour civilization. Before then, however, we must address some of the limitations of the Drake Equation.

The Drake Equation : Limitations

The biggest problem with the Drake Equation should be self-evident: we were forced to make a number of estimates in calculating a final value for N. For the terms appearing in the equation, our ability to estimate values can be summarized thus:

  • R* is well-known
  • fp is reasonably well-known
  • ne is uncertain
  • fl is highly uncertain
  • fi is extremely uncertain
  • fc is extremely uncertain
  • L is extremely uncertain

In fact, every time the Drake Equation is used to estimate N, a different value is found! Some scientists find a large value for N, others conclude that N is 1, indicating that we are alone in the Galaxy. The Universe finds a value of 10, five times smaller than the value found in this lecture.

A secondary problem with the Drake Equation lies in its own incompleteness: there may be a number of important factors which have been omitted, such as the probability that life develops in solar systems situated within dense molecular clouds, where no electromagnetic signals can escape.

Updated 2009-10-13 19:52:19