Drake equation

Drake Equation

The Arecibo message, an example of a communicative signal
Definition
Purpose	To estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.
Formula	$N=R_{*}\cdot f_{p}\cdot n_{e}\cdot f_{l}\cdot f_{i}\cdot f_{c}\cdot L$
Proposer	Frank Drake
Year	1961
Key Parameters	Star formation rate (R*), fraction of stars with planets (fp), number of habitable planets (ne), fraction where life emerges (fl), fraction where intelligence evolves (fi), fraction that develop communication (fc), lifetime of a communicative civilization (L).
Subject	Astrobiology, SETI

The Drake Equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy. It was formulated by Dr. Frank Drake in 1961 in preparation for the first scientific meeting on the search for extraterrestrial intelligence (SETI). The equation is not intended for a definitive numerical answer but rather as a framework for guiding scientific discussion and identifying key factors in the search for life beyond Earth.

The equation is most famously written as:

$$N=R_{*}\cdot f_{p}\cdot n_{e}\cdot f_{l}\cdot f_{i}\cdot f_{c}\cdot L$$

Parameter Definitions

Each factor in the Drake Equation represents a crucial astronomical, biological, or sociological term.

• $N$ – The number of civilizations in our galaxy with which communication might be possible.
• $R_{*}$ – The average rate of star formation in our galaxy.
• $f_{p}$ – The fraction of those stars that have planetary systems.
• $n_{e}$ – The average number of planets that can potentially support life per star that has planets.
• $f_{l}$ – The fraction of those habitable planets where life actually appears.
• $f_{i}$ – The fraction of life-bearing planets where intelligent life (e.g., civilization) evolves.
• $f_{c}$ – The fraction of intelligent civilizations that develop a technology that releases detectable signs of their existence into space.
• $L$ – The length of time such civilizations release detectable signals into space.

Historical Context and Use

Drake originally developed this equation for the "Order of the Dolphin" conference, held at the Green Bank Observatory in West Virginia. The goal was to organize the agenda for the search for extraterrestrial signals. By breaking down the large question of "how many are out there?" into smaller, more manageable scientific questions, the equation provided a roadmap for early SETI research.

Original Estimates (1961)

At the inaugural conference, Drake and his colleagues assigned the following rough values:

• $R_{*}$ = 1 star formed per year
• $f_{p}$ = 0.2 to 0.5 (20%–50% of stars have planets)
• $n_{e}$ = 1 to 5 (planets capable of supporting life)
• $f_{l}$ = 1 (100% of these planets develop life)
• $f_{i}$ = 1 (100% of life-bearing planets develop intelligence)
• $f_{c}$ = 0.1 to 0.2 (10–20% of intelligent life develops communication)
• $L$ = 1,000 to 100,000,000 years

Using these estimates yielded an $N$ between 20 and 50,000,000, emphasizing the vast uncertainty but suggesting the number could be large.

Modern Parameter Estimates

Since 1961, advances in astronomy, particularly with missions like the Kepler space telescope, have significantly refined some of the equation's factors.

| Parameter | Modern Estimate | Notes and Context | | :--- | :--- | :--- | | $R_{*}$ | ~1.5–3 stars per year | Based on our current understanding of star formation in the Milky Way. | | $f_{p}$ | ~1.0 | Studies indicate that nearly all stars have at least one planet (e.g., Cassan et al. 2012). | | $n_{e}$ | ~0.1 to 0.2 | Kepler data suggests that ~10-20% of Sun-like stars have a roughly Earth-sized planet in the habitable zone. (e.g., Bryson et al. 2021). | | $f_{l}$ | Unknown | This is one of the most uncertain parameters. Some estimates are optimistic (near 1), others very pessimistic. The rapid emergence of life on Earth is a key argument. | | $f_{i}$ | Unknown | Highly speculative, ranging from extremely low to near 1. | | $f_{c}$ | Unknown | Also speculative, depending on social and technological developments. | | $L$ | Unknown | Perhaps the most significant unknown. Ranges from <100 years (self-destruction) to >100,000 years (long-lived, stable civilizations). |

Criticism and the Fermi Paradox

The Drake Equation is a powerful heuristic, but it is not without its critics. The primary criticisms are:

• **The Equation is Not Falsifiable:** As a "guesstimate" based on several unknown factors, it cannot be proven true or false with current data.
• **It is Not an Equation of Physics:** It is a probabilistic sociological and biological formula, not a deterministic law.
• **It Ignores the Fermi Paradox:** The question "Where is everybody?" highlights the tension between high estimates of $N$ and the complete lack of observational evidence for other civilizations.

A related concept is the Great Filter hypothesis, which posits a stage in the development of life or intelligence that is extremely unlikely to be passed. If such a filter lies in our past (e.g., abiogenesis), then life is rare. If it lies in our future (e.g., sustainable self-destruction), then our prospects are bleak.

Modified Equations and Extensions

Several scientists have proposed modifications to the Drake Equation:

• **The "SETI" Drake Equation:** Some formulations separate $f_{i}$ and $f_{c}$ into additional terms.
• **The Astrobiological Copernican Principle:** This suggests that, in the absence of evidence to the contrary, Earth-like conditions are not special, potentially making $f_{l}$ and $f_{i}$ closer to 1.
• **The "Grabby Aliens" Model:** A recent model by Robin Hanson that treats the expansion of civilizations as a cosmological phenomenon.

See Also

• Arecibo message
• Fermi paradox
• SETI
• Great Filter hypothesis
• Habitable zone
• Life on Mars
• Astrobiology

References

• Drake, F. (1961). "Project Ozma". *Physics Today*.
• Bryson, S., et al. (2021). "The Occurrence of Rocky Habitable Zone Planets Around Solar-Like Stars from Kepler Data". *The Astronomical Journal*.
• Cassan, A., et al. (2012). "One or more bound planets per Milky Way star from microlensing observations". *Nature*.
• Ćirković, M. M. (2004). "The Temporal Aspect of the Drake Equation and SETI". *Astrobiology*.
• Hanson, R. (1998). "The Great Filter – Are We Almost Past It?".