Frank Drake is 90 years old today (May 28, 2020), making it a good day to ponder the odds for extraterrestrial life. Drake, an astrophysicist, has been involved in the search for extraterrestrial intelligence, including the founding of SETI, for decades. One of his best-known contributions was the development of the Drake Equation in 1961. The equation was originally intended to promote discussion between Drake and his colleagues on extraterrestrial life. The equation is still alive and relevant today with new revisions being proposed, debates on the values for its parameters, and a continuing appreciation of it from the general public. On the occasion of Frank Drake’s birthday, here is the Drake Equation plus two others inspired by it.

The Drake Equation estimates the number of communicating civilizations in the cosmos or more simply, the odds of finding intelligent life. The equation calculates the number of communicating civilizations by multiplying together estimates of several parameters. SETI’s web page displays the Drake equation as:

Where

- N = The number of civilizations in the Milky Way Galaxy whose electromagnetic emissions are detectable.
- R* = The rate of formation of stars suitable for the development of intelligent life.
- f
_{p}= The fraction of those stars with planetary systems. - n
_{e}= The number of planets, per solar system, with an environment suitable for life. - f
_{l}= The fraction of suitable planets on which life actually appears. - f
_{i}= The fraction of life-bearing planets on which intelligent life emerges. - f
_{c}= The fraction of 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.

A wide range of values have been proposed for each parameter but a modern optimistic estimate has

R=7, f_{p}= 90%, n_{e}= 0.3, f_{l }=10%, f_{i }= 1.0%, f_{c }= 1.0%, L = 10,000,000

which yields N = 189 civilizations in our galaxy.

The Drake Equation provides an estimate of the number of civilizations whose *electromagnetic emissions* are detectable. Astronomer Sara Seager proposed an equation that based on detecting planets whose biosignature gases can be detected. Biosignature gases, produced by living organisms, accumulate in a planet’s atmosphere to levels that can be detected with a remote space telescope. The Seager equation is:

N = N^{*} F_{Q} F_{HZ} F_{O} F_{L} F_{S}

Where

- N = the number of planets with detectable biosignature gases
- N
^{*}= number of M stars with I < 13 - F
_{Q }= fraction of quiet M stars - F
_{HZ}= fraction with rocky planets in the HZ - F
_{O}= fraction of observable=transiting systems observable with JWST - F
_{L}= fraction with life - F
_{S}= fraction with detectable spectroscopic signatures

Seager’s estimates for these parameters for M stars in the TESS/JWST survey are

N^{*} = 30000, (F_{Q} F_{HZ}) = 0.15, F_{O} = 0.001, F_{L} = 1.0, F_{S} = 0.5

Which yields N = 2 civilizations.

Sara Seager is giving an “Update on NASA’s TESS Exoplanet Mission” at the RASC Virtual General Assembly. Live streamed on Sunday June 7th, 2020 on the RASC YouTube channel www.youtube.com/c/rascanada.

Sara Seager posted a YouTube video honouring Drake and the influence he had on her own research.

A form of Drake’s equation was used by Gene Roddenberry to pitch Star Trek in 1964. Roddenberry was trying to justify the large number of inhabited planets in the show. He did not have a copy of the equation so he made up his own variant

with no explanation of the parameters. It is said that Frank Drake later pointed out to Roddenberry that a value raised to the first power is merely the value itself when he visited the Star Trek set.

Happy 90th Birthday to Frank Drake, a pioneer in the search for life elsewhere in the universe.