Hunting Aliens with Maths
Credit: University of Rochester

Hunting Aliens with Maths

24/05/2021Written by Alex Thompson

Can an equation written by Frank Drake in 1961 determine the number of active, communicative extraterrestrial lives in the our galaxy?

Book online now and upgrade to a free annual pass

mascot Telescope Right
Frank Drake in front of the National Radio Astronomy Observatory Green Bank Credit: National Radio Astronomy Observatory

For centuries humans have been fascinated with the prospect of intelligent alien life. In 1896 Nikola Tesla suggested a system that could be used to contact beings on Mars, whilst in the early 1900s Guglielmo Marconi stated that his stations had picked up potential Martian signals.

In 1961, at the first meeting on the search for extraterrestrial intelligence (SETI), Dr. Frank Drake proposed his equation to assist in searching for alien life as a way to stimulate scientific discussion.

It summarises the main concepts scientists must consider when proposing the chances of alien life.

“As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it’s going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This was aimed at the radio search, and not to search for primordial or primitive life forms.” Frank Drake

The artist's conception shows a hypothetical planet with two moons orbiting in the habitable zone of a red dwarf star.

So what is the equation Frank Drake Proposed?

N =  R x  fx  nx  fl  x  fx  fx  L

Admittedly this piece of algebra looks rather daunting on first inspection, however, if we break it down into its component parts, you’ll  see that each part of the equation simply represents one area scientists must consider as we go alien hunting.

So what does ‘N’ represent? This is the purpose of the Drake equation and it is simply the number of civilizations in our galaxy with which communication may be possible. The value of N is determined by the different factors in the rest of the equation.

R∗ = average rate of star formation

R∗ = average rate of star formation
Milky Way band. Credit: Bruno Gilli, ESO

This part of the Drake equation considers how many stars there are in the Milky Way, and how fast new ones are forming.

It is estimated there are currently between 100-400 billion stars in our galaxy with an additional 1.3-3 being born each year.

Obviously, more stars mean there’s more chance of life, but it also means it may take longer to explore them all.

fp = fraction of stars with planets

fp = fraction of stars with planets

Artist's concept of the exoplanet WASP-12b. Credit: NASA

Our next part of the equation relates to how many of these stars have planets orbiting them.

In 1961 it was estimated around 20-50% of all known stars had at least one planet orbiting the system, but scientists are now confident that the vast majority will have at least one exoplanet.

ne = average number of habitable planets per star

ne  = average number of habitable planets per star
Graph showing exoplanets and whether or not they fall within their stars habitable zone.

A very important part of the equation, as this question looks at the ‘habitable zone’.

If scientists know that a star has multiple planets orbiting, but none are within this illusive habital zone, there is little to no chance of life existing or thriving.

The habitable zone, commonly known as the ‘Goldilocks zone’, is the area where all the ingredients for life are just right.

It’s not too hot or cold for life to exist.

In our Solar System the only planet in the Goldilock’s zone is Earth, but other star systems could have several planets that fit the criteria.

fl = fraction of habitable zone planets that develop life

fl = fraction of habitable zone planets that develop life

Now, just because a planet inhabits a Goldilock’s zone, it does not follow that it will develop life.

Scientists have identified a number of habitable zone planets, but so far finding life itself has remained elusive.

It is hoped that future technology, such as the James Webb Space Telescope, will aid us in our search for life.

Even if we found life on just one planet, it would mean we are not alone.

fi = fraction of planets with life that that develop intelligent life

fi = fraction of planets with life that that develop intelligent life
Kepler telescope (artist's impression). Credit: NASA

It is highly likely that the first alien life forms we discover won’t look like us, but be microbial life.

When talking to Professor of Astrobiology, Professor Charles Cockell, as part of our LIVE Space Q&A sessions, we discussed that fact that here on Earth we buy chemicals to kill common types of bacteria, viruses and fungi, however, if we found them on another planet it would be one of the most important scientific discoveries in history.

Obviously, the chances of communicating with these basic forms of life would be impossible, so this part of the Drake equation looks at the percentage of potential intelligent life forms living on the planets in the habitable zones.

fc = fraction of civilizations that releases detectable signs of their existence

fc = fraction of civilizations that releases detectable signs of their existence
James Webb Space Telescope Mirror inside a clean room at NASA’s Goddard Space Flight Center Credit: NASA/Desiree Stover

So, we have a habitable planet, with intelligent life, but have they managed to develop technology to communicate with us?

NASA Goddard’s Sellers Exoplanet Environments Collaboration (SEEC) and the NASA Exobiology program have recently published a paper that says the easiest way to detect extraterrestrial civilizations is by searching for “technosignatures”, evidence of the use of technology or industrial activity in other parts of the Universe.

The next generation of telescopes will also be able to search for biomarkers, which could help highlight evidence for life on other planets through the detection of, say, CFCs or nitrogen dioxide.

L = Length of time these life forms are active

L = Length of time these life forms are active
Earthrise on Apollo 8. Credit: NASA

Our Milky Way is 13.5 billion years old.

Earth has only existed for a third of this time and Homo sapiens have only been on the planet for the last 300,000 years.

Therefore humans haven’t existed for 99.999% of the time the galaxy has been here. I

t’s entirely possible an intelligent life form tried to contact us before we even existed, in the same way that we are trying to contact them now.

We could be trying to communicate with a civilisation before they exist or even after they’ve become extinct.

To come into contact with an alien species both of our timelines would have to be aligned and exist at the same time.

NASA, ESA, G. Illingworth and D. Magee (University of California, Santa Cruz), K. Whitaker (University of Connecticut), R. Bouwens (Leiden University), P. Oesch (University of Geneva), and the Hubble Legacy Field team

It is entirely possible that there is a star out there with a planet in its habitable zone, where life is thriving and the inhabitants have developed to the point that they are able to communicate with us.

In fact, scientists at the University of Nottingham used the Drake Equation last year to estimate the value of N as being 36.

If this is a true estimate, then we are looking for 36 planets in a field of 100-400 billion stars.

It’s an incredible challenge but one that scientists are tackling head on, using the Drake Equation to guide their way.