An introduction to exoplanets
An introduction to exoplanets

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6  Where are the aliens? The Drake equation

Kepler’s results about the numbers of planets, especially small ones, are important for assessing the likelihood of life elsewhere in our Milky Way Galaxy. The Drake equation gives this likelihood in mathematical terms. This equation, invented by astronomer Frank Drake, is a way of estimating the number of active, communicative civilisations in the Milky Way. Basically, it’s an estimate of how likely it is that there is an advanced alien race somewhere out there that we might be able to detect signals from. The number of these civilisations is worked out by a long multiplication of lots of different factors, illustrated in Figure 8:

Number of civilisations =

Rate of star formation

× fraction of stars with planets

× average number of planets per star that can support life

× fraction of those planets that develop life

× the fraction of planets bearing life on which intelligent, civilised life evolves

× the fraction of these civilisations that have developed communications technologies that release detectable signs into space

× the length of time over which such civilisations release detectable signals.

A lot of the latter factors are things we don’t really know the answers to, especially things like the fraction of planets that develop life, but the results from Kepler have helped us to get a handle on the second and third points – the average number of stars with planets, and the average number of planets per star that can support life.

A pictorial representation of the Drake equation.
Figure 8  The Drake equation. If you are struggling to see the labels even in the larger version, try viewing an even larger version here [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

Activity 7  Is anyone out there?

Timing: Allow about 15 minutes

Visit the following BBC web page on the Drake equation How many alien worlds exist?

On this interactive site, you can change each of the values in the Drake equation and find out how that affects the chance of there being other civilisations nearby. Remember, the Milky Way is very big – even if there might be thousands of intelligent species on planets throughout the Milky Way, there may not be any close enough for us to communicate with. The Milky Way has a diameter of something like 200 000 light years – that’s about 2 × 1018 km – and so covers an area of the order of 1036 km2. A few thousand civilisations would be spread pretty thinly across that area, and with current technology we won’t be paying them a visit any time soon! Remember, even if we could travel at the speed of light (which we can’t!) it would still take four and a half years to travel just to our nearest star.

Click on the preset settings for ‘today’s optimistic estimate’. How many communicating civilisations would there be in the Galaxy?


Answer: 72 800

Note that this requires a reasonable percentage of all planets to be habitable, and for each habitable planet a virtual certainty of intelligent life evolving. We’d probably have to be quite lucky (or unlucky?) to encounter another intelligent civilisation.

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