The Drake Equation

R
Is defined as the rate at which suitable stars are formed. Modern observational astronomy has managed to define to a reasonable degree of accuracy both the number of stars in the Galaxy and its age. The Milky Way is believed to be approximately 10 billion years old and contain in the order of 300 billion stars, with both these values being correct to within 10%. We could therefore come up with a rough estimate of R=300 billion stars/10 billion years, giving an average rate of star formation of 30 stars per year. This is an order of magnitude estimate and perhaps we could arrive at a more accurate number by further analysis of what defines a suitable star. We are generally looking for sun-like or at the very least F, G, K or perhaps M type stars. These types of star have the long life on the main sequence required for potential intelligent life to evolve. With all these factors considered I believe the rate will be lower than the 30 stars per year previously stated, perhaps around 10 suitable stars per year. This term is probably the most clearly understood, with the underlying numbers known to a certainty of about 10%.

fp
Is defined as the probability of planets forming around a suitable star. Within the last decade or so this term has become much more quantifiable due to the continually advancing field of exoplanet detection. Currently 249 exoplanets have been discovered and this number is continually rising. The methods employed are becoming more sensitive and some large terrestrial type planets are now being found. Due to the techniques being employed, particularly Doppler spectroscopy, the type of planet being found tends to be large Jupiter like planets close in to the parent star. This bias is due to the fact that these types of planet have the most detectable effect on the star being analysed, terrestrial planets are much harder to detect. Other techniques such as gravitational micro-lensing, occultation and infrared interferometry stand a good chance of finding smaller worlds in the future. One of the most important results in regard to defining pp is from a long term micro-lensing study. It was established that fewer than a third of all G and K type stars have a Jupiter sized planet in a Jupiter sized orbit. Meaning solar systems superficially similar to our own are not that common around sun-like stars. As this term is only concerned with the probability of any type of planet forming around a star, it would seem that pp is going to be high. It seems likely that in the process of forming a star, a stellar nebula would also condense into one or more planetary bodies as well. Perhaps only systems with very low metallicities might this not occur. I would therefore estimate about 50% of stars have at least one planet of some description.

nE
Is defined as the average number of suitable planets in habitable zones per planetary system. The habitable zone is defined as the belt around a star where an orbit has to fall for a terrestrial planet to sustain water in a liquid form on its surface. Habitable zones migrate outward from the star during its lifetime and the planet would need to remain within this zone during the development of life. Habitable zones might also exist around giant planets and moons orbiting them might also have conditions suitable for life. Potentially the inward migration of these gas giants, or ‘hot Jupiters’, could potentially hamper terrestrial planet formation. Currently this term is not grounded in observational astronomy but proposed missions such as ESA’s Darwin may help to define it for the nearest few hundred stars. Theoretical simulations of potential solar system have also been carried out with millions of orbits calculated to examine the evolution and migration of planetary orbits. These results are pertinent to constraining the value of nE. Taking into account the narrowness of habitable zones generally available, and migration of ‘hot Jupiters’, perhaps around 20% of planetary systems have suitable planets falling in habitable zones. Although this estimate has some basis in actual results it is mostly guesswork and not as well constrained as the previous terms encountered so far.

pl
Is defined as the probability of life appearing on a suitable planet in a habitable zone. Life in this term means any type of life, including microscopic/bacterial organisms which must be considered a great deal more probable than complex multi-cellular life. The prospective solar system would require heavier elements and need to be in a benign area of the solar system. We currently have no proof of life existing on other planetary bodies, and the process of initially creating life is very poorly understood. Future missions to bodies in the solar system such as Mars and Europa may further shed light on this topic. Even if life is found in the solar system it would have to be proved it occurred independently of terrestrial life to be a significant result. The estimates in the previous terms all had some basis in observational astronomy or theoretical simulations but this term is now more of an educated guess. From the seemingly rapid appearance of life after the formation of Earth, it seems quite probable that life gets started almost as soon as it gets the chance. Therefore a value of a 25% seems realistic.

pi
Is defined as the probability of intelligence developing in life. The only evidence we have to estimate this term is the history of life on Earth. Throughout the 4 billion years of life existing on planet Earth, and the many millions of species that evolved only one species has developed intelligence. This would therefore seem to make it a very rare occurrence. Due to the very small evidence base we have for this term any number will be at best a guess, but perhaps around 0.1% would be reasonable. Of course this estimate might be way out, perhaps intelligence to the degree of humanity(!) is incredibly improbable. pc Is defined as the probability of intelligent life broadcasting across space. If we take the only example we know, humanity has been broadcasting detectable radio and TV signals for only around 70+ years. Therefore for most of civilized(?) human history this has not been the case. Some deliberate attempts have also been made to broadcast to alien civilisations, and to listen for signals broadcast from other life forms. Currently no positively alien broadcasts have been detected. It seems quite likely that once a civilization achieves intelligence and civilisation it is relatively fast in producing the technology that makes it detectable (even accidentally) to other listening civilisations. Therefore a number of about 10% seems as good as any.

T
Is the length of time such a civilization broadcasts detectable signals into space. This term is concerned with the lifetime of civilizations and whether the intelligent civilizations will be around at the same time to communicate with each other. Does the level of technology required to broadcast, also bring about technology that could wipe the whole civilization out? Are advanced civilizations short lived or do they solve their inevitable problems and last for extremely long periods? This term is also very difficult to quantify, but we know humanity has been detectably broadcasting for at least 70+ years. Being optimistic that once advanced civilization is achieved, it manages to solve its problems, an existence of many thousands or even millions of years might be achieved. For the sake of argument 10,000 years seems possible.

Put it all together and what have you got?

Once again...
N=R*pp*nE*pl*pi*pc*T.

Or in words... 
The number of civilizations broadcasting at any one time are:

Now plugging in the numbers that have been estimated (or perhaps plucked out of the air) above we arrive at the following.

N=10x0.50x0.20x0.25x0.001x0.1x10,000

N=0.25 Civilizations broadcasting at any one time. Meaning that we may well be the only broadcasting civilization around at the moment in the galaxy*.

*Of course this is just one estimate calculated using the values given above. Who knows what the actual number is, but the truth is out there...