The Drake Equation

The Drake equation was proposed by Frank Drake in 1961 to give a probability of life existing in the Milky Way Galaxy. The equation is a product of fractions and numbers that are not well known and are only estimated based on what we know. It is given by:

N = R_* * f_p * n_e * f_l * f_i * f_c * L

What do these variables mean? Let's look at each one individually.

R_* is the average rate of star formation in our galaxy. It tells us how many stars are born every year. When the formula was first published, a conservative estimate of 1 star per year was formed. Now, we know the number is around 7 stars per year.

f_p is the fraction of those stars that may have at least one planet. Originally, it was believe that a fifth to a half of all stars could have planets. Now, this number can range from 0.4 to 1.0, depending on the parameters. It is very likely that all stars will have planets form from their stellar nebula, so 1.0 is a reasonable assumption. To be conservative, however, many think that only 40% of all stars will have at least one planet around it.

n_e is the number of planets in that system that are Earth-like. These would be planets that are terrestrial and are in the habitable zone around their parent star. Originally, they thought that 1 to 5 planets around a star with planets would be in the habitable zone. Now, it may be estimated that one out of every five planetary systems would have a terrestrial planet in its habitable zone, or n_e = 0.4.

f_l is the fraction of those planets that will develop life. This number is very hard to estimate. The development of life could arise as soon as the right conditions on the planet exist. However, it may be that that primordial life could easily be snuffed out if the conditions change quickly. Original estimates suggest that if the planet is terrestrial and in the habitable zone, this fraction is 1.0. Modern analysis suggests it could be 13%.

f_i is the fraction of those planets that has life that develops intelligence. This fraction is subjective as we should define what is meant by intelligence. Beyond humans, some animals can display intelligence in the use of tools and language, however, we would not consider them intelligent in the same way humans are intelligent. Most animals are not self-aware, have no form of written communication, or use logic in any way. This number could be extremely low, 10^-10, or high, 1 (meaning that any planet that develops life will eventually have an intelligent species evolve.

f_c is the fraction of those intelligences that develop communication that reaches beyond their home planet. We have this capability already in the form of radio signals, but have only had it for the last 100 years. This is estimated to be between 10% to 20%.

L is the average lifetime of the species after developing communication. Factors that could effect this would be natural disasters or self-annihilation. Using all the above criteria, our lifetime is only 100 years. Estimates range between 1000 years and 1 billion years.

Combining these all together, conservative estimates give the number of intelligent species in the Milky Way to be 8x10^-20, which means that in all likelihood we are alone in the Milky Way and possibly, the entire Universe. Using the more hopeful statistics, estimates give that there are about 36.4 million intelligent species in the Milky Way (side note: there are about 100 billion stars in the Milky Way, which means that only 0.000364% of all stars may have intelligent life on one of their planets.) I’m more likely to believe in the higher number than the lower number, but I wouldn’t be surprised if there were less than 1 million intelligent species in the Milky Way. Also, if other intelligences exist, they are probably in the same location in the Milky Way as ours, the disk. The reason why is the age of the disk and the presence of metals in the disk as compared to the bulge and the halo. Also, in the disk, things are not as compact, which means that planets are probably far apart, on average.