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.



History Of the Observation of Galaxies

Galaxies were really only discovered recently in the history of astronomy. Up until the 1500s, the universe was thought to only compose a small sphere centered on the Earth, with all the stars on a fixed background at the outer edge of the sphere. With the dawning of the age of telescopes, things began (forgive the pun) to be seen more clearly.


Staring with Galileo, when he turned his telescope to the fuzzy patch of light that crossed the entire night sky, he noticed that the patch actually composed thousands of stars. He was able to conclude correctly that the Milky Way was actually part a large band of stars. The significance of his observation was not really known at the time.


Immanuel Kant was a German philosopher who also studied astronomy. He deduced that the Solar System was formed by the collapse of a rotating cloud (nebula). He also correctly concluded, using the knowledge that the Milky Way was actually a band of stars, that the Milky Way was a disk of stars. He also theorized that there could be many of the disk of stars which he called island universes.


The name "galaxy" comes from a Greek word, galaxias, which means "milky one", which is derived from the name of our galaxy, the Milky Way. Ancient astronomers though that the band of the Milky Way looked like milk that had been spilt across the sky, and the Greeks believed that it came from the breast of a sleeping Hera as she was nursing Heracles. When she woke up to discovered Heracles there, she pushed the baby away and what we see is the breast milk as it was sprayed into the night sky.


The first true catalogue of galaxies was not developed until the 1700s when Charles Messier started cataloguing objects in the night sky that were not stars or planets as he was searching for comets. In his catalogue, he discovered open and globular clusters, nebulae, and galaxies that were visible from the northern hemisphere (Messier was a French astronomer), and named them according to their order of discovery by him. A famous example of a galaxy that Messier catalogued was M31, which is commonly known as the Andromeda galaxy.


William Herschel and his son John also catalogued nebulae, clusters, and galaxies in the General Catalog (renamed New General Catalogue after updated by John Louis Emil Dreyer). The Andromeda Galaxy is NGC 224, so some objects in both the Messier Catalogue and the NGC overlap. The NGC does contain many more southern hemisphere objects than the Messier Catalogue.

Edwin Hubble took things even further when he began observing galaxies at Mount Wilson. He was provided significant evidence that these fuzzy patches of light in the Messier Catalogue and NGC were actually galaxies outside the Milky Way. Vesto Slipher was actually the first astronomer to provide evidence for extragalactic galaxies.

Hubble was able to differentiate between elliptical, spiral, and irregular galaxies, and in fact, thought that there might be an evolutionary sequence between the three types. He proposed something call the tuning fork diagram which shows what he believed to show the sequence. However, we now know that the sequence is not evolutionary, but is a good image to see the differences in galactic types.

Another thing Hubble used galaxies for was to determine the age of the Universe. He noticed that galaxies farther from the Milky Way seemed to be moving faster (recessional velocity). He knew the distances based on a standard candle, in this case Cepheid variable stars, and by using the Doppler shift in the spectrum, was able to formulate a simple equation to determine the age of the Universe:

v=H*d

• v is the recessional velocity in km/s
• d is the distance in Mpc = megaparsecs (a million parsecs)
• H is the Hubble constant in (km/s)/Mpc which today is approximately 67.80

The inverse of H gives the age of the Universe and converting everything, the age of the universe is approximately 13.8 billion years (give or take a couple of billion). This is also called the Hubble Time.