ASTRO 801
Planets, Stars, Galaxies, and the Universe

The Drake Equation

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Scientists expect that, if we discover life on Mars, it will most likely be simple bacterial life and not humanoid aliens like most of the martians you have seen in movies. This does not mean that scientists have completely ruled out the possibility of intelligent life in the Milky Way Galaxy, though. One of the tools that you can use to consider this topic is known as the Drake Equation, after astronomer Frank Drake who proposed it in the early 1960s. With this equation, you can estimate the number of communicating, intelligent civilizations that currently exist in the Milky Way.

The equation is:

    N = ( R* ) × ( f p ) × ( n e ) × ( f l ) × ( f i ) × ( f c ) × ( L )
  1. The individual terms are:

    • N = number of civilizations in the Milky Way Galaxy that are capable of producing signals that we can detect on Earth
    • R* = the rate at which stars capable of supporting life form in our Galaxy
    • f p = the fraction of those stars that have a planet or planets
    • n e = the average number of planets per planetary system that have an environment that can support life
    • f l = the fraction of those planets that can support life on which life actually develops
    • f i = the fraction of those planets with life where intelligent life develops
    • f c = the fraction of those intelligent civilizations that develop technology for communication
    • L = the average lifetime of those civilizations that develop technology for communication

    Several of these terms have values that we can estimate with some degree of accuracy. For example, we can estimate R* from our observations of star forming regions in the Galaxy. That number appears to be very close to 1 star per year. Also, from our observations of stars with protoplanetary disks and with extrasolar planets, we think that f p is likely 1 or close to 1, too. The rest of the values in the equation require you to either extrapolate using limited information or outright guess.

    For n e , we can use the Solar System as a guide. The Earth is in the CHZ. Venus and Mars are either close or in the CHZ depending on the model used. Europa, Ganymede, and Titan are outside of the CHZ, but may have environments that can support life. So, in the Solar System there is definitely one, and maybe more than one, planet (or moon) capable of supporting life. What we still do not know is if our Solar System is common or rare. If it is common, you might estimate say 2 objects per Solar System for n e . For f l , you have to make an educated guess. Scientists studying the origin of life think that, given the right conditions (temperature, presence of water, etc.), life may develop on every Earth-like world, or f l =1 . However, that may be too optimistic, so you might expect that 1 in 10, 1 in 100, or 1 in 1,000,000 develop life. However, if you think that Earth is alone in this regard, it might be as low as 1 in 100,000,000,000. The arguments for assigning values for f i and f c are identical. If you are optimistic, you would assign f i or f c =1 . If you are pessimistic, you would assign f i or f c =1 in 100,000,000,000, or anywhere in between.

    The final term, L, is the lifetime of an intelligent, communicating civilization. How do you estimate this value? If you consider Earth, we have only had the technology to communicate using light (e.g., radio or TV) for about 100 years. To estimate L, though, you have to decide how long our civilization will retain this capability. Will civilization end because of war, disease, or some other catastrophe in a few generations? If not, will our civilization last as long as the Sun remains on the Main Sequence? Your estimate may be anywhere from 1,000 years to 5,000,000,000 years. If you fill in values of 1 for all of the parameters for R* through f c , then the equation simplifies to N = L. So, in the optimistic case, your estimate for N will be equal to your estimate for the lifetime of a typical intelligent, communicating civilization.

    Try this!

    At PBS, they have a Drake equation calculator where you can put in values for these numbers to determine how many civilizations may be found in the Milky Way.

    1. Fill in values for a pessimistic case and determine N.
    2. Fill in values for your best guesses and determine N.
    How do these compare to the case where every parameter is 1? What do you think might be the range of the total number of intelligent, communicating civilizations in the Milky Way?

    Given the extent of the Milky Way, if the number N is small, the expected distance between Earth and any communicating civilization will be large. If N is large, the average separation between Earth and any communicating civilization may be small.