# The Drake Equation

-By Anuj M Medtiya

Are we alone in our Milky Way? Or even the universe? Do you ever wonder if aliens exist? If life forms do exist apart from on planet earth, how many different types of life forms and civilizations could exist in this massive universe?

I have always found this topic intriguing after I realized that our planet earth is nothing but a dot in our galaxy, our galaxy is nothing but a small dot in the entire universe, and planets and stars much greater than our Sun exist.

A Harvard professor named Harlow Shapley speculated that the universe has 10 million, million, million suns. Yes, you read correctly. 10 followed by 18 zeros! After his calculations about temperature, water, air etc., he arrived at an estimated figure of 100 million worlds where life could have been formed by evolution! Blimey! Even if life forms do exist on other planets, we cannot know if they are intelligent and scientifically developed to communicate with alien species. Many scientists have tried and are still trying to detect any radio signals from nearby stars and planets similar to ours.

Now, let me tell you about this scientist Dr. Frank Drake. He formulated an equation in 1961 to calculate a precise number of extraterrestrial life forms that were intelligent enough for radio communication. This came to be known as the Drake Equation. I’ll explain the mathematics involved in this astrophysics concept. What exactly is the Drake equation? The Drake equation is:

N = R * fp * ne * fl * fi * fc * L

You must be wondering that this equation looks really complicated with so many weird variables and not worth your time. But in actuality, it is quite interesting and easy to understand. Let me help you with it. We will take each variable in turn.

1) R

Did you know that new stars keep forming in the interstellar space due to concentration of clouds of dust and gas? Well, you do now. This variable represents the average rate of such star formation in our galaxy.

2) fp

As new stars are formed, some may have planets while some may not. Like the sun in our solar system has 8 planets, including Earth, revolving around it. This variable represents the fraction of those stars which may have planets. (E.g. if 10 stars are formed and only 5 have planets, the fraction will be 5/10)

For understanding the following variables, let us make a few assumptions about our solar system which will help you understand the concept better.

a. We will assume that Earth, Mars, Jupiter and Saturn all have habitable life supporting conditions such as air, water and food similar to that of Earth.

b. We will also assume that Earth, Mars and Jupiter have actual civilizations of living beings but Saturn does not.

c. Now we assume that life forms on Earth and Mars develop into intelligent life forms.

d. But, only the life forms on Earth have developed a technology which can be used for communication into space.

You will now understand more clearly why we made such assumptions.

3) ne

This variable represents the average number of planets which can potentially support life per star. In our example, our Sun (star) has 4 planets supporting life (Earth, Mars, Jupiter and Saturn).

4) fl

This variable represents the fraction of planets that could support life that actually develop life at some point of time. In our example, out of 4 planets which could support life, 3 have actually developed life forms. (fraction is 3/4) (Earth, Mars and Jupiter).

5) fi

This variable represents the fraction of planets with life that actually go on to develop intelligent life (civilizations). In our example, 2 out of 3 planets (2/3) with life actually had intelligent life civilizations (Earth and Mars), while Jupiter had primary unintelligent life forms such as plants and/or animals which are uncivilized.

6) fc

This variable represents the fraction of civilizations that develop a technology that releases detectable signs of their existence into space such as radio signals or other type of communication. In our example, 1 planet i.e. Earth out of the 2 planets with civilizations (Earth and Mars) (1/2) had actually developed radio technology for communication with outer space.

And lastly,

7) L

This represents the length of time for which such intelligent civilizations with developed technology release detectable signals into space. For example, let us assume that Earth released its radio detectable signals into space for 150 years and then stopped. So, L will be 150 years.

Thus, by multiplying these 7 variables, we finally arrive at:

8) N

This is the number of civilizations in our galaxy with which communication might be possible.

Here is a gist of the above explanation with a few pictures.

You must have noticed the colored bar in the photo at the top which tells us the certainty with which the values for these set of variables can be predicted or calculated. You can see that the variables are arranged in a decreasing order of certainty, which means that as we progress towards the right, the values become more and more difficult to estimate and are more hypothetical which we do not have the proof of.

Enough with the complexity of it. Let’s look at some of the interesting estimates calculated by some of the Oxford researchers who reformulated the Drake equation to arrive at these results.

The authors calculated that there is a 41% chance that we are alone in the galaxy Milky Way which seems very high. They also calculated that there is a 32% chance that we are alone in the entire universe. Let me show you how big the universe is!

You can see innumerable galaxies some small and some big. Milky Way is just one of them!

I hope you enjoyed this article and learnt something good from it. My inspiration behind this topic was “Doctor” Sheldon Cooper from the show ‘The Big Bang Theory’ where he recites the entire Drake Equation with its meaning. Season 2 Episode 20 – ‘The Hofstadter Isotope’ for the fans who would like to revisit it or you can also find it on YouTube. Thus, we can marvel at the brilliance of Dr. Frank Drake and see how math is an important aspect of Astrophysics.