# Calculating the Number of Observable Life-Supporting Planets

## Introduction

I like thinking about the possibility of habitable exoplanets. There are many interesting questions that people can ask about exoplanets. Here are a few questions that are interesting to think about:

1. How many intelligent civilizations are present in our galaxy?
2. How likely is it that a particular exoplanet could support life?
3. How many exoplanets are out there with detectable signs of life?

Question 1 is addressed by the Drake equation, which the Wikipedia covers nicely. I wrote about Question 2 in this post. I will discuss in this post an interesting article in Astrobiology magazine that addresses Question 3. The spirit of this work follows a similar path to that of Drake.

## Background

The best background information I could find is presented by Sara Seager, whose research is the subject of the Astrobiology article.

## Analysis

From the given number of planets examined, the article presents an equation that allows one to estimate the number of planets around these stars that are:

• rocky
• lie in the habitable zone
• support life
• the life is generating detectable biosignature gases.

Equation 1 was presented in the article.

 Eq. 1 $\displaystyle N={{N}_{X}}\cdot {{F}_{Q}}\cdot {{F}_{HZ}}\cdot {{F}_{O}}\cdot {{F}_{L}}\cdot {{F}_{S}}$

where

• N is the number of planets that have amounts of biosignature gases that can be detected from Earth.
• NX is the number of stars examined.
• FQ is the fraction of stars that are quiet (i.e. provide a stable source of energy for a planet). In the Astrobiology article, Sara said that the fraction of stars that are quiet is 15%.
• FHZ is the fraction of stars with rocky planets in the habitable zone.
• FO is the fraction of rocky planets in the habitable zone that are observable.
• FL is the fraction of rocky planets in the habitable zone that are observable and support life.
• FS is the fraction of rocky planets in the habitable zone that are observable, support life, and the life generates observable biosignature gases.

Equation 1 is only an estimate because many of its terms (other than NX and FQ) are unknown. However, we are beginning to get estimates for all the fractions. Sara Seager has estimated the fractions present in Equation 1 and these numbers project that two inhabited planets will be found in the next decade. She also published an interesting article that discusses candidate biosignature gases -- oxygen and ozone figure prominently.

Let's try an example calculation to see the kind of parametric values that we would need to have to find 2 habitable planets in the next ten years. My quick analysis assumes that we are looking close to the Earth (i.e. within 100 light-years). Figure 1 shows my speculations.

## Conclusion

I hope Sara Seager is correct about the odds being good on finding two inhabited planets in the next decade. I think this is the most interesting area in astronomy at the moment.

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### 4 Responses to Calculating the Number of Observable Life-Supporting Planets

1. jaksichja says:

Prof. Seager is highly regarded in the astrobiology community--
Prof. Drake is currently at the SETI institute--here is his latest vita:

http://www.seti.org/sites/default/files/Drake%20%20F%20CV%202008.pdf

And for an interesting interactive from the BBC (on the Drake equation):

http://www.bbc.com/future/story/20120821-how-many-alien-worlds-exist

• mathscinotes says:

Her work has been very interesting reading. My hope is that the new instruments coming on line over the next few years will make the spectroscopy of some of these new worlds a reality. Just imagine the excitement if one of these instruments showed signs of a biosignature gas like oxygen or ozone ...

Mathscinotes

• jaksichja says:

I agree!

2. Jerry Pasker says:

I have a question that involves math beyond what I'm capable of understanding. I understand the problem, (involves lasers and exoplanets and SETI) I just don't understand what math to use to arrive at even a "meatball" type of solution. Is there any way I could email you the question with my thoughts on it? Thanks.