Part IV The Equations

I realize this blog may be more mathematical and abstract than some people want to get into.  In that case you can pass to the next and final chapter of this series.

You can skip this one if you don’t want to get into detail of the math involved.

There are 2 equations that have been introduced over the last 50 years to describe the possibilities of most of these goals.     The Drake Equation and more recently the Seager equation.

The Drake Equation

  • N is the number of civilizations in our galaxy with which we might hope to be able to communicate

drake equation

  • R* is the average rate of star formation in our galaxy
  • fp is the fraction of those stars that have planets
  • ne is the average number of planets that can potentially support life per star that has planets
  • fl is the fraction of the above that actually go on to develop life at some point
  • fi is the fraction of the above that actually go on to develop intelligent life
  • fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
  • L is the length of time such civilizations release detectable signals into space

The Seager Equation:

  • N is the number of planets with detectable biosignature gases

seager equation


  • N* is the number of stars within the sample
  • FQ is the fraction of quiet stars
  • FHZ is the fraction with rocky planets in the habitable zone
  • FO is the fraction of observable systems
  • FL is the fraction with life
  • FS is the fraction with detectable spectroscopic signatures

Corollaries to Drake Equation:

The Drake equation is actually missing a critical parameter which is

  • D is the effectiveness of our search

I also wish to define these additional quantities:

  • Ns is the number of stars in the region we are looking
  • Ll is the number of years that living things exist on a typical planet
  • Li is the number of years sentient creatures exist on a planet
  • Nc is the number of advanced civilizations we will detect in a region of space

Nc = R* x Fp x Ne x Fl x Fi x Fc x L x D

The additional variables we need to know to come up with an alternate version of Drake or Seager for a region of space and for different questions are as follows:

  • N* is the number of stars we will observe in our survey

N* = Ns x D

where Ns is the total number of stars and D is the percentage of the total we will look at comprehensively.

I assert as well:

Ns x D ~= R* x L


Ni =  Ns x D x Fp x Ne x Fl x Fi x Fc

  • Where Ni is the number of sentient species

Nl =  Ns x D x Fp x Ne x Fl

  • Where Nl is the number of planets with life

Nh =  Ns x D x Fp x Ne

  • Where Nh is the number of planets that may support life


We now have all the material we need to consider the goals and possibilities of life.

In this series

Part I – Goals for our desire to understand and find extraterrestrial friends

Part II – how big is our search area?

Part III – what are the problems in finding life

 Part IV the equations 

Part V  the conclusions