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Gonzalez and Richards: Drake Equation

Assumptions and implications are not the same thing.

Posted Wednesday, November 09, 2005 by Gerald Vreeland

In the previous episode, I had remarked that the Drake Equation (an odd attempt to reduce the possibility of finding life “out there somewhere” to statistical terms) is obsolete and ought to fall into disuse.  I seem to remember that, much earlier, I had promised that I would address the issue of Gonzalez and Richards revising the equation to fit what they feel are the advances in modern science.  Trust me, if we are looking for a number between 0 and 1, we will find ourselves much closer to 0.

Here is the old one, in case you’ve forgotten:  

 

N = No X Fp X ne X fl X fi X fc X fL  

 

Here’s the breakdown:

 

 No= the total number of stars in the galaxy

 

fp= the fraction of stars with planetary systems

 

ne= the number of habitable planets in each system (sub-e is “earth-like”)

 

fl= the fraction of those planets where life emerges from inorganic matter or organic precursors. 

 

fi= the fraction of those planets where intelligent beings evolve

 

fc= the fraction of those planets where intelligent beings develop sophisticated communication

            technology

 

fL = the fraction of the average planetary lifetime wherein there is an advanced civilization

 

Here is the revision by G & R:

 

            N = N* X fsg X fghz X cr X  fspir X fchz X  fp X fi X fcir X foxy X  fmass X  fcomp X  fmoon X fwater

X ftect X flife X  fimp X  frad X  flcomp X fltech X fL   [1]

 

Briefly N =

 

N*is the total number of stars in the galaxy

 

 fsgis the fraction of stars that are early G dwarfs and a few billion years old. 

 

fghzis the fraction of stars that remain in the Galactic Habitable Zone

 

fcris the fraction of stars that remain near the corotation circle and have low eccentricity galactic orbits. 

 

 fspiris the fraction of stars that remain outside the spiral arms. 

 

fchzis the fraction of stars that remain with at least one planet in the circumstellar habitable zone. 

 

 fpis the average number of terrestrial planets in the Circumstellar Habitable Zone. 

 

fiis the fraction of systems that remain with only a few planets comparable to Jupiter in large nearly circular orbits. 

 

fciris the fraction of systems that remain with terrestrial planets in the Circumstellar Habitable Zone with low orbital eccentricities, outside dangerous spin-orbit, and giant planet resonance (minimum eccentricity due to large planet gravitation). 

 

foxyis the fraction of planets that remain near enough to the inner edge of the CHZ to allow high oxygen and low carbon dioxide concentrations in their atmospheres. 

 

 fmassis the fraction of planets that remain approximating the proper mass. 

 

 fcomp is the fraction of planets that remain with proper concentration of sulfur in their cores. 

 

 fmoonis the fraction of planets that remain with a large moon and the right planetary rotation period to avoid chaotic variations in its obliquity. 

 

fwateris the fraction of planets that remain with the right amount of water in the crust.

 

ftectis the fraction of planets that remain with steady tectonic plate cycling. 

 

flifeis the fraction of planets that remain where life appears. 

 

 fimpis the fraction of planets that remain with low numbers of critical impacts (comets, asteroids, meteorites). 

 

 frad is the fraction of planets that remain with a low number of critical transient radiation events (e.g., local gamma bursts). 

 

 flcompis the fraction of planets that remain where complex life appears. 

 

fltechis the fraction of planets that remain where technological life appears. 

 

fL   is the average lifetime of a technological civilization. 

 

= either God or Luck in my opinion.  Playing the odds on luck of this type would be sheer probabilistic suicide.  All that order and intricacy begs for a Divine explanation.


[1] From G & R Appendix A pp. 338-9. 

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