Wednesday, 16 April 2008

The Drake Equation = Number of Detectable Civilisations in Our Galaxy


Work out for yourself aided by the brilliant BBC 'Horizon' programme videos on the Drake Equation the number of Detectable Intelligent Civilisations (N) in the Milky Way Galaxy.

Drake Equation: N = Rs x Fp x Ne x Fl x Fi x Fc x L

I calculate (my maths is probably wrong!) that the possible range is huge: there may be many billions or only one Detectable Intelligent Civilisation (us!) in the known Universe. My calculations of the worst and best cases for Detectable Intelligent Civilisation are based on the estimates given in the BBC 'Horizon' video.

  • Rs = rate of star formation (20 per year)
    • 20 per year x 10 billion years = 200,000,000,000 = 200 billion stars in our Milky Way galaxy
  • Fp = fraction of stars with planetary systems (0.1)
    • 0.1 x 200 billion stars = 20 billion
  • Ne = average number of planets which could support life per star with planets = 0.2 to 0.4
    • 8 billion (20 billion x 0.4) best case
    • 4 billion (20 billion x 0.2) worst case
  • Fl = fraction of earth like planets that contain life = 0.9 to 1 x 10-6
    • 7.2 billion (8 billion x 0.9) best case
    • 4000 (4 billion/1 million) worst case
  • Fi = fraction of planets that contain life that evolves into intelligent life = 0.5 to 1 x 10-6 (1 in a million)
    • 3.6 billion (7.2 billion x 0.5) best case
    • 0.004 (4000/1,000,000) worst case
  • Fc = fraction of worlds that develop science and technology = 1 (best case) to 1 x 10-3 (worst case)
    • 3.6 billion (3.6 billion x 1) best case
    • 0.000004 (0.004/1000) worst case
  • L = longevity of civilisation (years) / Age of Galaxy = 0.01 (100 million /10 billion) (best case) to (100/10 billion) 0.000000001 (100/10 billion) (worst case)
  • N = 3.6 x 10 power 7 = 36 million (3.6 billion x 0.01) best case
  • N = 4 x 10 power minus 13 (0.000004 x 0.000000001) worst case
  • N (universe) best case = 3.6 x 10 power 17 (3.6 x 10 power 7 x 100 billion (10 power 11)
  • N (universe) worst case = 1 civilisation (4 x 10 power minus 13 x 100 billion (1 x 10 power 11 galaxies)
Other information: wikipedia Drake Equation

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