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UT AST 309L - Evaluating your Drake Equation

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Evaluating your Drake EquationBasic Ideas• Number of Civilizations in our Galaxy– Product of rate of emergence and L• Running product gives rate for each step• Until L, we have rates• Through fc, we get “communicable”civilizations– Multiplying by L gives the number (N)• Assumes “steady state” between birth anddeath of civilizationsDrake Equation: N = R* fp ne fl fi fc LN = number of communicable civilizations in our galaxyR = Rate at which stars formfp= Fraction of stars which have planetary systemsne= Number of planets, per planetary system, which are suitable for lifefl= Fraction of life bearing planets where intelligence developsfc= Fraction of planets with intelligent life which develop atechnological phase during which there is a capacity for and interest in interstellar communicationL = Average of lifetime of communicable civilizationsr = Average distance to nearest civilization*Distance to Nearest Neighbor1. Assume civilizations spread uniformlybut randomly through galaxyr = radius of imaginary sphere centered on usthat touches nearest civilizaztionsearch vol ∝ r3⇒ r = 104 ly N1/3usGalaxyNearest civilization*rDistance to Nearest NeighborIf N < 8000, r from previous formula is 500 lyAbout equal to thickness of GalaxyUse cylinder for search vol ∝ r 2 hso r = 5 ×104 ly N1/2rhNearest civilization *Happy Feller505050505050Birthrate1fl1fi1fc5 × 109L2.5 × 1011N1.6 ly1150EstimaternefpR2.5 out of 4 starsIf N > 8000,r =104 light yearsN1/3If N <8000,r =5 × 104 light yearsN1/2Angela Angst5 × 10–85 × 10–65 x 10–40.050.55Birthrate0.01fl0.01fi0.01fc100L5 × 10–6N---0.10.15EstimaternefpRNever two civilizationsat same timeIf N > 8000,r =104 light yearsN1/3If N < 8000,r =5 × 104 light yearsN1/2Mr. Average Guy0.941.562.234.45510Birthrate0.5fl0.7fi0.6fc1 × 106L9.4 × 105N1000.890.510EstimaternefpR 1 out of4 × 105 starsIf N > 8000,r =104 light yearsN1/3If N < 8000,r =5 × 104 light yearsN1/210 × 105 = 106Evaluating YOUR Drake Equation• Almost no answers are wrong– It must be possible for us to exist– N must be no greater than the number ofstars in the Galaxy• May imply limit on L• Ways to evaluate:– Plug into equations– Use calculator on web– Ask us for helpYour Drake EquationBirthrateflfifcL NEstimaternefpRIf N > 8000,r =104 light yearsN1/3If N < 8000,r =5 × 104 light yearsN1/21051061071081010410310210102103104510r (ly)Nr (ly)NNote log scales2 3452 345Points to bear in mind• r is based on assuming spread uniformly– Could be less in closer to center of MW• r is based on averages– Could be closer but unlikely• r is less uncertain than N• Since signals travel at c, time = distance in ly• If L < 2r, no two way


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