Drake’s Equation
ASTR 1420
Lecture 19
Sections 12.1
Average score = 75.7
• Frank Drake
Drake Equation
Drake Equation
o estimating the
probability of
communicable ET
o at the moment, we only
focus on our Galaxy
o currently at the SETI institute Berkeley
o In 1961, at a meeting of about a dozen scholars
at Green Bank, WV.
o about the number of radio(?) transmitting
civilizations
Drake Equation (textbook version)
N = NHP × flife × fciv × fnow
N
NHP
flife
fciv
fnow
number of transmitting civilizations
number of habitable planets in our Galaxy
fraction of planets with life
fraction of intelligent worlds capable of interstellar communication
fraction of such civilizations right now
Drake Equation (Carl Sagan’s version)
N = N* × fplanet × nE × flife × fintell × fciv × fL
N
number of transmitting civilizations
N*
fplanet
nE
flife
fintell
fciv
fL
number of stars in our Galaxy
fraction of stars with planets
number of habitable planets per star
fraction of planets with life
fraction of worlds with intelligent life
fraction of intelligent worlds capable of interstellar communication
the fraction of a planetary lifetime with a technological civilization
Drake Equation (Carl Sagan’s version)
N = N* × fplanet × fE × flife × fintell × fciv × fL
N
number of transmitting civilizations
×
N*
×
fplanet
×
fintell
×
fEarth
×
fciv
×
flife
=
flong
N
Drake Equation (original version)
N = R* × fplanet × nE × flife × fintell × fciv × L
R* : average star formation rate
There are ~200 billion stars in our Galaxy.
Our Galaxy is about 10 billion years old.
 about 20 stars are born per year
R* ≈ 20
Drake Equation (original version)
N = 20 × fplanet × nE × flife × fintell × fciv × L
fplanet : average fraction of stars with planets
• Planet formation process is universal (angular momentum conservation)
• Exo-planets are being discovered nowadays  Doppler result indicates that
at least ~20% of stars have planets.
• Microlensing study suggests fplanet ≥ 1
fplanet ≈ 1
Drake Equation (original version)
N = 20 × 1 × nE × flife × fintell × fciv × L
nE : average number of Earth-like planets per star system
• Planet formation process is universal (angular momentum conservation)
• Rocky planets are formed closer to the central star.
• Close to a unity??
nE ≈ 0.5?
Drake Equation (original version)
N = 20 × 1 × 0.5 × flife × fintell × fciv × L
flife : average fraction of Earth-like planets with life
• Uncertain. One of the main goals of astrobiology.
• Life on Earth arose very early on
 implying that this fraction not so small?
flife ≈ 50%
Drake Equation (original version)
N = 20 × 1 × 0.5 × 0.5 × fintell × fciv × L
fintell : average fraction of life-bearing planets with intelligent species
• Uncertain. One of the main goals of astrobiology.
• Intelligence is an advantageous evolutionary niche (E.Q. evolution)
fintell ≈ 50%
Drake Equation (original version)
N = 20 × 1 × 0.5 × 0.5 × 0.5 × fciv × L
fciv : average fraction of civilizations capable of interstellar communication
•
•
•
•
have to use some sort of symbolic languages.
Will intelligent life want to communicate to others?
Inputs from anthropologists, psychologists, philosophers, and theologians
Quite uncertain.
fciv ≈ 50%
Drake Equation (original version)
N = 20 × 1 × 0.5 × 0.5 × 0.5 × 0.5 × L
N≈L
Frank Drake’s California license plate
Drake Equation (original version)
N≈L
L
average lifetime (in years) that a civilization
remains technologically active
•
•
How long will the civilization use radio communication?
Will they be around long enough to send messages and get a reply?
•
We leaked radio communications from our TV/Radio broadcasts
o
o
•
nowadays, mostly via cable
but, telephone communications through a cable now became wireless…
At least for us, L~50 yrs
Average Distance between Civilization
Our galaxy can be approximated as a thin disk
R (50,000 Ly)
T (1000 Ly)
Average Distance between Civilization
R
T
d
Volume of our Galaxy = πR2 × T
Total number of Radio civilizations now = N
d
d
Volume occupied by each civilization = πR2 × T / N = d3
Average distance b/w civilizations = d
R  T 
d  

 N 
2
1/ 3
Average Distance between Civilizations
T
d
R
If N=10,000 and with R= 50,000 light-years, T= 1,000 light-years…
 50,000 1,000
1/ 3
d  
    2510,000,000  922Ly
10,000


2
1/ 3
First Radio broadcasting December 24, 1906 from Brant Rock, Massachusetts.
First major TV broadcasting : 1963.
 barely reached ~100 Light-years from Earth…
Most Optimistic
Estimate
N  40,000,000 civilizations
d  58 Light-years …
R*
20 stars/yr
fplanet
1
nE
2
flife
1
fintell
1
fciv
1
L
1 million yrs
5 nearest stars to Earth
Proxima Centauri 4.24 Ly
α Centauri A
4.35 Ly
α Centauri B
4.35 Ly
Banard’s Star
5.98 Ly
Wolf 359
7.78 Ly
If true, we should have already detected or
been contacted or visited by them…
Pessimistic Estimate
N  1 or 2 civilizations
average distance  ?
R*
20 stars/yr
fplanet
0.5
nE
0.5
flife
0.5
fintell
0.5
fciv
0.01??
L
100 yrs
T
R
bad approximation!!
Pessimistic Estimate
R*
20 stars/yr
fplanet
0.5
nE
0.5
flife
 0.5
fintell
0.5
fciv
0.01??
L
100 yrs
N  1 or 2 civilizations
d  R / N  25,000Ly
If true, we may be effectively the only one.
Should we set out a bold journey to the infinity
and beyond?
d
In summary…
Important Concepts
Important Terms
• Drake Equation = calculating the
number of communicable alien
civilizations in our Galaxy
• Drake Equation
• Understand each term
• Logics behind all Equation Terms!
• N≈L
Chapter/sections covered in this lecture : 12.1
SETI: next class