1. The Father of SETI
In 1961, Frank Drake organized a conference at the Greenbank Observatory to discuss the possibility that we could carry out an experimental program designed to detect alien communications.
“As I planned the meeting, I realized a few days ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it's going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This, of course, was aimed at the radio search, and not to search for primordial or primitive life forms.” Frank Drake

2. The Drake Equation N = R*  f⨀  fp  nE  fl  fi  fc  L
N = The number of intelligent civilizations in the Milky Way Galaxy capable of interstellar communication
R* = Rate at which stars form in the Milky Way
f⨀ = Fraction of those stars that are sun-like
fp = Fraction of those stars that have planets in stable orbits
nE = Number of those planets that fall within the CHZ
fl = Fraction of those planets where life actually evolves
fi = Fraction of those planets where intelligence evolves
fc = Fraction of those planets where intelligent life develops a civilization capable of communication
L = ‘Longevity factor’ ─ how long the civilization exists

3. Question
The Drake equation allows us to estimate the number of ______.
intelligent humans that have been superseded by more intelligent apes
habitable planets on which life has arisen
years intelligent civilizations manage to survive before going extinct
the number of female ducks impregnated each year
intelligent civilizations capable of interstellar communication that currently exist in our galaxy

4. An Example… How many students N attend Prof. Cassiday’s class.
Let’s plot student attendance vs. time ....
Suppose students walk into class at the rate of …
R = 1/minute. 10
Further suppose they can ‘stand it’ for no more than …
L = 10 minutes … and then they leave
‘Population’ stabilizes at N = Rate  Lifetime
N = R  L 5 5 10
minutes

5. The Drake Equation N = R*  f⨀  fp  nE  fl  fi  fc  L
The term in the box is the rate Rciv at which intelligent, communicative civilizations emerge in the Milky Way Galaxy.
L is their lifetime … how long they live after reaching the stage of intelligence capable of communicating … before they go ‘belly up’ !
Thus, the number of such civilizations alive and communicative in the Milky Way is
N = Rciv x L

6. The Drake Equation N = R*  f⨀  fp  nE  fl  fi  fc  L
Note: R* = N* / TMW
N* = The number of stars in the galaxy
TMW = The age of the Milky Way Galaxy
In words ─ The rate at which stars form in the galaxy is just the total number of stars (N*) divided by how long it took them to form, which is the age of the Milky Way Galaxy (TMW). Substituting these factors into the above yields …
N = (N* / TMW) f⨀  fp  nE  fl  fi  fc  L

7. N = (N*/TMW)  f⨀  fp  nE  fl  fi  fc  L
The number of stars in the Milky Way is relatively well known … it’s approximately N* = 250  109 stars.
The age of the Milky Way is relatively well known … it’s approximately TMW = 10  109 years.
Thus ─ the rate of star formation in the Milky Way is ─ R* = N* /TMW = 250 x 109 /10  109 years = 25/yr.
Next … estimate f⨀

8. 33 Stars Within 12.5 LY
If we knew the distribution of stars as a function of mass (stellar mass distribution function) … then we could make a rough estimate of how many stars are like our Sun.

9. Stellar Mass Distribution
Number of stars n per unit mass
There are many more small stars in the galaxy than there are large stars!
Fraction of stars 0.5 < m <1.5 is f⨀ ~ 10% ... But should we include stars in binary systems?

10. N = R*  f⨀  fp  nE  fl  fi  fc  L
What about multiple star systems?
Stable orbits of planets in multiple star systems are almost impossible. Over time, the planet would either be ejected into space, crash into one of the stars, or be thrown into a highly elliptical orbit.
Unless the two stars are very far apart, binary stars cannot have planets. This eliminates perhaps half the sun-like stars in the sky … and there is one more problem.

11. Galactic Habitable Zone
Sun-like stars must fall within the Galactic Habitable Zone (GHZ)…
not way out from the galactic center in order to have enough ‘heavy’ elements to form planetary systems
not too close to the galactic center where stars are packed too close together and there is too much radiation.

12. N = R*  f⨀  fp  nE  fl  fi  fc  L
About 50% of the stars lie outside the GHZ, which eliminates them… so putting together all the factors …
f⨀ = x x =
The right mass
No binaries
In GHZ
Next up … fp … the fraction of sun-like stars that have planets.

13. N = R*  f⨀  fp  nE  fl  fi  fc  L
Most Sun-like stars form in hot, open clusters like the Orion Nebula and only about 10% of them form where there is enough dust to form planetary systems!
Thus, too little dust reduces fp by 90% … fp ~ 0.10

14. N = N*  f⨀  fp  nE  fl  fi  fc  fL
To support life, a planet must be in the habitable zone. nE ~ 1 for our solar system …
But current estimates of the thickness of the CHZ indicates that we were lucky and that a planet like Earth falling within the habitable zone has a chance as low as 1% . We’ll pick the geometric mean … nE ~ 0.10.

15. N = R*  f⨀  fp  nE  fl  fi  fc  L
If a planet forms within the HZ, chances are good that it will have liquid water and that some kind of life will emerge … it did on Earth.
Thus, we estimate fl ~ 1

16. Question
Life on Earth appears to have arisen quite easily and quite rapidly after the Earth became habitable. This suggests that the factor flife in the Drake equation—the probability that life arises on a habitable planet—could be close to _______.
1.0
0.25
0.5 10

17. N = R*  f⨀  fp  nE  fl  fi  fc  L
Does evolution inevitably lead to at least one intelligent organism on a planet? (fi=1)
For 2.5 billion years on Earth, life did not evolve past single-celled organisms. Is the development of complex (and intelligent) life rare? (fi<<1)

18. N = R*  f⨀  fp  nE  fl  fi  fc  L
There are other factors besides ‘forming within the CHZ’ that limit the evolution of intelligent life. For example … What if the Earth had no moon?

19. N = R*  f⨀  fp  nE  fl  fi  fc  L
Planets without large moons may have the direction of their spin axis shift over time. This may produce long term climatic shifts.
Mars
Million Years ago

20. N = R*  f⨀  fp  nE  fl  fi  fc  L
The tidal effect of the Moon may have helped trigger the convection on the Earth that led to the multi-plate tectonics!
Consider Venus, about Earth’s size, but no moon. The crust is like a lid that doesn’t move much horizontally, and the magma and heat are blocked by this lid on the surface. The Earth instead has rolling convective motion that drags the crust, and then the crust plunges back down into the mantle and gets recycled.

21. N = R*  f⨀  fp  nE  fl  fi  fc  L
If you would take away the Moon suddenly, it would change the global altitude of the ocean! Right now there is a distortion which is elongated around the equator, so if we didn’t have this effect, suddenly a lot of water would be redistributed toward the polar regions.

22. N = R*  f⨀  fp  nE  fl  fi  fc  L
The eyesight of many mammals is sensitive to moonlight. The level of adaptation of night vision would be very different without the Moon. Many of these species have evolved in such a way that their night vision could work in even partial lunar illumination, because that’s when they are most active. But they can be more subjected to predators, too, so there is a balance between your ability to see and your ability not to be seen. The Moon has completely changed evolution in that aspect.

23. N = R*  f⨀  fp  nE  fl  fi  fc  L
The Earth would be rotating more rapidly! The Sun does cause tides in the Earth's oceans, but its tidal effects are weaker than those of the Moon. The initial rotation period of the Earth was about 6 hours ─ without a Moon, it would have slowed to about 10 hours due to solar tides.
What consequences might follow from such a fast rotation?

24. N = N*  f⨀  fp  nE  fl  fi  fc  fL
What if the Earth had no 5 AU?
Devastating impacts would be more frequent!

25. Suppose a 10 km – sized asteroid did not strike the Earth 65 Mya …

26. The Dinosaurs Would Have Had Us for Lunch!

27. Suppose Western Science Never Emerged …
No other civilization ever pursued the idea of constructing mathematical models to explain the observed behavior of nature.
Given all these caveats … it appears that the evolution of intelligence is not a given! We guess fi ~ 0.1

28. Assuming primitive life emerges on a planet, why is the emergence of intelligence not a given, i.e., fi < 1? (We picked 0.1)
Question
It took ~4 billion years for intelligent life to emerge on Earth under favorable circumstances, which might be extremely rare.
The Earth acquired a sizeable Moon … by accident … that stabilized its axis of rotation, which established a stable environment for life for billions of years.
The Earth was close … but not too close … to a giant planet, Jupiter, that protected it from frequent devastating impacts.
If an impact hadn’t triggered the extinction of dinosaurs 65 million years ago, intelligent humans would never have evolved.
All of the above were contributing factors.

29. fc ~ 1 N = N*  f⨀  fp  nE  fl  fi  fc  fL
What fraction of intelligent life communicates? Some may not develop the technology to do so or it may choose not to do so…
fc ~ 1
This is hard to believe … if a civilization reaches the stage of ‘operational intelligence’ it is almost impossible to imagine that it will not develop the technology to communicate and will not wish to do so …

30. The Drake Equation N = R*  f⨀  fp  nE  fl  fi  fc  L R (per yr)
R* = Rate stars form in Milky Way
f⨀ = Fraction that are sun-like
fp = Fraction that have planets
nE = Number of planets within CHZ
fl = Fraction where life evolves
fi = Fraction that become intelligent
fc = Fraction that communicate
R* = 25/yr 25
f⨀ = 0.025
0.625
fp = 0.1
.0625
nE = 0.1
6.25 x 10-3
fl = 1
6.25 x 10-3
fi = 0.10
6.25 x 10-4
fc = 1
6.25 x 10-4
The rate at which intelligent, communicative civilizations form in the Milky Way is…
Rciv = 6.25 x 10-4 / yr and N = Rciv x L
The value of Rciv is highly uncertain … thus, it really makes no sense to quote the number to 3 decimal place accuracy, so we’ll round it off to Rciv ~ 10-3 /yr and N = Rciv L ~ 10-3 L
(L = ?)

31. N = N*  f⨀  np  fl  fi  fc  L
Earth spent the first 4.5 billion years of its life without hosting a civilization. Humans achieved the technology to communicate ~ 50 years ago. How long will we continue to exist ??
Extreme Optimistic Case: We continue as a civilization until the HZ moves beyond Earth :
L = 109 yrs and N = L = 1,000,000
Extreme Pessimistic Case: We destroy ourselves in the next 50 years:
L = 100 yrs and N = L = 0.1
The average lifetime of species is currently estimated to be ~ 1 ─ 10 Myr! Assuming that human longevity is no better than average, we’ll guess that L ~ 1 miilion years!

32. Other Estimates Factor Us ─ ET Class Drake-Sagan (Optimistic)
Trefil & Hart
(Pessimistic)
R* = N*/TMW
25 / yr
30 / yr
20 / yr f⨀
0.025
0.1
0.001 nE 1 fl
1.0
0.005 fi
1/3
0.0001 fC
Rciv
10-3 /yr
1 /yr
10-10 /yr L
1 million yr
1 billion yr
100 yr
N = Rciv L
1000
1 billion
10-8

33. How Many ET’s ?
Drake and Sagan ????
ET 1080 Estimate ????
N = 10-3 L