The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)
-
Upload
mathresources -
Category
Documents
-
view
110 -
download
3
description
Transcript of The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)
![Page 1: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/1.jpg)
The Drake Equation
![Page 2: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/2.jpg)
Does life existelsewhere
in the universe?
Pho
to c
ourt
esy
of
NA
SA
![Page 3: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/3.jpg)
And might there be other advanced civilizations out there?
Imag
es c
ourt
esy
of R
. Fem
mer
![Page 4: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/4.jpg)
What are the chances of technologically-advanced
civilizations elsewhere in the universe?
And how many such civilizations, if any,
might there be?
Imag
es c
ourt
esy
of R
. Fem
mer
![Page 5: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/5.jpg)
We don’t know yet……
Imag
es c
ourt
esy
of R
. Fem
mer
![Page 6: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/6.jpg)
But we can conduct a preliminary analysis using “The Drake Equation”
Pho
to c
ourt
esy
of
NA
SA
![Page 7: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/7.jpg)
The math that we will use is known as The Drake Equation
N = ( R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 8: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/8.jpg)
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 9: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/9.jpg)
The equation was originally developed by
Dr. Frank Drake
When he was professor of physicsand astrophysics at the
University of California, Santa Cruz
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 10: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/10.jpg)
What possibilities can its mathematics suggest?
![Page 11: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/11.jpg)
Drake’s Equation
We would like to estimate “N” – the
potential numbers oftechnologically
advanced civilizations
elsewhere in the universe
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
of
NA
SA
![Page 12: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/12.jpg)
Drake’s Equation
We would like to estimate “N” – the
potential numbers oftechnologically
advanced civilizations
elsewhere in the universe
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
The number will vary, of course, with different starting assumptions
Pho
to c
ourt
esy
of
NA
SA
![Page 13: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/13.jpg)
Drake’s Equation
We would like to estimate “N” – the
potential numbers oftechnologically
advanced civilizations
elsewhere in the universe
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s equation allows us to test alternateassumptions in a methodical and analytic way
Pho
to c
ourt
esy
of
NA
SA
![Page 14: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/14.jpg)
The good news is that the math itself will be done by this presentation
![Page 15: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/15.jpg)
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
We start with an estimateof the number of stars
Pho
to c
ourt
esy
of
NA
SA
![Page 16: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/16.jpg)
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Footnote: After completing this introductory presentation , we
could use Drake’s equation to test other estimates
such as the “fraction of stars with suitable characteristics” (not all stars are sun-like, for example)
We start with an estimateof the number of stars
Pho
to c
ourt
esy
of
NA
SA
![Page 17: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/17.jpg)
Fractionof stars that have
planets
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
of
NA
SA
![Page 18: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/18.jpg)
We can employ different estimates here to testthe effects if planets turn out to be extremely
common - or if they are comparatively rare
Fractionof stars that have
planets
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
of
NA
SA
![Page 19: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/19.jpg)
What fraction of planets areHABITABLE
(earth-like, for example)
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
of
NA
SA
![Page 20: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/20.jpg)
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Not all planets , for example, are likely to be suitable for life
We want only ‘earth-like’ planets or others whose conditions allow life to exist
What fraction of planets areHABITABLE
(earth-like, for example)
Pho
to c
ourt
esy
of
NA
SA
![Page 21: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/21.jpg)
What portion of habitable planets are actually inhabited
by LIFE-FORMS of any sort?
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Marine plankton
Yeast cells
Anything like these?
Artw
ork courtesy of R. Fem
mer
![Page 22: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/22.jpg)
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
What portion of INHABITED planetsinclude ‘intelligent’ life?
Pho
to c
ourt
esy
John
Mos
esso
, lif
e.nb
ii.g
ov
![Page 23: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/23.jpg)
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Tool-making? Mathematical? Technological?
On earth, there are multiple ‘degrees’ of
intelligence
Which organisms would satisfy the definition we would use? Chimps?
Dolphins? Only humans?
What portion of INHABITED planetsinclude ‘intelligent’ life?
Pho
to c
ourt
esy
John
Mos
esso
, lif
e.nb
ii.g
ov
![Page 24: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/24.jpg)
*
What fraction of planets with intelligent beings will also have
CIVILIZATIONS?
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
NA
SA
![Page 25: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/25.jpg)
*
What fraction of planets with intelligent beings will also have
CIVILIZATIONS?
And must they be technologically-advanced civilizations or not?
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
NA
SA
![Page 26: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/26.jpg)
We will be saving this factor for later
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
NA
SA
![Page 27: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/27.jpg)
Part Two
Let’s insert some numerical estimates and see what results we obtain
![Page 28: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/28.jpg)
Early analyses using Drake’s equation oftenemployed estimates of the number of stars
in the Milky Way galaxy
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
of
NA
SA
![Page 29: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/29.jpg)
Early analyses using Drake’s equation oftenemployed estimates of the number of stars
in the Milky Way galaxy
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
For this presentation, however, assume that an approximate number of stars in the entire universe is something like 1 x 10
This would mean that the value of R* would be100,000,000,000,000,000,000,000
total stars
23
Pho
to c
ourt
esy
of
NA
SA
![Page 30: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/30.jpg)
23If the number of stars present in the universe is 1 x 10
What if PLANETS are RARE and only
1/10th of 1% have planets?
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 31: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/31.jpg)
23If the number of stars present in the universe is 1 x 10
What if PLANETS are RARE and only
1/10th of 1% have planets?
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
31 out of 1 x 10
…1 out of 1,000…
![Page 32: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/32.jpg)
100 000 000 000 000 000 000 000
1000
Do the calculation1. x 10 23
![Page 33: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/33.jpg)
100 000 000 000 000 000 000 000
1000
Do the calculation
100 000 000 000 000 000 000
1. x 10 23
![Page 34: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/34.jpg)
100 000 000 000 000 000 000 000
1000
Do the calculation
100 000 000 000 000 000 000
1. x 10 23
1 x 10 divided by 1 x 10 = 1 x 10 23 203
![Page 35: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/35.jpg)
So if there are approximately 100,000,000,000,000,000,000 planets
What if EARTH-LIKE planets are rareand only 1/10th of 1% of planets are HABITABLE?
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Pho
to c
ourt
esy
of
NA
SA
![Page 36: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/36.jpg)
So if there are approximately 100,000,000,000,000,000,000 planets
What if EARTH-LIKE planets are rareand only 1/10th of 1% of planets are HABITABLE?
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
1 out of 1 x 10
…1 out of 1,000…
3
Pho
to c
ourt
esy
of
NA
SA
![Page 37: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/37.jpg)
100 000 000 000 000 000 000
1000
Do the calculation1. x 10 20
![Page 38: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/38.jpg)
100 000 000 000 000 000 000
1000
Do the calculation1. x 10 20
100 000 000 000 000 000
![Page 39: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/39.jpg)
100 000 000 000 000 000 000
1000
Do the calculation1. x 10 20
1 x 10 divided by 1 x 10 = 1 x 10
100 000 000 000 000 000
20 173
![Page 40: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/40.jpg)
1 x 10 divided by 1 x 10 = 1 x 10
100 000 000 000 000 000
20 17
100 000 000 000 000 000 000
1000
Do the calculation1. x 10 20
So this would suggest approximately 100,000,000,000,000,000
planets with conditions suitable for life
3
![Page 41: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/41.jpg)
![Page 42: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/42.jpg)
Even if, however, there were approximately100 000 000 000 000 000
habitable earth-like planets
What if development of LIFE on habitable planets is also RAREand only 1/10th of 1% of habitable planets are hosts to life ?
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 43: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/43.jpg)
Even if, however, there were approximately100 000 000 000 000 000
habitable earth-like planets
What if development of LIFE on habitable planets is also RAREand only 1/10th of 1% of habitable planets are hosts to life ?
*
Drake’s Equation
N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
1 out of 1000
![Page 44: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/44.jpg)
100 000 000 000 000 000
1000
Do the calculation1. x 10 17
![Page 45: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/45.jpg)
100 000 000 000 000 000
1000
Do the calculation1. x 10 17
100 000 000 000 000
![Page 46: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/46.jpg)
100 000 000 000 000 000
1000
Do the calculation1. x 10 17
100 000 000 000 000
1 x 10 divided by 1 x 10 = 1 x 10 17 143
![Page 47: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/47.jpg)
100 000 000 000 000 000
1000
Do the calculation1. x 10 17
100 000 000 000 000
1 x 10 divided by 1 x 10 = 1 x 10 17 143
So this would suggest approximately100,000,000,000,000
planets with some sort of life
![Page 48: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/48.jpg)
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
So if there are approximately 100 000 000 000 000
planets with life-forms of some sort,
What if INTELLIGENT life is a rare occurrence and only 1/10th of 1% of planets develop intelligent beings?
![Page 49: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/49.jpg)
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
So if there are approximately 100 000 000 000 000
planets with life-forms of some sort,
What if INTELLIGENT life is a rare occurrence and only 1/10th of 1% of planets develop intelligent beings?
…1 out of 1,000…
1 out of 1 x 10 3
![Page 50: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/50.jpg)
100 000 000 000 000
1000
Do the calculation1. x 10 14
Art
wor
k co
urte
sy o
f R
. Fem
mer
![Page 51: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/51.jpg)
100 000 000 000 000
1000
Do the calculation1. x 10 14
100 000 000 000
1 x 10 divided by 1 x 10 = 1 x 10 14 113
If correct, this would mean approximately100 000 000 000
planets with intelligent life
![Page 52: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/52.jpg)
ADVANCED CIVILIZATIONS
Photo courtesy of N
AS
A
![Page 53: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/53.jpg)
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
So even if there might exist approximately 100 000 000 000
planets that are home to some form of intelligent life,
What if ADVANCED CIVILIZATIONS rarely develop and only 1/10th of 1% of planets develop advanced civilizations
Drake’s Equation P
hoto
cou
rtes
y of
N
AS
A
![Page 54: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/54.jpg)
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
So even if there might exist approximately 100 000 000 000
planets that are home to some form of intelligent life,
What if ADVANCED CIVILIZATIONS rarely develop and only 1/10th of 1% of planets develop advanced civilizations
Drake’s Equation
…1 out of 1,000…
1 out of 1 x 10 3
Pho
to c
ourt
esy
of
NA
SA
![Page 55: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/55.jpg)
100 000 000 000
1000
Do the calculation1. x 10 11
Pho
to c
ourt
esy
of
NA
SA
Pho
to c
ourt
esy
of
NA
SA
![Page 56: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/56.jpg)
100 000 000 000
1000
Do the calculation1. x 10 11
100 000 000
Pho
to c
ourt
esy
of
NA
SA
Pho
to c
ourt
esy
of
NA
SA
![Page 57: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/57.jpg)
100 000 000 000
1000
Do the calculation1. x 10 11
100 000 000
1 x 10 divided by 1 x 10 = 1 x 10 11 83
Pho
to c
ourt
esy
of
NA
SA
Pho
to c
ourt
esy
of
NA
SA
![Page 58: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/58.jpg)
100 000 000 000
1000
Do the calculation1. x 10 11
100 000 000
1 x 10 divided by 1 x 10 = 1 x 10 11 83
So this would suggest the possibility of100 000 000
planets with technological civilizations
Pho
to c
ourt
esy
of
NA
SA
Pho
to c
ourt
esy
of
NA
SA
![Page 59: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/59.jpg)
![Page 60: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/60.jpg)
Think how amazing it would beif 100,000,000 planets
with civilizations actually exist
This seems very impressive
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
![Page 61: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/61.jpg)
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
Recall, however, this factor , which we deferred earlier
Can you guess what it is?
![Page 62: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/62.jpg)
Recall, however, this factor , which we deferred earlier
It is
…. time ….
Can you guess what it is?
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
![Page 63: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/63.jpg)
because our own planet has had dozens of great civilizations,but only over the last century do we meet a definition
of “technologically advanced” communicative civilizations
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
This factor is
…. time ….
and it is very sobering
For example, radio telescopes
![Page 64: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/64.jpg)
Thus, this factor ,
L , represents thepercentage
of a planet’s lifetime
that is marked by the presence of intelligent beingswith a technologically-advanced communicative civilization
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
Drake’s Equation
Images courtesy of R
. Femm
er
![Page 65: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/65.jpg)
If civilizations do not begin instantly,
take a long time to appear and develop,
and do not last forever
and only exist FOR TINY FRACTIONS of their planet’s total lifetime
![Page 66: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/66.jpg)
or for only a tiny portion of the totalelapsed time of the
universe itself
Pho
to c
ourt
esy
of
NA
SA
![Page 67: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/67.jpg)
Then we must divide once again
![Page 68: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/68.jpg)
Suppose that somehow 1 x 10 advanced civilizations manage to develop
If, however, they only exist for a 1 x 10 portion of their planet’s lifetime **
8
- 7
Then
1 x 10 8
1 x 10 71 x 10 1= = 10
Ear
th is
abo
ut 4
.4 b
illi
on y
ears
old
![Page 69: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/69.jpg)
1 x 10 8
1 x 10 71 x 10 1= = 10
Thus, given the estimates suppositions, and
assumptions that we haveused in this sample analysis
Just ten planets with technologically advanced civilizations
might exist ata particular moment in time
![Page 70: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/70.jpg)
Employing the estimates and mathematics used in
our example, there may be only TEN
other advanced civilizations
out there somewhere at this moment in time
![Page 71: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/71.jpg)
or there could be NONE at all
![Page 72: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/72.jpg)
we may be it…
![Page 73: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/73.jpg)
It makes you think - doesn’t it ?
![Page 74: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/74.jpg)
What responsibility does thisplace upon our shoulders?
![Page 75: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/75.jpg)
Pho
to c
ourt
esy
of
NA
SA
![Page 76: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/76.jpg)
![Page 77: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/77.jpg)
Footnotes
For convenience, this presentation assumed a 1/10 th of 1% probability for each factor in its discussion
But the percentages that one chooses to assign to each factor can and should be modified on the basis of humankind’s ever-increasing knowledge and understandings
For example, solar systems with multiple planets may not be rare at all, but may be very common so that the equation could be run again to reflect a much higher number of planets
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 78: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/78.jpg)
On the other hand, many stars are very different than our sun and may be unsuitable for sustaining life as we know it
In that case, the value that that we assign to factor R* should probably be adjusted
We could adjust R* downward, for example, by adding a factor fs to the equation to incorporate a “fraction of suitable stars” into our estimates
Footnotes
*N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*
![Page 79: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/79.jpg)
Footnotes
Many scholars and authors have utilized and discussed Drake’s equation
A web search of books and other resources will reward viewers of this presentation with many additional insights concerning its implications and applications
Particular credit should go to Frank Drake, however, and his fellow astronomer Carl Sagan
![Page 80: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/80.jpg)
Made available courtesy of
The Wecskaop ProjectWhat Every Citizen Should Know About Our Planet
Images courtesy of R
. Femm
er
![Page 81: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/81.jpg)
Images courtesy of R
. Femm
er
![Page 82: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/82.jpg)
Images courtesy of R
. Femm
er
![Page 83: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/83.jpg)
Images courtesy of R
. Femm
er
![Page 84: The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)](https://reader033.fdocuments.net/reader033/viewer/2022061119/546a871eb4af9f8c7d8b4cf1/html5/thumbnails/84.jpg)