The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)

The Drake Equation

Does life existelsewhere

in the universe?

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And might there be other advanced civilizations out there?

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What are the chances of technologically-advanced

civilizations elsewhere in the universe?

And how many such civilizations, if any,

might there be?

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We don’t know yet……

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But we can conduct a preliminary analysis using “The Drake Equation”

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The math that we will use is known as The Drake Equation

N = ( R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

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)*

What possibilities can its mathematics suggest?

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)*

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Drake’s Equation





N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

The number will vary, of course, with different starting assumptions

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Drake’s Equation





N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

Drake’s equation allows us to test alternateassumptions in a methodical and analytic way

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The good news is that the math itself will be done by this presentation

Drake’s Equation

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

We start with an estimateof the number of stars

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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

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Fractionof stars that have

planets

Drake’s Equation

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

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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)*

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What fraction of planets areHABITABLE

(earth-like, for example)

Drake’s Equation

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

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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)

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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?

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ork courtesy of R. Fem

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Drake’s Equation

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

What portion of INHABITED planetsinclude ‘intelligent’ life?

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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?

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What fraction of planets with intelligent beings will also have

CIVILIZATIONS?

Drake’s Equation

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

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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)*

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We will be saving this factor for later

*

Drake’s Equation

N = (R ) ( fp ) (ne) ( fl ) ( fi ) ( fc ) ( L)*

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Part Two

Let’s insert some numerical estimates and see what results we obtain

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)*

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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

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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)*

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…

100 000 000 000 000 000 000 000

1000

Do the calculation1. x 10 23

100 000 000 000 000 000 000 000

1000

Do the calculation

100 000 000 000 000 000 000

1. x 10 23

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

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)*

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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

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100 000 000 000 000 000 000

1000


100 000 000 000 000 000 000

1000


100 000 000 000 000 000

100 000 000 000 000 000 000

1000


1 x 10 divided by 1 x 10 = 1 x 10

100 000 000 000 000 000

20 173

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


So this would suggest approximately 100,000,000,000,000,000

planets with conditions suitable for life

3

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)*

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

100 000 000 000 000 000

1000


100 000 000 000 000 000

1000


100 000 000 000 000

100 000 000 000 000 000

1000


100 000 000 000 000

1 x 10 divided by 1 x 10 = 1 x 10 17 143

100 000 000 000 000 000

1000


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

*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?

*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

100 000 000 000 000

1000


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100 000 000 000 000

1000


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

ADVANCED CIVILIZATIONS

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*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

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*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

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100 000 000 000

1000


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100 000 000 000

1000


100 000 000

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100 000 000 000

1000


100 000 000

1 x 10 divided by 1 x 10 = 1 x 10 11 83

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100 000 000 000

1000


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

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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

*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?

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

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

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

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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

or for only a tiny portion of the totalelapsed time of the

universe itself

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Then we must divide once again

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 **

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Then

1 x 10 8

1 x 10 71 x 10 1= = 10

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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

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

or there could be NONE at all

we may be it…

It makes you think - doesn’t it ?

What responsibility does thisplace upon our shoulders?

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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)*

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)*

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

Made available courtesy of

The Wecskaop ProjectWhat Every Citizen Should Know About Our Planet


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The Mathematics of Drake's Equation - Planets, stars, and life elsewhere? (ppt presentation)

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