Radio Signal From Alien

8/3/2019 Radio Signal From Alien

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Calculating the probability of detecting radio signals from alien civilizations

Marko Horvat11Faculty of Electrical Engineering and Computing, University of Zagreb

Unska 3, HR-10000 Zagreb, CroatiaE-mail: [email protected]

Abstract.Although it might not be self-evident,it is in fact entirely possible to calculate the

probability of detecting alien radio signals byunderstanding what types of extraterrestrial

radio emissions can be expected and what properties these emissions can have. Using the Drake equation as the obvious starting point,

and logically identifying and enumeratingconstraints of interstellar radio communicationscan yield the probability of detecting a genuinealien radio signal.

Keywords: SETI, extraterrestrial intelligence,extraterrestrial communication, extraterrestrial

life, interstellar communication, extraterrestrialradio waves, Drake equation, cosmology

1. Introduction

The primary goal of SETI (Search forExtraterrestrial Intelligence) projects is toreceive a signal from an extraterrestrialcivilization. Today, SETI projects predominantly listen to radio signals, although

there are also SETI projects that search foroptical [1] [2] [3] [4] and microwave [5] [6]

electromagnetic frequencies.The possibility of detecting an alien

electromagnetic signal other than the radio oneis not explicitly elaborated in the article but the

same principles and algebra apply to all types of

electromagnetic signals.Strictly speaking, all the signals that an aliencivilization could transmit can be divided intotwo distinct categories: a) intentional signalswhich are meant for our civilization and aredeliberately sent towards the Earth; and b)unintentional signals which are not really meantfor our civilization they are only accidentallydirected towards the Earth. The intentionalsignals could also be called deliberate and the

unintentional random orinvoluntary signals.

A clear example of an intentional radio emissionis the well-known message sent in 1973 from

Arecibo radio-telescope towards the M13

globular cluster. Examples of unintentional radioemissions are much more common they areour own radio and TV signals; and of course, allother electromagnetic emissions produced by

radars, microwave communications, etc. Thesesignals are emitted constantly, indiscriminately

and equally in all directions. They are notdirected towards a specific celestial coordinateand their emitting strength is determined by themean sensitivity and distance of a radiolistener or a TV viewer.

As we compare these two types or categories ofsignals, it is obvious that unintentional signals

are much, much weaker in strength than theintentional electromagnetic emissions, but they

have far longer duration. In a nutshell, it can besaid that intentional radio emissions are

relatively strong but brief signals directed at a

specific point in space, and the unintentionalradio emissions are weaker but also longerlasting signals directed everywhere, toward all

points in space equally. The properties of bothtypes of signals are listed in Table 1.

It is important to understand that it is ratherunlikely that intentional alien radio signals could be constantly emitted over a significantly long period of time, i.e. a few decades or centuries, because that would be an extremely power and

resource consuming endeavor. More so, if suchan altruistic alien civilization would want to

cover a number of star systems with itsintentional signal.An evolved alien civilization that woulddeliberately and constantly send radio messages

toward solar systems potentially harboringintelligent life is really hard to imagine,especially if the civilization discovered how toefficiently travel and communicate over

interstellar distances. This would also make thealtruistic civilization extremely impractical. But

although such a civilization is practicallyimprobable, it is still theoretically possible.


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However, the conclusion is that if we ever wereto receive a radio message from an aliencivilization, it would most likely be a type ofunintentional radio signal. The probability ofreceiving an intentional radio signal is far

smaller and harder to calculate, since itsparameters are, at this point in the development

of our astronomy and astrobiology, dependanton subjective analysis.

Further, it should also be pointed out that radiois not the best way to communicate over large

interstellar distances. It is slow, liable totransmission errors and, due to usage ofrelatively long frequencies, radio cant carry alot of data. Therefore, it is logical to assume that

a constantly developing civilization, such asours, will eventually discard radio as means of

communication, or at least largely minimize itsuse. We already know of several better methodsof communication, like fiber-optic cables ordirectional lasers which are very difficult orentirely impossible to detect over interstellar

distances. So, it is quite probable that, at somepoint in every civilizations development, all its

radio emissions will completely stop. This will

make the civilization totally radio silent andthus completely undetectable by the SETI

projects.All propositions described above can be

summarized in the following conclusions:1. If we ever receive an alien radio signal, it is

unlikely that the signal will be meantspecifically for us. It is far more likely that

this signal will be a random aliencommunication.

2. There is a specific time interval duringwhich an alien civilization uses radiocommunications. Before this interval, radiois beyond the civilizations technical reach,and after this interval radio will be

considered obsolete. We have to be listeningwith our radio telescopes during this period

of the alien civilizations development toreceive their radio signal.

3. It is necessary to define a strictly definedvolume of space in which alien radio

transmissions are strong enough to be pickedup. The Earth, i.e. our radio receivers, must

be inside this volume of space in order to beable to detect alien signals.

All reasoning about other civilizations has tostart from observations of the only alien

civilization we know of our own. Simply put,

humankind is the only civilization that we knowof and the only test subject upon which we canmodel the behavior of other civilizations thatmight exists in the Universe. Other paths ofcivilization development, concerning interstellar

communications in particular, are entirelypossible, but we have to ask ourselves which isthe most probable? And, the answer lies insimple logic and basic common sense.

2. Defining the variables

As was explained in the introduction, it isassumed that all civilizations cant and dont useradio during their entire existence. Surely, it

would be very difficult to imagine a civilizationthat along with invention of fire and wheel also

invents coil, capacitor, resistor, radio antennaeand the entire science of electronics. Therefore,it should be assumed that an average time ofcivilization radio usage must exist. This timeinterval will be called tcomm. In line with this

thinking, it is also quite reasonable to assumethat civilizations don't last forever but that they

all have certain average life span tciv.Naturally, tcomm can never be larger than tciv:

Rtcomm

Rtciv

civcomm tt

10 civ

comm

t

t

(1)

This time ratio is very important. It will be

denoted as ft. The time ratio describes the probability that our civilization is searching the

skies for a radio signal while an alien civilizationis indeed transmitting its radio signals.

[ ]1,0=civ

commt

t

tf (2)

Due to limitations of radio communicationtechnologies over interstellar distances thereduction of electromagnetic signal strength is

directly proportional to the square of thedistance traveled and limited sensitivity of ourradio receivers, signals emanating from an aliencivilization could only be detected within a

certain radius around the alien radio transmitter.


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Therefore, it is necessary to introduce anothervariable called Vcomm that describes the volumeof space around the alien radio transmitter inwhich its signal is detectable. Obviously, ifsensitivity of the receiver is better or if the signal

is stronger, volume Vcomm is larger. Since radioreceivers can never be 100% perfect, a technical

impossibility, the receivers will never be able toreceive an infinitely weak signal. The

consequence is that Vcomm will always have afinite size that influences the probability of alien

signal detection.Vcomm of the intentional radio signal can greatlyvary with the signals emitting strength. It ishard to predict mean strength of a radio signal

deliberately sent to us. Perhaps it might be verystrong, perhaps not. Perhaps the Earth can sit

right in the middle of the signals path, perhapsnot. On the other hand, Vcomm of unintentionalradio signals, because they would be omnidirectional, depends exclusively on the meansensitivity of our own receiving antennas and the

predicted average strength of alien unintentionalsignals. In order to get the latter value, we can

use the average emitting strength of our own TVand radio signals.

Along with Vcomm we must also consider astrictly defined volume of space, e.g. a galaxy, a

cluster of galaxies, the entire Universe, in which

alien civilizations could exist. This volume ofspace is denoted by Vspace and all civilizationsthat we might detect are located in it.

Since electromagnetic waves spread through 3-dimensional space in spheres, it is possible to

use simple geometric formula for the volume ofa sphere and describe Vcomm and Vspace by theirrespective radiuses rcomm and rspace:

RVcomm

RVspace

3

commr3

4=commV

3

spacer3

4=spaceV

(3)

The mutual relationship of Vcomm and Vspace can

also be determined:

spacecomm VV

10 space

comm

V

V

(4)

By substituting (4) with radiuses rcomm and rspacewe get the following:

spacecomm rr33

103

3

space

comm

rr (5)

Now, it is possible to define another importantratio, volume ratiofv, as:

[ ]1,03

3

=space

comm

vr

rf (6)

The volume ratiofv describes the probability that

an alien civilization is close enough to the Earthfor its signals to be detected with our radioequipment.The volume ratio can be visualized as in Figure

1. In this figure, the Earth is shown at the centerof an imaginary sphere in space, while two solar

systems with alien civilizations are within ourrcomm and thus detectable. Three solar systems

are outside our communications range andcannot be detected. One solar system with an

alien civilization is outside of the scope ofinterest, i.e. further away than rspace.

As we move on with the analysis of interstellarcommunications between different civilizations,

we must also keep in mind that at each momentin time Nac alien civilizations can occupy the

same volume of space Vspace. Theoreticallyspeaking, we could contact any number of thesecivilizations: one, two, several, or even none.The value ofNac is calculated with the well-known Drake (or Drake-Sagan) equation [7]:

Lcilepc ffffnfNN *= (7)

The number of currently existing alien

civilizations Nac is simply the number of allcivilizations minus one, i.e. with our humancivilization omitted:

1= cac NN (8)

A very important feature ofNac is that it is aconstant. This is guaranteed by the premise of

the Drake equation: the average number ofcivilizations in a galaxy always remains the

same. If a civilization dies out and vanishes, it is


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immediately replaced by a new civilizationalthough at an inferior level of technicaldevelopment.After we have summed up and defined all pertinent variables, we can formulate the

probability function that describes the detectionof radio signals from alien civilizations.

3. Calculating the probability

The probability that we want to calculate in

this article, i.e. the probability of detecting radiosignals from any alien civilization, will besimply called p. In order to get p, we must takefew preliminary steps and determine several

other probabilities that will eventually lead us toour final goal.

First, we must calculate the probability ofreceiving a signal from exactly one aliencivilization. This probability will be denotedp.It consists of two other probabilities which arecalculated by mathematical ratios described in

the previous section time ratio ft and volumeratiofv as in (9):

vtffp = (9)

In probabilitypwe are imagining a sphere as in

Figure 1 where the Earth is located at the centerof the sphere and exactly one alien civilization is

somewhere inside Vcomm. We are also taking intoaccount the time factor and considering onlythose alien civilizations that are using radio atthe same time as we, the listeners, are.

The reasoning behindpcan be interpreted likethis: if exactly one alien civilization using radiois in our communications range, than we shallcertainly have an opportunity to detect itsometime during the existence of ourcivilization.

Now whenpis known, it is possible to find outthe probability that we will never detect radiosignals from one alien civilization. This

probabilityp

is the exact opposite ofp:

pp = 1 (10)

Using the equation above, we can calculate theprobability p

that we will neverdetect signals

from Nac alien civilizations. We simply have torepeat the stochastic event pNac times:

acNpp = (11)

As can be seen, p

gets smaller when Nac gets

bigger. This is exactly what should be expected; probability that we will never detect even a

single alien civilization decreases if there aremore alien civilizations to detect. The decreaseis exponential. The more alien civilizations are

out there, the less likely it is that we wont detectany of them.

At this point our mathematical apparatus isalmost complete for the construction of theequation calculating the final probabilityp.The probability of detecting signals from alien

civilizations is equal to the probability ofdetecting a signal from at least one alien

civilization. And this probability is our goal. Wecan detect signals from any number of

civilizations, but signals from just onecivilization will also do the trick quite nicely.

To contact at least one alien civilization meanscontacting 1, 2, 3, ... , n, n + 1 (n is a wholenumber greater than zero) civilizations. Inmathematical and logical terms, the exactopposite ofat least one is none. Since (11) gives

the probability of detecting none aliencivilizations, the probability p of detecting atleast one alien civilization, is obtained by

logically, and probabilistically, negatingp

:

pp =1 (12)

Individual occurrences of probability p (9) are

independent of each other. Or, in other words,the existences of different alien civilizations are

mutually independent their existence is neithercaused nor affected by each other. Because ofthis, p has a binomial distribution [8], [9] and itis possible to construct the mathematical

expression below:

0)1(1 ppN

Np ac

N

civ

civ

= (13)

The equation above using binomial distributionfor the reoccurrence of independent stochastic

events, describes the probability that a SETIproject, which scans all radio frequencies all thetime, will detect a random signal from at leastone and at the most,Nac alien civilizations.


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This is almost exactly what we want to get, butthere is one more step to make or two as isdescribed in the next section. But first (13) hasto be reduced with two simple expressions:

1=

ac

ac

NN

1)1( 0 =p

(14)

And now, by introducing (9), (10) and (11) into

(13), we get the equation which describes theprobability of detecting radio signals from aliencivilizations:

( ) acNvtffp = 11 (15)(15) calculates the probability that an ideal SETI

project, which scans the entire sky on allfrequencies, will detect radio signals from an

alien civilization. The equation can be appliedfor both unintentional and intentional types of

signals.

4. Refining the probability

Two more restrictions must be introduced in

(15) to make it realistic, practical and trulyapplicable. The first restriction concerns the

number of scanned wavelengths or frequencies,and the second restriction is related to thenumber of extra-solar systems that a SETIproject observes during its operation.

Ideally, if a SETI project observes allwavelengths that alien civilizations could use for

interstellar communications, there are norestrictions or limitations. Obviously, in the

search for extraterrestrial radio signals, we mustlisten on as many radio channels as possible

preferably, on all. But if only a part of availablewavelengths is observed, as is the case with anyrealistic situation, then, this wavelength problemdoes exist and it reduces the probability in (15)This restriction is called thewavelength ratiof:

[ ]1,0

f (16)

The ratio can be calculated discretely or

continuously depending on how the wavelength problem is defined. The simplest way to

calculatefis to divide the length of the spectrumof all wavelengths observed by the SETI project

( o ) with the spectrum length of all

wavelengths that alien civilizations use for radio

communication ( c ):

c

of

= (17)

The discrete way of calculatingf is analogous tothe previous equation but, instead of thecontinuous length, the number of respectivewavelengths is used:

c

of

= (18)

o is the number of all observed wavelengths

and c the number of all wavelengths used for

alien radio communications.In both equations, the following relationshipsapply:

co

10

c

o

co

10 c

o

Determining the true value of c can be tricky

since we can only make educated guesses. A

very rough, but a practical estimate for c is 1,

which takes into account only the famous

wavelength of neutral hydrogen at 21cm. Moreprecise estimates of c will increase its value.

The same applies to c .

The second limitation to the probability in (15)

is in many ways similar to the wavelength ratio.As an example, it is easy to imagine that an alienradio signal, continuous and unintentional orintermittent and intentional, reaches the Earth,

but we cant hear it because our radio antennasare directed elsewhere. This premise is well-

known and the rationale how to counter it is

built into every SETI project: Have more radio


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telescopes, scan as much sky as possible andincrease the likelihood of detecting alien radiosignals. As a compromise to scanning everyvisible star in the sky (obviously a verydemanding task) an educated guess can be made

and only those extra-solar systems where lifecan thrive are scanned. Of course, to be valid,

this guess has to have a reasonable degree ofcertainty. A perfect, but impossible, SETI

project would scan the whole sky. Only then, itcould be guaranteed that no signal has been

overlooked.The second limitation to (15) is thearea ratiofA:

[ ]1,0Af (19)

The area ratio can also be calculated

continuously, taking into account the sky areaitself, or discretely, by counting the number ofobserved extra-solar systems. Thinkingcontinuously, we take the area of sky observed

by a SETI project ( oA ) and divide it with the

area of the entire sky ( cA ):

c

oA

A

Af

= (20)

In discrete terms, we will use the number ofextra-solar systems that are observed by the

SETI project ( oA ) and divide it with the

number of solar systems where alien

civilizations can exist ( cA ). As with f and

parameters c or c , one is more or less in

the dark when trying to establish the true value

of cA .

c

oA

AAf = (21)

Since both restrictions, f and fA, affect allobservations equally, they are applied to the joint probability ofp in (15), and not to theprobability p of the signal detection of anindividual alien civilization (9).

Finally, after applying f and fA to the (15), itrealistically describes the probability of

detecting radio signals from an alien civilization:

( )( )acNvtA ffffp = 11 (22)(22) gives the probability that a realistic SETI

project, which scans only a portion of the sky ona finite number of frequencies, will detect radio

signals from an alien civilization. The equationcan best be applied to unintentional, and onlytheoretically, to intentional type of signals.Changing the value of either factorf orfA must be done very carefully since they have a big

impact on the final value of the probability ofdetecting unintentional alien radio signals p. In

order to simplify matters and maximize p, wecan assume f = 1 and fA = 1. Although thisrepresents only the best possible situation that ishardly achievable, it can be used to set the upper

limit ofp.Perhaps the last, but certainly not the least

important fact about the parameters in (22),, isthat they fall into two distinct categories:

variables and constants. We, the observers, caninfluence values off, fA and fv but we cannot

modifyft andNac. The latter two parameters are preset and cannot be affected by observers.Therefore, it can be said that f, fA and fv arevariables, andft andNac are constants.

5. Applying the figures

Let's take a set of different values and applythem to (22).The result is in Table 2.

The table is divided into 4 sections, each with 5cases, with the case 15 being the near-optimum

case. First three sections cover variations intcomm, tciv, rcomm, rspace andNac parameters leadingto the best case. The last section in Table 2 testshow variations inf andfA affect the best case.The first five cases in the table take modestvalue fortcomm of only 500 years, rspace is roughlyequal to the radius of our galaxy and rcomm is a

realistic 1/5th

of rspace. Nac is conservative,ranging between 5 and 30 alien civilizations inthe galaxy while tciv varies between 4 millionyears and 500 000 years. As can be seen, these

figures give a very small, almost negligible,probability p. The primary reason is long

civilization lifespan and short usage of radiotechnology. Improving our detectioncapabilities would also improve the wholepicture.

The cases marked 6 to 10 introduce morevariations in figures of the first five cases. tcomm

is increased to 1000 years, ratio of rcomm and


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rspace is and it is assumed that the number ofalien civilizations in our galaxy is larger, varyingfrom 60 to 140. However, these cases also yielda very low probability of detecting alien signals

p. A small tcomm / tciv ratio has the greatest

negative impact and is the main reason of lowpwhich, even increased value of Nac, cannot

overcome. Only the 10th

case has a noticeablep but that dictates a very high number of alien

civilizations in the galaxy (140). Since they havea lifespan of 500 000 years, it means that a great

number of civilizations would have to beapproximately at the same development level an interesting implication.The third set of cases (11-14) assumes relatively

high value of 2500 years for tcomm and shortvalue of 250000 years for tciv . The ratio rcomm /

rspace is perfect 1.0. Nac is reasonable, rangingbetween 10 and 100. This set of cases finally has

a significant p: 10% - 65%. Only this setrepresents successful SETI projects withtangible success factor. It is good to know whatare the prerequisites of such SETI projects.

The 15th

case should represent a desirableoptimum: 300 alien civilizations, our receiversare perfect, tciv is short and tcomm is long. Thiscase gives a near 100% success rate. This is

certainly very appealing from the standpoint ofany SETI project. But the most interesting thing

demonstrated in the 15th

case is the exponentialdependence ofp to Nac: Nac = 100 gives p =63.397%;Nac = 150, p = 77.855%;Nac = 200, p= 86.602%;Nac = 250, p = 91.894%,Nac = 300,

p = 95.096%;Nac = 350,p = 97.033%; andNac =

400, p = 98.205%. With 200 or 250 aliencivilizations using radio in our communication

range, we can be almost completely certain thatwe will pick up at least one of them.Finally, the last set (cases 16-20) works with the best cases (11-15) and experiments with

different values offandfA in an attempt to give

them a realistic outline. The last set of caseslooks promising: the lowest probability is about0.3% while the highest is over 50% (53.491%)

The result in Table 2 can be broadly commentedon like this: the probability of detecting alien

civilizations by SETI projects can be either verysmall or very high. Minute variations in theequations parameters have a great influence onthe final probability.The highest probability of contact is achieved in

the scenarios with many alien civilizations thathave comparably short life spans and long usage

of radio communications. At the same time, ourlistening techniques have to be near perfect.The reasons behind this optimum probability areunderstandable; compared with their lifetime,civilizations always have relatively short radio-

communication status. If there are a lot of them,in other words if they die rather quickly and

are replaced with new civilizations, then, atevery point in time, there is a fair number of

them that are using the radio. Long-livedcivilizations pass their radio-communication

status and still remain inNac but are undetectableby radio. In some respect, they are occupying a place inNac where some younger and radioactive civilization might sit.

It is somewhat paradoxical that we should beopportunistic for short-lived alien civilizations,

when at the same time, we want to learn moreabout them.

6. Conclusion

When knowing the probability of contactingaliens with our radio telescopes, one very logical

question immediately pops up: when will ithappen? In order to answer this important

question, we have to look at the only time factorin the whole equation ft. This ratio cannot yield

the exact time when the event would occur

because it describes only the overlapping, orsynchronization, of radio usage by our twocivilizations. There is no moment in time

embedded in the ratio. Therefore, it becomesobvious that the exact date of contacting aliens

remains unknown. We may contact themtomorrow, maybe in a hundred years, or maybeit will take even longer. Furthermore, the timeratio ft represents an average value. It variesfrom one civilization to another, and with our

current knowledge of astrobiology, we can onlyspeculate about its exact value. In fact, it would

be reasonable to assume thatft follows Gaussiandistribution.The probability of radio-contacting aliencivilizations consists of two disjunctive subsets:

the probability of receiving intentional aliensignals and the probability of receivingunintentional alien signals. The detection probability of intentional signals is assumed to

be negligible or zero, and this article focusedonly on the unintentional signals. Since

unintentional signals are emitted non-stop, andnot only during 73 seconds, like the intentionalArecibo radio message, another major and


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unpredictable time constraint defining themessages duration could have been taken out ofthe final (22). At this point in our development,we have to concentrate our efforts on detectingthe involuntary alien emissions, e.g. the alien TV

and radio. Only with these types of signals, it isrealistically possible to make an educated guess

about their detection.As our science, especially astronomy and

astrobiology, undoubtedly evolves, we shallcertainly be capable to understand better all the

factors behind the probability of detecting radiosignals from alien civilizations. We shall be ableto refine the probability, improve it, and finallybuild upon it to gain more knowledge about our

galactic surroundings and the Universe we areimmersed in.

7. References

[1] Lampton, M. (2000). Optical SETI: The NextSearch Frontier, Bioastronomy 99: A New Era in

the Search for Life.

[2] Howard, A. & Horowitz, P. & Coldwell, C.AN ALL-SKY OPTICAL SETI SURVEY,

Department of Physics, Harvard University,Cambridge, MA 02138 USA.

[3] Howard, A. & Horowitz, P. (2001). OpticalSETI with NASAs Terrestrial Planet Finder,Department of Physics, Harvard University,

Cambridge, MA 02138, USA, Icarus 150, 163167 (2001).

[4] Kingsley, S. A. & Bhathal, R. (2001). TheSearch for Extraterrestrial Intelligence (SETI) in

the Optical Spectrum III, Proceedings of SPIE,Vol. 4273, pp. 173-177.

[5] Comparing Five Current Microwave SETI

Projectshttp://www.setileague.org/general/compare.htm

[6] Microwave SETIhttp://asrg.contactincontext.org/seti/microwave

%20seti.html

[7] Sagan, C. & Drake, F. (1975). The search forextraterrestrial intelligence, Scientific American,vol. 232, May 1975, pp. 80-89.[8] Evans, M. & Hastings, N. & Peacock, B.

(2001). Statistical Distributions, Third Edition,Meas. Sci. Technol. 12 117, New York: Wiley,

pp. 221.

[9] Skellam, J. G. (1948). A ProbabilityDistribution Derived from the BinomialDistribution by Regarding the Probability of

Success as Variable Between the Sets of Trial,Journal of the Royal Statistical Society. Series B

(Methodological), Vol. 10, No. 2, pp. 257-261.


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8. Tables

Signal type

Unintentional Intentional

Meanstrength Low Low/Medium/High

Directed No YesContaining

specificinformation

No Yes

Duration Long Short

Attributes

Detectionpossibility

Low/Medium/High Low

Table 1 Comparing types of alien signals

1 2 3 4 5 6 7 8 9 10

tcomm 500 500 500 500 500 1.000 1.000 1.000 1.000 1.000tciv 4.000.000 2.000.000 1.000.000 750.000 500.000 4.000.000 2.000.000 1.000.000 750.000 500.000rcomm 10.000 10.000 10.000 10.000 10.000 25.000 25.000 25.000 25.000 25.000rspace 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Nac 5 10 15 25 30 60 80 100 120 140f 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000fA 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000

p 0,012% 0,050% 0,150% 0,333% 0,598% 0,747% 1,980% 4,878% 7,691% 13,070%

11 12 13 14 15 16 17 18 19 20

tcomm 2.500 2.500 2.500 2.500 2.500 2.500 2.500 2.500 2.500 2.500

tciv 250.000 250.000 250.000 250.000 250.000 250.000 250.000 250.000 250.000 250.000rcomm 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000rspace 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Nac 10 40 80 100 300 10 40 80 100 300f 1,000 1,000 1,000 1,000 1,000 0,250 0,500 0,750 0,750 0,750fA 1,000 1,000 1,000 1,000 1,000 0,125 0,250 0,250 0,500 0,750

p 9,562% 33,103% 55,248% 63,397% 95,096% 0,299% 4,138% 10,359% 23,774% 53,491%

Table 2 Probability of detecting radio signals from alien civilizations


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9. Figures

Figure 1 Two-dimensional visualization of the volume ratio

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Radio Signal From Alien