Beyond the Drake Equation


In 1961, astronomer Frank Drake proposed a method of estimating the number of civilizations in our Galaxy that could be detectable from Earth. He wrote it as an equation, but it may be more useful to think of it as a series of questions: How many stars are born every year? What fraction of them have planets? How many planets does each such star have? What fraction of those planets can support life, and of those, how many planets actually give rise to life? What fraction of those living planets give rise to intelligent beings? And of all those planets with intelligent beings, what fraction will produce radio transmissions that would allow us to notice them, and how long would they continue to transmit them?

These questions have definite answers; we just don't know what most of those answers are. But the answers to these questions are not beyond our reach. As we build better and better telescopes, and as we learn more and more about our own origins and that of our planet, the answers to these questions will gradually be revealed. We may know many of the answers within the next ten to twenty years.

Even back in 1961, it was obvious that these were answerable questions, so a group of scientists and engineers gathered together to discuss the possibility of using astronomical techniques to search for evidence of intelligent life beyond the Earth. They have become known as The Order of the Dolphin.

They made educated guesses about the answers to each of these questions, and tried to place reasonable upper and lower bounds on the value of each corresponding term of the Drake Equation. Since they had little direct observational evidence to support their views, they had to rely on their considerable experience in the fields of science relevant to these questions, such as astronomy, chemistry, and biology. And although their estimates were based primarily on theoretical arguments, they are still widely used almost four decades later; all our explorations since then have not led to any major disagreements with the ranges of values they determined.

The Order of the Dolphin chose to concentrate on searching for civilizations that are similar to our own, those that reveal their presence by making radio transmissions. But no attempt was made to ask questions about civilizations that are much older than ours, because such questions did not seem relevant to the astronomical searches they were proposing, and perhaps because at that point our collection of known examples drops from one to zero.

Soon we will be making increasingly accurate measurements of many of the terms, removing much of the uncertainty. So it seems appropriate to investigate ways of going beyond the original Drake Equation, to make educated guesses about the civilizations that may have already passed beyond the technologically adolescent phase where we are now.

This page includes a calculator, where you can try out your own educated guesses about the answers to each of the questions considered here, and see where your guesses take you.

Popular values have already been entered in all of the boxes, but you can change any or all of them. Enter values as decimal digits, with or without a decimal point. Be careful; if you enter zero for any term in the Drake Equation, you are saying that we ourselves cannot exist.

You can also enter values using floating point notation: for example, 2e-3 = .002, 5e6 = 5000000, and so on.

If you type in something that isn't a number, or leave a box blank, your browser will probably give you some kind of error message.

If you are using an older browser, the calculator may not work. But the page should look very much the same, so you can do the calculations manually.

This page contains many links to other pages. If you follow any of these links and then come back to this page, your browser might forget any numbers you may have already entered here, and if so, you would have to re-enter them. Links that lead away from this page (and which may open a separate window) are marked like this: away


This is the equation Frank Drake wrote on the blackboard in 1961:


N = R fp ne fl fi fc L


Each term to the right of the equals sign represents one of the questions we asked earlier:

R is the rate of star formation within the Galaxy, expressed in stars per year;

fp is the fraction of stars that form planets;

ne is the average number of planets each such star possesses, which are capable of supporting life;

fl is the fraction of those planets where life actually occurs;

fi is the fraction of life-bearing planets where intelligence arises;

fc is the fraction of intelligent life-bearing planets where intelligent beings develop the ability to communicate beyond their own world; and

L is the length of time, in years, that such communications remain detectable.


By estimating values for each of these terms and multiplying them together, one arrives at:


N, the estimated number of detectable civilizations.


We begin with:



How many stars form each year within the Milky Way Galaxy? The Order of the Dolphin estimated that about one new star is born every year. This is an observable quantity, and astronomers are reasonably certain that this value is close to the correct one, but many tend toward higher values, perhaps ten to twenty stars per year. More details...

Your estimate (stars per year):

R =



What is the fraction of stars that form planets? The Order estimated between one fifth (0.2) and one half (0.5); until recently, there was little observational data to help with this number, and there still isn't very much. (And for all the terms after this one, there is essentially no data, so other methods were used to arrive at numbers.) More details...

Your estimate (must be between 0 and 1):

fp =



How many planets does each stellar system contain, which are capable of sustaining life? The Order estimated between one and five. However, recent results indicate that our Solar System may be uncommonly rich in the heavy elements that are necessary for chemistry-based life-forms, so perhaps a lower number may be appropriate. More details...

Your estimate:

ne =



What fraction of those planets actually develop life? The Order came to the conclusion that all planets capable of sustaining life will eventually develop life, so they said this number is around one. More details...

Your estimate (must be between 0 and 1):

fl =



On what fraction of life-bearing planets do intelligent beings arise? The Order agreed, all of them. However, recent results relating to the role of orbital resonances in planetary stability may point to a lower number. Also, some researchers think that intelligence may often take longer to develop than the amount of time available during the lifetime of the parent star. So it might be reasonable to choose a number lower than 1. More details...

Your estimate (must be between 0 and 1):

fi =



On what fraction of planets carrying intelligent beings will those beings develop the ability to communicate their existence to others? (Note that this includes planets where beings unintentionally announce their existence, by beaming episodes of soap operas and such into the cosmos, as we do.) The Order estimated this number to be between 0.1 and 0.2. More details...

Your estimate (must be between 0 and 1):

fc =



Finally, what length of time, in years, will such communicating civilizations typically remain detectable? This period of time is not thought to be indefinitely long, even if a civilization does not destroy itself. If we succeed in running fiber-optic cables to every home on Earth, and switching all our mobile communications to spread-spectrum digital, we would become much harder to detect from far away. The Order estimated between 1,000 and 100,000,000 years. More details...

Your estimate:

L =


Now, click this button to multiply these numbers together:


Your answer:

N = detectable civilizations.

The lower and upper bounds for all these terms, as estimated by the Order of the Dolphin, lead to the result that the number of detectable civilizations in this Galaxy may only be a few dozen, or may be many millions. These results, and the results that more recent investigators have gotten, have led to a series of very sophisticated searches for evidence of intelligent life beyond the Earth. Almost all of the funding for these efforts comes from the pockets of private individuals, companies, or philanthropic institutions.

The Drake Equation, as originally envisioned, was intended to justify efforts to search for evidence of extra-terrestrial intelligent life (SETI) by means of radio astronomy. But we can go beyond its original use.

Consider what happens if we ignore the last term, L. Multiplying the other numbers together, we get:

Rc = R fp ne fl fi fc

where we define Rc as the rate at which communicating civilizations arise in this Galaxy, expressed as the number of civilizations per year. Your estimates give this value:

Rc = new communicating civilizations arising every year.



Now, let us define an explorer civilization as one which achieves the ability to communicate, and then spreads beyond its home world, and continues to exist in one form or another indefinitely after that. Let us then define another term:

fx is the fraction of all communicating civilizations that become explorer civilizations.

Optimists generally estimate this number equals one. More details...

Your estimate (must be between 0 and 1):

fx =


Now define Rx = Rc fx

as the rate at which explorer civilizations arise, expressed as the number of explorer civilizations arising per year.

Now click this button, so we can do some more figuring:

By your estimates, then:

Rx = new explorer civilizations arising every year.

Therefore, the number of explorer civilizations that have arisen in the last billion years is

1,000,000,000 Rx =

and the number of explorer civilizations that have arisen in the last million years is

1,000,000 Rx =

[Note: here, we are using the American terminology, where one billion = 109 = 1,000,000,000.]

By definition, explorer civilizations last forever, so all of the ones that have arisen in the past are still in existence; therefore, if we subtract these two numbers, we get the number of explorer civilizations between one million years old and one billion years old:

999,000,000 Rx =

[Note to mathematically sophisticated readers: Of course, we can use calculus to get where we are going here, but this page is intended to be intelligible to people who aren't comfortable with calculus.]

So the explorer civilizations between one million years old and one billion years old outnumber the younger ones by a factor of 999.

In other words, 99.9% or more of the explorer civilizations in the Galaxy are more than one million years old. (Unless, of course, you are a real pessimist, and entered a zero in one of the boxes above.)

And as long as you assume that Rx has not changed much in the last few billion years or so, which seems like a fairly reasonable (but not necessarily correct) assumption, then, by the same reasoning, most of the explorer civilizations in the Galaxy should be more than one billion years old.

From all of this, we can conclude that the probability that the Earth will be discovered by a relatively young explorer civilization, before being discovered by old ones, is essentially zero. We can also conclude that any extraterrestrial civilizations that exist nearby, if there are any, are probably much older than we are. It is highly improbable that there are any nearby civilizations that are roughly contemporary with our own. More details...

Let us go further. It seems safe to assume that explorer civilizations will be even more aware of their surroundings than we are. After all, our awareness of the Galaxy around us is limited by the relatively primitive state of our observing devices; civilizations that have much more experience in space should be able to build much better telescopes.

We can already monitor the nearest stars for evidence of the use of radio communications, and hopefully we will someday be able to monitor the nearest stars for signs of non-intelligent life as well. This should be possible because living organisms, even very primitive ones, sometimes have the ability to alter the atmospheres of their home planets; such alterations might be detectable from great distances by using instruments called spectrographs, mounted in very large space telescopes.

In the foreseeable future, we could build space telescopes large enough to monitor the planets surrounding thousands of nearby stars for signs of life, and it seems reasonable that older explorer civilizations will be able to monitor many more than this. Since we have shown that most explorer civilizations could be many millions of years old, it is conceivable that each such civilization could monitor a significant fraction of the stars in the Galaxy.

Let us define yet another term:


nmx is the number of stars that are monitored regularly by each explorer civilization, on average.

This number ought to be rather large, so just guess... The default value in the box below is one million stars. There are about a million stars within 400 light-years of us, and this distance represents less than 1% of the diameter of our Galaxy. Most of the bright stars you can see in the night sky are less than 400 light-years away. More details...

Enter your estimate:

nmx = stars monitored regularly by each explorer civilization.



Finally, how many stars are there in the Galaxy? Astronomers say between 100 billion and one trillion. [As before, we are using one trillion = 1012 = 1,000,000,000,000.] More details...

Let us define:

ns is the number of stars in the Galaxy.

Enter your estimate (must not be zero):

ns = stars in the Galaxy.


Once more, click this button to recalculate:

Now earlier, we figured that there should be about

1,000,000,000 Rx =

explorer civilizations that have arisen in the last billion years. Let us use this number as the number of explorer civilizations in the Galaxy, for the purposes of the following calculations; it simplifies things somewhat. Let's call this number:

nx9 =1,000,000,000 Rx = , the number of explorer civilizations.

If you assume that explorer civilizations are evenly distributed among the stars, then we can estimate how many explorer civilizations are monitoring each star. It's just the number of explorer civilizations in the Galaxy, times the number of stars monitored by each, divided by the number of stars in the Galaxy:

nx9 nmx / ns = explorer civilizations monitoring each star.

So we have reached the conclusion that we are being simultaneously monitored by that number of explorer civilizations. Assuming, of course, that your estimates are correct.

Note that the Earth's atmosphere exists in a state of chemical disequilibrium, and has done so for a significant fraction of its existence. If anyone out there bothers to examine it spectroscopically, which is possible to do from a considerable distance, it would stick out like a sore thumb. So if the number above is much greater than one, it would seem to imply that somebody out there has known for a long time that there is life on our planet.



Let us take the above reasoning further. If we define nvx as the number of stars that are actually visited by each explorer civilization (in person or robotically or whatever), then a similar formula will give an estimate for the number of explorer civilizations that would be expected to visit our Solar System. More details...

Enter your estimate:

nvx = stars visited by each explorer civilization.


One final time, click this button to recalculate:

Now we can estimate how many explorer civilizations visit each star, on average. It's the number of explorer civilizations in the Galaxy, times the number of stars visited by each, divided by the number of stars in the Galaxy:

nx9 nvx / ns = explorer civilizations visiting each star.

Note that this is averaged over all stars. Of course, some stellar systems may be considered relatively boring, because their stars are doomed to blow up in a few million years or because they don't have any interesting planets, and they may not be visited very often. So the number of explorer civilizations that visit interesting stellar systems (like ours) may be larger than this.

In addition, recall that we limited ourselves to explorer civilizations less than one billion years old, so the true number may be larger still.

Although your estimates may indicate that we could have many visitors, remember that these visits could be distributed over a very long period of time. A large numerical result does not imply that visits are happening now, but may imply that many visits have taken place in the distant past.

To summarize, if we define Nx as the number of explorer civilizations (of age ax years or less) that monitor/visit each star, and nx as the number of stars monitored/visited by each such civilization, we get

Nx = R fp ne fl fi fc fx ax nx / ns

For a wide range of numbers that are considered reasonable by researchers in relevant fields, this equation yields results that are larger than one, implying that we should already be under surveillance, and that we should have already been visited. But it is important to recognize that this equation may greatly underestimate the actual numbers, because it does not take into account the possibility that some explorer civilizations might begin to multiply exponentially when they reach a certain age...


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More details follow:


The Drake Equation: Parameters


These are the parameters used in the Drake Equation:

N = R fp ne fl fi fc L

R is the rate of star formation within the Galaxy, expressed in stars per year.

This is the only parameter in the original Drake Equation that is known with any accuracy. Astronomers and astrophysicists have built up a detailed picture of the life cycles of stars, and stars can be observed throughout most of the stages of stellar life. The Order of the Dolphin assumed that this number was around one star per year, but recent results indicate the true value may be as high as ten to twenty stars per year.

Some stars are probably unsuited for the development of life-bearing planets. Very small stars, although long-lived, may not produce enough heat to keep their planets from freezing solid, and very massive stars explode shortly after they form. It seems the Order of the Dolphin assumed this factor into R, and considered only the birthrate of "suitable" stars similar to the Sun, while others prefer to include this factor in one of the later parameters. Take your choice.

Recent results have indicated that the Milky Way may be larger than once thought, and that it may be a "barred spiral" rather than a "spiral" galaxy. If it really is significantly larger, then the star formation rate would have to be increased, because it is calculated based on the number of stars in the Galaxy.

It should be noted that this parameter has not necessarily been the same throughout time. There are observations indicating that when the universe was about one third its present age, the starbirth rate was substantially higher than it is now. This may imply that most of the Sun-like stars in this Galaxy are billions of years older than the Sun, and that our civilization may be a latecomer.

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fp is the fraction of stars that form planets.

The Order of the Dolphin estimated that this number lies between 0.2 and 0.5, and this is still a popular range of values.

Most stars occur in binary or multiple star systems. Because of orbital dynamics considerations, planets that form in single star systems (like our own) are more likely to have stable orbits.

It is widely thought that most single Sun-like stars have planets. Stars form from clouds of gas and dust, and such clouds generally possess angular momentum (they rotate). As the cloud particles orbit the central mass concentration that will become the star, they collide with each other, gradually averaging their angular momentum vectors (and their orbital revolution axes) until they all orbit with the same axis of revolution, forming a disk. Some of the particles will fall into the star, and some will be blown away from the system when the star ignites, but some remain within the disk. Such protoplanetary disks have been observed around nearby young stars, but they are not stable; the matter they contain has to go somewhere, and much of it must eventually gather together to form planets. (However, sometimes protoplanetary disks are destroyed away before they can form planets.)

Astronomers have been trying to reduce the uncertainty in this parameter by observing the presence of planets around other stars. At the moment, this can only be done by measuring tiny motions in the central star, and then inferring from that the mass and orbit of the planet. Several such possible planets away have been inferred, but there is some controversy over these results.

It would be far preferable to directly image distant stellar systems, and count their planets. This requires very specialized instruments, and may not be possible at all from the surface of the Earth. There are now instruments on the drawing boards to do exactly this, and the first may be launched in only a few years. So we may have a fairly precise measurement of this parameter within the next decade or two.

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ne is the average number of planets each such star possesses, which are capable of supporting life.

The Order of the Dolphin estimated that this is between one and five. In 1961, relatively little was known about the other planets and moons within the Solar System, but it was assumed that planets in the zone where liquid water can exist would be the most likely to be capable of supporting life. Venus, Earth and Mars lie within or near this zone, so the Order settled on three planets, plus or minus two.

Today we know a lot more about our Solar System. There are now four widely-discussed possibilities: Earth, Mars, Europa, and Titan. (Technically, Europa and Titan aren't planets, but they are large, complex worlds, and it is conceivable that life could arise in such places.  So we should count them as planets, at least as far as the Drake Equation is concerned.)

We know the Earth is capable of supporting life, such as it is, and we are now exploring Mars. We already know that Mars once possessed substantial quantities of liquid water, and many researchers think that life could have arisen there. NASA is now engaged in a series of missions to Mars, and is planning to launch spacecraft specifically designed to look for evidence that life once existed there. And the discovery of the famous Martian meteorite away has brought this question into sharp focus. (For more details, see An Exobiological Strategy For Mars Exploration away ).

Europa away , one of Jupiter's large moons, has intrigued planetary scientists ever since the Voyager spacecraft returned pictures of its very young and bright surface almost two decades ago. Many researchers suspected Europa had ice floes floating on an ocean of liquid water, kept warm by the gravitational influence of nearby Jupiter and other moons, and Arthur C. Clarke even worked this idea into the plot of his book 2010: Odyssey Two, and the two books later in the series. The Galileo spacecraft away has now sent us much more detailed pictures of Europa, lending considerable support to this hypothesis. Most recently, the Galileo Extended Mission away has returned magnetic data consistent with the presence of a conductive liquid under the ice. NASA is now planning to launch a new probe to examine Europa much more closely. The Europa Orbiter Mission away will utilize radar and other techniques to measure the thickness of Europa's icy crust, and the depth of any oceans. If oceans are found there, we may eventually send a robotic submarine to look around beneath the ice.

Titan, the largest moon of Saturn, may be most tantalizing and mysterious object in the Solar System. It is larger than Mercury and Pluto, and is nearly as big as Mars. It has a dense atmosphere, even denser than our own, and may have methane oceans and hydrocarbon rains. Most researchers think Titan is too cold to have developed life, because liquid water cannot exist there, but it is widely thought that pre-biotic chemistry may be happening there at the very least. If it is possible for life to develop in solvents other than water, then Titan may have many surprises in store for us. The Cassini spacecraft away, launched in 1997, is now scheduled to deliver a probe to the surface of Titan on January 14, 2005.

It is also conceivable that the giant gas planets in our Solar System may be capable of supporting life. However, these environments are so totally alien to us that we can barely begin to speculate on these possibilities.

Within the next few decades, we should have determined with some degree of certainty which planets and moons in our Solar System are capable of supporting life, or ever were. So we should be able to reduce considerably the uncertainty in this parameter.

However, recent observations indicate that our Solar System may be uncommonly enriched in the heavy elements necessary for chemistry-based life-forms, so counting planets within our Solar System may be somewhat misleading. It will be necessary to look at planets in other stellar systems, and instruments are being designed to do this. If a planet can be imaged at all, then it should be possible to obtain spectroscopic measurements, and such measurements can reveal the presence and even the composition of a planet's atmosphere. We may be making such measurements within the next decade or so.

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fl is the fraction of those planets where life actually occurs.

The Order of the Dolphin came to the conclusion that all planets capable of sustaining life will eventually develop life, so they assumed this number is around one.

It now appears that life on Earth arose very quickly after the Earth had cooled enough to allow liquid water to accumulate on its surface, so there is some confidence in this number. Life appears to be almost inevitable under the right circumstances.

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fi is the fraction of life-bearing planets where intelligence arises.

The Order of the Dolphin agreed, all of them. But it is now thought that this number may be somewhat less than one.

Some planets may develop life, and then fail to sustain it. This may have happened on Mars, and may be a common fate for many planets.

Some planets may fail to recycle critical materials. For example, if all available supplies of a particular material become locked into rocks, and plate tectonics does not occur, then those materials may become lost to the biosphere, and the whole system can grind to a halt.

Many other things can go wrong. For example, some planets may fail to develop feedback systems to maintain their temperature in the proper range.

There has also been a lot of discussion on the role of catastrophes in the development of life and intelligence. Catastrophic events can cut life short, but can also encourage the evolution of new species. Some planets might experience catastrophes much more frequently than the Earth, and some far less frequently. For example, it has been suggested that the Earth is partially shielded from devastating comet impacts by the presence of Jupiter.

There has also been much discussion of the role our Moon plays in the stability of the Earth's biosphere. It appears to be rare for a small planet to have such a large moon.

We also don't know how long it typically takes for intelligence to develop. On the Earth, it took 4.55 billion years, but it might take much longer on some planets, and might happen faster on others. If it takes longer than about ten billion years on a given planet, it will all be for nought, because that's when Sun-like stars grow old and destroy their planets.

It is commonly thought that intelligence, having adaptive value, will eventually evolve on any planet that can produce and maintain complex ecosystems for a sufficiently long time, provided its star doesn't consume it first. So this number is still frequently assumed to be close to unity, but we won't really know if this is reasonable until we find some examples of intelligent life on other planets.

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fc is the fraction of intelligent life-bearing planets where intelligent beings develop the ability to communicate beyond their own world.

The Order of the Dolphin estimated this number to be between 0.1 and 0.2, on the basis of the observation that there may be planets where intelligent beings arise who never develop a technological civilization, such as dolphins, and also that there may be technological civilizations that take great care never to advertise their presence.

The Order was just guessing here, and we can do little better at this time.

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L is the length of time, in years, that such communications remain detectable.

The Order of the Dolphin estimated between 1,000 and 100,000,000 years.

This period of time is not thought to be indefinitely long, even if a civilization does not destroy itself. If we succeed in running fiber-optic cables to every home and business on Earth, and switching all our mobile communications to spread-spectrum digital, we would become much harder to detect from far away, and perhaps after much less than 1,000 years.

This parameter is critical to the use of the Drake Equation in relation to SETI searches. If it is typically a small number of years, then it would be very hard to find anything out there. The Order of the Dolphin realized early on that most of the other parameters tend to cancel each other out, leaving the Drake Equation (short form): N = L.

There is a great deal of uncertainty in this parameter, and we won't know at all what the true range of values is until we have found a lot of civilizations out there. But we can forget about this parameter, and explore other variations on the Drake Equation, using the parameters below.

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These are parameters we can use to go beyond the original use of the Drake Equation:

Nx = R fp ne fl fi fc fx ax nx / ns

(for nx, substitute nmx or nvx as appropriate)


fx is the fraction of all communicating civilizations that become explorer civilizations, where an explorer civilization is defined as one which achieves the ability to communicate, and then spreads beyond its home world, and continues to exist in one form or another indefinitely after that.

Optimists generally estimate this number equals one.

We have no examples of explorer civilizations as defined here, but we may become one ourselves. Once a civilization spreads beyond its home world, which we may be mere decades away from doing, then all its eggs no longer reside in one basket, and it should be able to continue spreading in spite of any catastrophes which may befall any one planet.

It can be argued that the vast distances between the stars will prevent civilizations from spreading beyond their home stellar systems. But as Gerry O'Neill away pointed out nearly three decades ago, the surface of a planet is a really terrible place for an advanced technological civilization to grow. Once a civilization develops the ability to build worlds of its own design, then travelling between the stars, even at non-relativistic speeds, becomes a viable option.

The value you assume for this parameter will presumably be based on the degree of optimism you hold for the fate of the human race. If you believe that we and our descendents will remain trapped within the gravitational well of our Sun until it swallows us up, then you will probably choose a low value for this parameter (like zero). But if you believe it is inevitable that we will spread into space indefinitely, then you will probably choose a higher value (like unity).

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ns is the number of stars in the Galaxy.

Astronomers say this is between 1011 and 1012. Out of all the parameters we examine here, this is one of the few that is known with any degree of certainty.

As stated above, some researchers think the Milky Way may be substantially larger than once thought, and may contain even more than 1012 stars.

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nmx is the number of stars that are monitored regularly by each explorer civilization (of age ax or less).

This number will probably depend on the age of each explorer civilization. Older ones should be able to monitor more stars.

At the moment, we can monitor exactly zero planets beyond our Solar System. We have only been doing astronomy in space for a relatively short time, and we have not yet been able to muster the resources needed to build the really large space observatories needed to examine planets around other stars. But this will come to pass shortly.

Once this happens, then the historical trends of astronomy are expected to continue for the indefinite future: We will be able to see farther and farther into space with each passing year, and the depth of our vision should continue to follow an exponential curve.

Historically, astronomers double their depth of vision (the distance to which they can see a given type of object) every few decades or so. This is because it takes about that long to figure out (technologically and financially) how to build an instrument twice as big as the previous one, and because it takes about that long to prepare the questions that arise from the answers provided by the previous instrument.

In recent decades, this trend has slowed somewhat, because we are nearing the physical limits on instruments that can be deployed on the Earth's surface, and getting instruments into space has been very expensive. But now we have finally entered the era of space astronomy away.

If we ever become a true spacefaring civilization, with the ability to build and maintain very large space facilities using materials from space, then we should have no trouble doubling the size of our astronomical instruments at the traditional pace. Furthermore, since the zero-G environment of space does not place any inherent limits on the size of space structures, we should be able to continue doubling for many generations. And any other spacefaring civilization out there should be able to do the same.

Assume for the moment that we will develop the technology to allow us to spectroscopically examine the atmosphere of one nearby extrasolar planet around the year 2000, and that we will double the distance at which we can do this every twenty years. Every time we double the distance, we can see a volume of space eight times larger, so we can see eight times as many planets. Therefore, in the year 2000 we can see one planet, in 2020 we can see eight, in 2040 we can see 64, in 2060 we can see 512... and in the year 2300, we can see 815, or about 1013 planets. That's about how many planets there probably are in the entire Galaxy, and in only three hundred years of looking. Three hundred years doing space astronomy is practically no time at all for a typical explorer civilization.

Of course, we may not be able to continue doubling at that rate for three centuries. (If we did, we would be building space telescopes hundreds of kilometers across.) But the point remains: Really old explorer civilizations, which could be many millions of years old (and which may be able to deploy deep-space observatories far from home), should have little trouble monitoring a significant fraction of the planets in this Galaxy.

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nvx is the number of stars that are actually visited by each explorer civilization (of age ax or less) (in person or robotically or whatever).

As above, this number will probably depend on the age of each explorer civilization. Older ones should be able to visit more stars.

However, the ability to visit other stars does not necessarily imply a desire to do so. Some ancient explorer civilizations may choose not to travel, for whatever reason. Monitoring planets telescopically is a passive activity, not requiring that you leave home, but travelling between the stars is another matter entirely.

It has been proposed that advanced civilizations may explore distant stellar systems using intelligent robotic probes, commonly called von Neumann probes (after John von Neumann away, an early thinker on self-reproducing automata). Such probes could maintain themselves, and even reproduce themselves, using raw materials found during their wanderings.

It could be that virtually all interstellar exploration is done by von Neumann probes. Such probes could reproduce like bacteria, multiplying their numbers in a characteristic period of time (the generation time). A single von Neumann probe could produce 1012 progeny, one probe for every star in the Galaxy, in only forty generations. Even if the generation time is as long as one million years (you have to include the time it takes for each probe to travel to another star), it would only take forty million years for the descendents of a single probe to visit all the stars in the Galaxy. This is a short time in the scheme of things.

Since we don't see these things all over the place, some conclude that there are no von Neumann probes. But we should not jump to this conclusion; it could be that all of the von Neumann probes ever deployed were programmed only to observe, and not to interfere with living planets. This would seem to imply something about the motives of all advanced civilizations that deploy such devices (if there are any).

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Further details:

How old is the nearest extraterrestrial civilization? And how old is the oldest?

We have defined explorer civilizations to be those that have spread beyond their home world, and continue to exist indefinitely after that. Therefore, the number of explorer civilizations must increase monotonically.

Let us define the age of an explorer civilization as the number of years since it became one. Since we have not quite reached that status ourselves, but could become one in the next century or so if we put our minds to it, we may wish to consider ourselves almost of age zero.

Since it seems reasonable to assume that Rx has been roughly constant in recent times, at least for the last billion years or so, then explorer civilizations should be evenly distributed across the age spectrum. The number of explorer civilizations between one million and two million years old should be roughly equal to the number between two million and three million years old, and so on.

Therefore, the explorer civilizations between 100 million and one billion years old should outnumber explorer civilizations between 10 million and 100 million years old by a factor of ten, should outnumber explorer civilizations between one million and 10 million years old by a factor of a hundred... ...and should outnumber explorer civilizations between 1000 and 10,000 years old by a factor of 100,000.

To put it another way, less than one in 100,000 explorer civilizations should be less than 10,000 years old.

Assume for the moment that there exists a nearby explorer civilization, less than 100 light-years from here, that is no more than 10,000 years beyond us. That would imply that there should be, within that volume of space, at least nine others that are between 10,000 and 100,000 years old, at least 90 others that are between 100,000 and one million years old, at least 900 others between one million and ten million years old, at least 9000 others between ten million and 100 million years old, and at least 90,000 others between 100 million and one billion years old. That's a total of at least 100,000 explorer civilizations occupying a spherical volume of space 200 light-years across. Since this volume of space is known to contain only about 15,000 stars, this would imply that explorer civilizations outnumber stars in this Galaxy by a factor of a least six. This is nonsensical, so our initial assumption must be invalid, and the average distance between young explorer civilizations (of age 10,000 years or less) must be considerably greater than 100 light-years.

Obviously, the nearest explorer civilization should be very old. But how old? This depends greatly on the nature of Rx. Throughout most of these discussions we have been assuming that it has remained roughly constant in recent history, but this is just an approximation. This number varies throughout the history of the universe; obviously, it was once equal to zero, and becomes non-zero as explorer civilizations arise, so it is a function of time. What is the shape of that function? Is it a monotonically increasing rate, corresponding to the gradual enrichment of the cosmos in the heavy elements necessary for life? Or did it increase for a while, level off, and then decrease, corresponding to the similar behavior in the rate of star formation? We really don't know.

The Drake Equation, and the other equations here that go beyond it, assume a steady-state universe. Our universe is manifestly not steady-state, but the steady-state assumption is not too unreasonable over time scales of up to a billion years or so, and besides we cannot do much with these equations without it. So it is reasonable to say that the nearest explorer civilization should be many millions of years old, with the older ages being more likely, but once you get up into the billions of years, you have to stop somewhere. It is not reasonable to say that explorer civilizations between one billion and ten billion years old will outnumber the ones between 100 million and one billion years old by a factor of ten, because there probably aren't any that are ten billion years old (and if there are any, they are probably exceedingly rare, because Rx started out small.)

The universe is now thought to be between about 8 billion and 15 billion years old, and most researchers think it's more than 11 billion years old (because we can observe stars which appear to be that old). So how long did it take for the first planets suitable for life to arise? And on them, how long did it take for the first life to arise? And how long did it take for the first explorer civilization to appear? Obviously, it is possible to write modified versions of the equations we are already using to explore these questions, but the parameters within these equations are much more uncertain than the highly uncertain parameters we have already considered.

We can be reasonably certain that our planet, and its Sun, formed when the universe was already billions of years old. But could similar planets have arisen much earlier, say, less than a billion years after the Big Bang? We know that there were stars in existence this early, and that some of them were pumping heavy elements out into space. So perhaps this is possible.

Intelligent life arose on the Earth about 4.55 billion years after it formed. Could there be planets out there where intelligent life arose more quickly? We really don't know; 4.55 billion years could be unusually long, or unusually short, or quite typical.

At this point, all we can say is this: We cannot rule out the possibility that there may be civilizations out there that are several billion years older than our own.

Go back.


The Fermi Paradox

Before Frank Drake wrote his equation on the blackboard, others were thinking about the ideas embodied within it. One of these early thinkers was physicist Enrico Fermi.

Fermi spent much of World War II at Los Alamos, where he helped develop the atomic bomb. One of the side benefits of the Manhattan Project was the gathering together of a great number of brilliant minds in an isolated setting where the distractions of civilization were scarce, which resulted in a lot of spare time being consumed in intellectual discussions unrelated to nuclear destruction. Thanks to Fermi, some of that spare time was spent talking about putative alien civilizations.

Fermi realized that intelligent life ought to be widespread throughout the cosmos, and should have been so for a very long time. He also realized that the first spacefaring civilization to arise in our Galaxy should have already spread to every part of the Galaxy. But if that is the case, he asked, "Where are they?" This has become known as the Fermi Paradox.

In those days, it was commonly believed (at least in America) that aliens had never visited our planet. Widespread popular belief in UFOs was still years in the future. Fermi (and probably most of his colleagues at Los Alamos) assumed the lack of evidence for alien visitation was due to a complete lack of visits. But given what they suspected about the abundance of intelligent life in the universe, this did not seem to make sense.

A number of ideas have been put forth to resolve this apparent paradox. One of the most popular is the "ET Hypothesis", which posits that we are being visited, and that UFO sightings (as well as abductions, cattle mutilations, crop circles, etc.) are the evidence. Needless to say, this hypothesis is controversial and highly problematical, and most serious scientists won't get anywhere near it.

Another popular idea is that we are completely alone in the Galaxy, or that any other civilizations are so rare and distant that they have not gotten anywhere near here as yet. This is entirely possible, but reflects a rather pessimistic view of the questions embodied in the Drake Equation.

A third hypothesis is that intelligent life is widespread, as many researchers suspect, but that we cannot see blatant evidence of it for some reason. A number of suggestions have been put forward to explain how this could come to be, including what has come to be commonly called The Prime Directive. But all possible explanations for this hypothesis have one thing in common: They must apply to every civilization out there, without exception. If even a small fraction of extrasolar civilizations violates an interstellar quarantine, we should find evidence, and we don't; this would seem to imply that someone is enforcing our isolation. In any case, we can be reasonably sure of one thing: Nobody is aggressively appropriating all of the available resources in the Galaxy at an exponential rate, even though this would seem to be possible to do.


What is possible in this universe, anyway?

It is a widely held belief among scientists that some things are simply not possible. In other words, there exist physical laws that limit what you can do, and as long as you remain within this physical universe, you cannot violate those laws. It is conceivable that we have no idea what those ultimate laws really are, or that they may indeed be unknowable in some sense, but until we see evidence that a really elegant physical law has been violated, Occam's razor would seem to demand that we stick with it.

One physical law that is directly related to the subject at hand is that associated with the speed of light. If it truly is impossible to travel faster than the speed of light, and if it truly is energetically very expensive to travel near the speed of light, then this places severe constraints on all discussion of interstellar travel. But if it is possible to circumvent this limit in some way, then the whole tone of the discussion changes.

Methods of traveling quickly and cheaply between the stars are a common staple of science fiction, and are collectively known as FTL (Faster-Than-Light). Popular FTL methods include warping space and wormholes. These methods are essential to most science fiction stories that involve interstellar travel, and indeed were invented so that it would be possible to tell compelling space travel stories. But so far, these inventions must be viewed only as literary devices, and not actual technologies.

Some who believe in the ET Hypothesis as an explanation for UFOs say that such observations constitute evidence that FTL is possible, but this is a logical fallacy. Even if UFOs are real, and even if they come from beyond our Solar System, this does not constitute proof of FTL, because it is already known that interstellar flight is possible without FTL.

Nobody has ever actually seen anything move faster than light. Indeed, since we see with photons, and nobody has ever come up with a way of having photons get from a FTL vehicle to your eye, one would not expect to see such things even if they exist. Of course, some people say they have been told (perhaps by some alleged extraterrestrial) that FTL is possible, but this is only hearsay evidence. And some people claim to have traveled by means of FTL to other worlds, but one can think of a number of explanations for this kind of experience; even if such people are not deluded, and have really met aliens and "experienced" such travel, this does not constitute proof of FTL, because one would expect alien visitors to have a sufficiently advanced technology so that they could give a human any kind of "experience" they desire, without any need for that human to actually travel anywhere.

But perhaps the biggest problem with FTL is that it appears to be incompatible with the belief that intelligent civilizations are widespread. If intelligent life is commonplace, and if FTL is possible, then one would expect this technology to be possessed by a wide variety of different species of intelligent creatures, perhaps with widely varying ethical notions, and then one would have to come up with some compelling explanation for why none of these species produces any individuals inclined to littering or grafitti. (Or, you have to postulate that some external agency has a 100% success rate in keeping joyriders away from quarantined planets.)

Occam's Razor

The principle of Occam's razor is a cornerstone of modern scientific thought. Named for William of Occam (also spelled Ockham), a 14th century philosopher, it is a principle of parsimony. Given a choice between two or more viable explanations for some phenomenon, Occam's razor cuts away the more complex explanations in favor of the simplest.

For example: For centuries, astronomers attempted to devise mechanistic models to explain the complex motions of the planets through the sky. Unfortunately, they were hobbled for many years by a philosophical compulsion to make the heavens perfect. Since everything in the sky was observed to go round and round, it was thought that everything had to be made from perfect circles. But in order to make the models match the observations, it became necessary to put more and more circles into the models, and they evolved into horribly complicated monstrosities, having wheels within wheels within wheels.... It wasn't until Kepler came along that a simple model was derived, based on ellipses instead of circles. But people then had to redefine their notion of simplicity before they could accept Kepler's laws.

Occam's razor is frequently wielded by those who wish to speculate on the nature of extraterrestrial intelligence. But it seems quite likely that we may have to redefine our notion of simplicity, perhaps many times, before we will find any truth with this tool.

For a more comprehensive discussion, see What is Occam's Razor? away

Searching for Planets


At present, the only method we have for searching for planets outside our Solar System is by looking for the gravitational effects they have on the stars they orbit. This can be done by using Doppler shift observations to measure very small movements of the star. However, this method is fraught with difficulties, and many of the results away remain controversial. And in any case, this method cannot tell you if a given planet harbors life.

It would be highly desirable to see planets directly, but unfortunately, this is extremely difficult. Extrasolar planets lie very near their stars when viewed from Earth, and they tend to be concealed within the glare of the star. Planets are many orders of magnitude dimmer than the stars they orbit.

When the image of a distant star is focused onto the image plane of a telescope, the image of the star does not focus to a point. Instead, it focuses to a small disk, of finite size, and this disk is enlarged by various effects. In most telescopes in current use, this disk is large enough so that the images of any planets orbiting that star will appear inside the star's image disk, and be completely obscured.

There are several phenomena that cause the image of a star to blur into such a large disk. The worst is the blurring caused by looking through the Earth's atmosphere; while there are techniques for partially counteracting this effect, it is far better to eliminate it completely by placing the telescope above the atmosphere, in space.

Another effect that can cause the star's image to enlarge is commonly referred to as glare. Ideally, all of the light that enters an instrument should follow the designed light path, ultimately arriving at the detector where all of it is absorbed at 100% efficiency. But in any real-world optical system, light does not always go where the system designer desires. No material object is completely black, so a small amount of the light entering the instrument will be reflected and/or diffracted into paths that the designer of the instrument did not intend, and a small amount of the light arriving at a given light detector will be reflected elsewhere rather than being absorbed. This happens within electronic image detectors, photographic emulsions, and even the human eye; when light strikes a light receptor within your eye, a small amount of it can bounce around inside the eye and within the retina itself, eventually striking other receptors, so the light from even a point source, if bright enough, will be detected by more than one receptor (try looking [very!] briefly near the Sun sometime, and before your eyes instinctively blink shut, you'll see this effect). Similarly, when a photographic plate is used to take a picture of a field of stars, the image of a given star will become larger as the exposure time is increased, because more and more photons are bouncing around inside the photographic emulsion before being absorbed. In addition, electronic image detectors sometimes experience charge leakage from one pixel to the next, and this is can also result in the enlargement of images. This type of glare is difficult to eliminate completely, but by careful design, it is possible to use various nulling techniques to reduce this type of glare to any desired degree, short of perfection, in a sufficiently large telescope.

A third effect that can enlarge the image of a star is the most fundamental, that of diffraction. A phenomenon known as Fraunhofer diffraction causes the light from a star, or even from a point source, to spread out into a disk of finite size, known as the Airy disk; the size of this disk corresponds to an angular resolution of 1.220 w / a radians, where w is the wavelength of the light being observed and a is the diameter of the telescope aperature. If the image of a planet falls inside the Airy disk of its star, then there is no way of separating the two. And even if the image of a planet does not fall inside the Airy disk of its star, the image of the planet can still be obscured, because Fraunhofer diffraction causes a small amount of the star's light to be distributed well outside the star's Airy disk. Fortunately, as long as two objects are separated by a non-zero distance, it is always possible to design a telescope that will separate their images far enough for them to be resolvable (but it may require a very large telescope).

Once you have a telescope that can separate out the image of a planet from its parent star, then the possibilities open up. By examining the colors of the light from an object, it is possible to derive a large amount of information about that object. One can often tell what kinds of materials a planet is made of, and whether it has an atmosphere, and if so, what the composition of that atmosphere is.

These kinds of measurements can sometimes tell you whether or not a planet carries life. We know this because the Earth's atmosphere has a detectable signature of life: it is in a state of chemical disequilibrium, containing large amounts of free oxygen, and life is the only known natural process that can produce such a state.  If we see an atmospheric composition at a distant planet that we cannot explain as a non-living natural phenomenon, then that may indicate the presence of life.

A number of efforts are underway to build instruments to image extrasolar planets, and make measurements of them. The first attempts to do so will be undertaken by ground-based observatories, such as the Keck Observatory away in Hawaii. But because they are handicapped by the Earth's atmosphere, they may not find very many planets, and may not be able to provide very much information about them. For these kinds of searches, the future lies in space.

The first space-based instruments specifically designed to look for planets are already being designed, and may be launched within the next decade.

For more details, see:

The Exploration of Neighboring Planetary Systems (ExNPS) Study away

NASA's Origins Program away

Other Solar Systems? away

Darwin Mission - Lists of Extra-Solar Planets away

Interferometry list away

Interferometer Projects away

SIRTF (Space Infrared Telescope Facility) away


The Search for Extra-Terrestrial Intelligence (SETI)

The first systematic search for extraterrestrial intelligence, using the techniques of radio astronomy, was conducted by Frank Drake in 1960. It was named "Project Ozma" away, after the princess in L. Frank Baum's Oz books.

Since then, many searches have been undertaken, using better and better equipment. Searches are also being conducted for signals outside the range of radio astronomy.

A number of tantalizing signals have been seen, but none could be verified; they were one-time transient events. Those parts of the sky have been occasionally re-examined, and they appear silent.

For details on recent and current SETI activities, see:

The SETI Institute away

The Planetary Society away

The SETI League, Inc. away

Small SETI Observatory away


Big Ear Radio Observatory away

Cosmic Search Magazine away

A very comprehensive document, published by NASA in 1977: The Search for Extraterrestrial Intelligence, SETI away

Scientific American: Article: The Search for Extraterrestrial Intelligence: 1/97 away

The Telson Spur: Field Nodes -- Visions (2): SETI (Bioastronomy) away contains a very large number of relevant links.

SETI - References for List of Searches away

SETI etc. (W6/PA0ZN) away

The SETI League Technical Manual away shows you how to build your own SETI receiver, as does:

Amateur SETI: Project BAMBI away

SETI@home away allows you to participate in SETI searches from your own home, even if you don't have your own radiotelescope! SETI@Home provides a screensaver program that you can run on your own computer, which automatically downloads and analyzes SETI data collected by the world's largest radiotelescope, the 1000 foot dish at the Arecibo Observatory.


For an excellent recounting of the early history of the field, and of The Order of the Dolphin, see:

Is Anyone Out There?, by Frank Drake and Dava Sobel, Delacorte Press, New York, 1992. ISBN 0-385-30532-X.


Go back.


The Order of the Dolphin

In early November, 1961, a group of scientists and engineers met at the Green Bank Observatory to discuss the possibility of using the techniques of radio astronomy to detect evidence of intelligent life outside our Solar System. The Drake Equation was first discussed here.

At the end of their three day meeting, they decided that the group should have a name. Inspired by John Lilly's tales of dolphin intelligence, they agreed to be known as The Order of the Dolphin. They were:


Dana Atchley

Melvin Calvin

Frank Drake

Su Shu Huang

John Lilly

Philip Morrison

Bernard Oliver

J. Peter Pearman

Carl Sagan

Otto Struve


It should be noted that many of the ideas discussed at this meeting had already appeared in a seminal letter by physicists Giuseppe Cocconi and Philip Morrison entitled "Searching for Interstellar Communications" away, published in the journal Nature (volume 184, no. 4690, pages 844-846, September 19, 1959).

Morrison was undoubtedly influenced by his Los Alamos colleague, Enrico Fermi, who was thinking about these ideas during the early 1940's. See The Fermi Paradox, above.

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Are We Alone?

Also at this site:

The Many-Worlds Interpretation of Quantum Mechanics


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