Has Earth been detected?

Given that in the last ten years we have found roughly 250 planets outside our solar system, it is perhaps prudent to ask whether an alien civilization may have already detected our own planet and its biosphere during the approximately three billion years it has harboured photosynthesising life.

The Drake equation, the famous speculative tool to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact, was not intended to address this question but can be modified to do so. Unfortunately (but perhaps not surprisingly) this exercise necessarily involves some mathematical notation, but bear with me – it is relatively simple and in the end you will have a tool to answer (or rather, speculate) this question yourself.

The Drake equation reads:

N = R* × fp × ne × fl × fi × fc × L

where N is the number of extraterrestrial civilizations which we might be able to contact, R* is the number of stars forming in the galaxy per year, fp the fraction of those stars that have planets, ne the average number of habitable planets per star that has planets, fl the fraction of habitable planets on which life emerges, fi the fraction of life-harbouring planets on which intelligence evolves, fc the fraction of civilizations that start to emit detectable signals into space, and L the average number of years such civilizations continue to emit signals into space.

Drake and his colleagues originally came up with N = 10. With different assumptions we can end up with vastly varying N values, ranging for example from 0.0000001 to 5000 (see examples here). But N is the estimated number of civilizations in the Milky Way which we might be able to contact, not the probability that the Earth and its biosphere have been detected by an extraterrestrial civilization sometime during the last three billion years. For that, we need to change the equation a bit.

Given a maximum detection distance from us, for each star within that distance there is a possibility that an alien civilization residing in that system has found Earth. That possibility can be quantified as probability:

p = fp × ne × fl × fi × fs × fd

where fp, ne, fl and fi are the same as in the Drake equation, fs is the fraction of civilizations that conduct exoplanet searches and fd is the fraction of Earth-like planets actually detected in those searches. This equation assumes that life and intelligence emerged always within the last three billion years, excluding the possibility of emergence and extinction before photosynthesising life appeared on Earth.

Given the probability of single detection above, we can formulate the probability that Earth has not been detected for a given number of stars S within the maximum detection distance:

p0 = (1 – p)S

Now let’s plug in some numbers. I assume that alien civilizations are interested in and capable of detecting Earth-like planets within 100 light-years from they home stars. According to the Gliese Catalogue of Nearby Stars, 3rd Edition, there are 1064 stars within 50 light-years from our solar system (although it is a conservative estimate because not all stars have been catalogued). After a bit of calculation using the volume equation of a sphere and assuming constant density of stars, we end up with 8512 stars within 100 light-years from us. This will be the value of S. For fs and fd we assign values 0.1 and 0.5, respectively, and for the rest of the variables we use the original values of Drake and his colleagues (fp = 0.5, ne = 2, fl = 1, fi = 0.01).

So, what is the probability that Earth has not been detected? It is 0.01, so the probability that Earth has been detected by an alien civilization is 0.99 or 99 percent. Now go speculate.

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16 Responses to Has Earth been detected?

  1. Mobius says:

    Given that Drake’s is nothing but a guess, your math doesn’t work.

    Drake’s and String Theory aren’t true science by any strict definition of science.

    Despite this, I tend to think that it is likely Earth has been noticed. After all, we live inside a radio-sphere which is now 200 light years across, and that is actually visible against an A4 sized image of the galaxy.

  2. archblogger says:

    Hi Mobius 🙂 As I wrote, the Drake equation is a speculative tool. This does not render it completely useless though. As to my math, the equation should be fine. The end probability is not meant to be taken too seriously – it is, after all, speculation.

    I can understand someone stating that Drake equation is not science, but if String Theory is not perfectly valid science, what it is? (Although I guess it really should not be called String Theory but String Model or String Hypothesis since it has no experimental support.)

  3. Pink says:

    Assuming for the moment that the math is correct (and I’m not an adequate judge), alien conspiracy theorists could have a blast with this one. Also, every child who loves ET may just be thinking that their dream has come true.

  4. personally, I don’t buy it for a moment.

    Thanks for posting this, it is an interesting read.

  5. The possibility of other worlds with living organisms ie creatures is immense. A religious book call ‘Ramayana’ written by Goswami Tilsi Das has mentioned that there are innumerable worlds where there is life but of quite different type than is seen in our world. He has also mentioned that the basic building blocks have quite common features which happen to be the menifestation out of one underlying supporting power which may be called the ‘brahman’ and who only gets embodied in the way desired by his devotees according to their own preferences. In a way this is equal to dream state of erthlings but can not be understood until the union with the supreme reality is established by the soul of the devotee. The true nature of the GOD is reflected upon such a soul which as soon as knows the GOD becomes one with him and looses identity. Actually the words are not entirely capable of communicating the whole truth , the truth therefore has to be revealed by the GOD himself according to his own sweet will to the deserving souls in worly bodies.

  6. Please read the name of author as ‘Tulsidas’ instead of ‘Tilsidas’ and he was born in 16th century in India and what he propounded has been picked up from the timeless ‘Vedas’

  7. the forester says:

    Considering all of the above, I find the resounding silence from extraterrestrial sources to be extremely significant. By all strict materialist understandings of the universe, other civilizations should be out there — but they’re not.

  8. coaks says:

    “You’re so wise. You’re like a miniature Buddha, covered in hair.” – Anchorman

    http://www.coaks.wordpress.com

  9. archblogger says:

    Hi Pink, you just might be right about the blast 🙂 I need to write a follow-up emphasizing the speculative nature of the equation and especially the result of my example. I can easily come up with another example with probability of detection less than one percent.

    Briefly before I post a follow-up: krsnakhandelwal, with respect, my view is that any religious text has very little to say about the universe we live in. the forester, strictly speaking we really do not known whether they should be there or not, because we have no idea about the probability of life evolving intelligence, and we do not know whether they are there or not either.

    Thanks for the comments all.

  10. kashifalvi says:

    i don’t think so, plus “The Drake equation” its not happening. see every theory is based on may and may not(might come in contact)
    we should consider earth detected in earth it self at the moment.

  11. Yesterday I posted a modification of the Drake equation that was intended as a speculative tool – no, rather a […]

  12. Jon Chance says:

    A very interesting read …..

    The Drake Equation and yours are both speculative tools, that much I agree apon. Have we been detected , assuming there is other lifeforms out there with the technology to do so , More then likely. why haven’t we been contacted … Who is to say we haven’t , If we haven’t been contacted , the reasons may be as follows….

    1)We haven’t been able to get along with ourselves , how are we going to get along with another civilization ?

    2) A reinforcment of the first speculation , They may be waiting to see if we can get along with each other or destroy each other via nuclear war or other technology.

    3) we are but a child race that needs to mature before we can be contacted …

    4) for star trek fans … A prime Directive such as no contact until FTL technology.

    I am sure that you can think of many more reasons why no contact has been made , if they are out there. If you can’t … ask any conspiracy theorist , I am sure they will give you more then you can handle as to why

  13. Adam J says:

    Another reason…

    5) Aliens have recieved our signals, TV Programmes, Military broadcasts and Radio, and decided they dont want to contact a species that invented 24 hour shopping channels, World war and bad music of any sorts.

    6) They’re decoding our signals wrong for what ever reason, and its coming over as completely random white noise and fuzz.

    But then, I’d rather fuzz than QVC…

  14. jeremy says:

    I hope someone’s detected us, we’re going to need help soon… or now.

  15. Boris says:

    Of course has been detected. See Dr. Peter Sturrock’s “The UFO Enigma,” or Richard Hall’s “The UFO Evidence.” They’re coming here, so evidently they have detected us.

  16. archblogger says:

    Well, for people who – unlike me – are convinced that aliens are visiting Earth all the time the answer to my question is obvious. But if one does not blindly believe in anything without evidence, the question is valid.

    Although I could accept a claim of visiting aliens if evidence would support it, the evidence just is not there. And do not bother to try to convince me otherwise, I am well aware of the existing evidence, which is inconclusive.

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