The Drake Equation in its usual form is used to estimate the possible number of extraterrestrial civilizations in our galaxy, but I thought it might
be interesting to slightly modify it in order to estimate the chances that a civilization on another planet close enough to detect our radio signals
has detected our presence and decided to visit us. Apparently the first radio signal at a frequency high enough to penetrate Earth's ionosphere was
the opening ceremony of the 1936 Olympics[1]. Since radio waves travel at the speed of light that means any star system without a radius of 82 light
years could potentially detect our signals.
This is a nice number to use for our estimate because it's extremely unlikely that our radio signals would even be detectable amongst the background
noise beyond 80 light years and because it's extremely unlikely any species further than 80 light years from us could reach us since it would take 80
years even traveling at the speed of light. In order to make the estimation we can adjust the Drake Equation to take into account only the star
systems within range of our radio signals instead of the whole galaxy. The result of this calculation will hopefully provide some insight into the
likelihood of ET's detecting our presence and visiting our planet.
So here is the modified equation:
N = Ns · Fp · Ne · Fl · Fi · Fc
Ns = the number of star systems close enough to detect our radio signals
Fp = the fraction of star systems that have planets in stable orbits
Ne = the average number of potentially habitable planets per star
Fl = the fraction of those planets that develop reproducing life forms
Fi = the fraction of those planets on which intelligent life does evolve
Fc = the fraction of those civilizations which detect our signals and travel to us
The number of star systems close enough to detect our radio signals
This is rather easy to calculate since we know the density of stars in our region of the galaxy and we know the volume of space covered by our radio
signals. The stellar density near the Sun is estimated as 0.004 stars per cubic light year[2] and using the equation to calculate the volume of a
sphere we find that a sphere with a radius of 82 light years has a volume of 2.31×10^6 cubic light years. Multiplying the stellar density by the
volume of space filled by our radio signals, we find that there are approximately 9240 star systems within an 82 light year radius of our star
system.
The fraction of star systems that have planets in stable orbits
Wikipedia states that "recent analysis of microlensing surveys has found that fp may approach 1 — that is, stars are orbited by planets as a rule,
rather than the exception; and that there are one or more bound planets per Milky Way star."[3] This means that the fraction of stars that have
planets orbiting them is very high, so for Fp I feel a value of 0.95 is easily justified but still accounts for the fact not quite every star has
planets in orbit. In other words we're assuming that 95% of all stars have orbiting planets.
The average number of potentially habitable planets per star
According to the latest space surveys "there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars"
within our galaxy[3]. Since there is around 100 billion stars in our galaxy and virtually all stars have planets this implies the value for Ne is
roughly 0.4 but researches have also shown that only about 10% of star systems contain the right elements and suitably low radiation levels to support
life, which implies the value for Ne is below 0.1[3]. However I know some people will take issue with a value that low so we'll split the difference
and use 0.25, meaning for every 4 star systems there is 1 habitable planet on average.
The fraction of those planets that develop reproducing life forms
The chances of a reproducing organism assembling itself from a random collection of chemicals is extremely small, however biological life arose on
Earth shortly after favorable conditions presented themselves, so given billions of years the probability may become substantial. The problem is that
the only example we have is our own planet so any estimates of Fl suffer from anthropic bias. Wikipedia states that "From a classical hypothesis
testing standpoint, there are zero degrees of freedom, permitting no valid estimates to be made". This means the only logical value we can use for Fl
is 0.5 because we're uncertain either way.
The fraction of those planets on which intelligent life does evolve
This is another difficult variable to estimate but out of the 8 million species on Earth we are the only one which developed civilizations with
advanced technology, implying the value of Fi is very small. However when millions of species have billions of years to evolve there's more chance at
least one of them will evolve into a civilized species with an understanding of science. However in order for that to happen the creatures must avoid
extinction and have favorable conditions which last billions of years. There's at most a 1% chance all the right things will occur, but I want the
result to be optimistic so we'll use 0.01 for Fi.
The fraction of those civilizations which detect our signals and travel to us
The value of Fc is going to be very small just like Fi because detecting our radio signals from such long distances is very difficult and involves a
lot of luck because they have to be looking in the right place, for those at 80 light years it would be an almost impossible challenge. Also the
chance they will develop technology for interstellar travel is very small since we know it's a tough problem and a warp drive is required to make it
feasible at all, and we're not entirely sure such a drive can even be built. However lets be optimistic and assign Fc a value of 0.1, meaning a 10%
chance any given civilization manages to reach us.
So the resulting calculation will look as follows:
N = 9240 · 0.95 · 0.25 · 0.5 · 0.01 · 0.1
N = 1.09725
Well that's rather interesting result, the answer is basically one, meaning we are that one civilized species in our neighborhood of the galaxy,
although we obviously haven't developed interstellar travel yet. The only variables which have a substantial impact on the final result are Fi and Fc
because they are the only really small fractions and we didn't even use a very small value for Fc. The other variables can be changed within reason
without impacting the final result very much. However Fi and Fc are also two of the hardest variables to estimate, which is why I tried to be
optimistic.
Even so the result still shows us we are probably the only intelligent species in our region of the galaxy and we almost certainly have not been
visited by ET's. If we plug in more realistic values for Fi and Fc we find that there's an exceptionally low probability we have been visited by
extraterrestrials. This is an important result because it shows us that if there are indeed advanced crafts moving around our atmosphere then there's
very little chance they are controlled by beings who traveled here from another planet using a propulsion mechanism capable of FTL speeds.
1]
briankoberlein.com...
2]
en.wikipedia.org...
3]
en.wikipedia.org...edit on 8/4/2018 by ChaoticOrder because: (no reason given)