An artist’s conception of Pioneer 10 drifting silently around the galaxy.
The Drake Equation may be due an overhaul.
Its fun to sit and think how many extraterrestrial civilizations might be out there. First expressed by astronomer Frank Drake in 1960, the Drake Equation frames the question of how many civilizations might in our galaxy for us to potentially communicate with in mathematical terms.
When you run the numbers, you quickly begin to realize, however, that the factors move from the known to the unknown as you travel through the equation from left-to-right. We have a pretty firm estimate on the rate of star formation in our galaxy, for example, but not such a great grasp on how often life, let alone radio telescope-constructing intelligent life, arises.
And the very last factor of longevity of said civilization in Drake’s equation may be the kicker. Do sentient, space-faring species last for geologic timescales, or are we too smart for our own good?
We’d like to create an interesting addendum to Drake’s equation that we’ve been thinking about for some time.
We’ve actually be throwing out our very own “Messages in a Bottle” in the form of spacecraft escaping the solar system since the start of the Space Age. Five spacecraft — plus their rocket boosters — are on trajectories that are destined to take them out of the solar system: Pioneers 10 and 11, Voyagers 1 and 2, and New Horizons. The Pioneers and Voyagers each carry messages for any extraterrestrial salvagers that come across them, while New Horizons carries a collection of artifacts such as a Florida and Maryland state quarter that’ll REALLY confuse ET. (“Are they a race of intelligent, bald-headed slug-foots?” they’ll ask themselves, looking at the bust of George Washington).
The Voyager “Golden Record” in the laboratory. Credit: NASA/JPL.
But shouldn’t an emerging civilization be doing the same? And shouldn’t “alien space junk” litter the Milky Way?
Its an interesting thought experiment to run through: we’ll call it “The Estimation of ET Artifacts in the Milk Way.” Now hang on, a Saturday morning thought experiment lies ahead. We’re also going to get just a bit “mathy” but trust us, it’ll be worth it!
First, for the purposes of this exercise, we’ll use the answer to Drake’s equation we spitbllaed some years ago (feel free to insert your own, you may be just as right) as 270 for the number of alien civilizations currently in existence.
We’ll also use the same average length of the average civilization at = 10,000 years.
Now, the age of the Milky Way galaxy is estimated to be some 12.6 billion years.
Now comes the interesting part. Most of the hypothetical artifacts still orbiting the Milky Way will have been launched by civilizations that have long since left the cosmic stage, which is a nice way to say they’ve gone extinct. Hey, it happens to the best of space-faring civilizations.
Therefore, we’re not only interested in civilizations that are currently active, but also those that once were players on the galactic scene.
Let’s place T1 or the time since the first civilization arose in our galaxy at a nice round 10 billion years.
This would give us the number of civilizations (Ce) that have existed to date as = 10 billion years/10,000=1,000,000 x 270,000,000.
Now, we Earthlings have launched 5 spacecraft escaping the solar system in 50+ years of space-faring.
Let’s assume this as a rough rate of R at 1 spacecraft (S1) per every 10 years ( or a 1-to-5 ratio counting boosters)
Using D for our answer from Drake’s Equation, we get;
Ce*T1*R= S1 or;
10,000/5=2,000 or spacecraft launched per lifespan of a given civilization, and times 270,000,000 civilizations= 540,000,000,000 or 5.4 x 1011 artifacts out there, currently orbiting the Milky Way galaxy.
Wow, that sounds like a lot, right?
The Humans were Here: a diagram of the plaque affixed to the Pioneer 10 & 11 spacecraft. Credit: JPL/NASA.
But the galaxy is a big place.
Now, how close might the nearest alien artifact be? The problem now becomes a simple issue of volume versus density.
Let’s look at the volume of the galaxy as a cylinder.
The radius of the Milky Way is approximately 50,000 or 5 x 104 light years, and the height of the cylinder it fits into is about 1,000 or 1 x 103.
Now to find the volume of the galaxy, we plug in:
V = pi(3.1416) x (50,000^2) x 1,000
And come up with 7.854×1012 cubic light years
That comes out to not quite cubic 8 billion cubic light years for the volume of our galaxy!
Now, dividing the number of derelict alien spacecraft S1 by the volume of the galaxy, we get:
540,000,000,000/8,000,000,000= or 67.5 objects per cubic light year.
That’s encouraging, Buuuut…
a 1 light year = 63,240 Astronomical Units, or A.U.s.
Cubed, that’s = 25,291,558,022,400/67.5 = or one artifact per 373.7 billion cubic A.U.s.
That’s a LOT of ground to cover.
Wondering if there’s any alien goodies in our solar system?
Well, the distance inner edge of the Oort cloud is estimated to be 4,000 A.U.
This would make the volume of the solar system = 201 million cubic A.U.s, and the chance of an alien artifact adrift in our solar system less than 1 in a 1,000.
Using the outer edge distance for the Oort cloud at 50,000 AU = gives the volume of the solar system at 31.4 billion, with a slightly better than 1-in-10 chance.
But the nearest star system, Alpha Centauri is 4.4 light years distant, which equals a sphere 243 cubic light years in volume, with lots of elbow room for alien space junk!
Of course, we can think of several objections to this rough estimation: this assumes that civilizations rise and fall at a uniform rate, and they continue to launch objects out of their respective solar systems at once per decade. And it also assumes said spacecraft and civilizations are distributed evenly, when it may well be case that a galactic “habitable zone” exists.
Still, it fun to think of what might be out there, drifting around… and worth keeping an eye out for!