Last week The Universe In this column, I answered a reader’s question about galaxy collisions in an expanding universe. The answer concerns the vast distances, impenetrable forces, and ultimate fate of the cosmos.
Not all queries are enough so serious. For example, reader David Erickson had this in mind: “If there were aliens 66 million light years from Earth, what size telescope would they need to see the dinosaurs?” »
Ha! I love this question. I’ve thought about it myself, but never did the math, except thinking “Probably pretty big”, which turns out to significantly underestimate the actual answer. But what’s really great is that confronting this admittedly bizarre thought experiment has real implications for the future of science.
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First of all, why does it matter that aliens are 66 million light years away? This is because light travels a distance of one light year per year through space, and the impact of the asteroid Chicxulub that wiped out the non-avian dinosaurs occurred about 66 million years ago. The light from this event would be reaching a galaxy located approximately 66 million light years away. At this distance, observers could still see (the very last) dinosaurs, provided they were willing to build a very large telescope.
Now the question needs to be split into two parts: how big is a dinosaur at that distance, and how big does a telescope have to be to see something that size?
Because the sky looks like a gigantic sphere surrounding us, astronomers use angles to measure the apparent size. The basic unit for this is the diploma; for example, the angle between the horizon and the point directly above an observer, called the zenith, is 90 degrees. The Moon has an apparent size of about 0.5 degrees in diameter.
The size of an object depends on its physical size and its distance from anything looking at it. There is a nice little formula called small angle approximation which connects the two. There are many different ways to represent this equation, depending on the units you use. To get degrees, you take the physical size of the object, multiply it by 57.3, and divide it by the distance. So an object one meter wide, such as a small large-screen TV, would have an apparent size of one degree at a distance of 57.3 meters.
For our dinosaur, let’s choose everyone’s favorite terrifying carnivore, a Tyrannosaurus rex. T. rex varying in size, but let’s say the one the aliens want to observe is 10 meters long.
The distance is 66 million light years, which is quite a hike. We need this in meters, so after the conversion (“Let’s see, let’s multiply by 10 trillion, take the 2”, and so on) we get a staggering distance of 6.6 × 10.23 meters.
Incorporating this into our formula, we see that a T. rex seen from this distant galaxy would have an apparent size of about 10-21 degree. That’s a sextillionth of a degree, or a zeptodedegree, if you like fun math prefixes. It’s incomprehensibly tiny. But to be honest, it’s quite far.
Great, that’s one of the two key questions answered! Now, how big a telescope do you need to see something this Lilliputian?
You might think we need magnification to spot our beast from so far away, but this is not exactly the case. In a word, something small and very far away will look like a dimensionless point. If you enlarge this point in an image, you simply enlarge the pixels. To see it as more than a point, you have to resolve it. So what we really need is to see a T. rex and not a point is high resolution.
Resolution is an inherent property of all telescopes and depends primarily on the size of the telescope mirror. There is another formula for this, called The Dawes limit. This too can be expressed in different ways, but if you use degrees and meters it becomes: resolution in degrees = 3.2 x 10-5 / D, where D is the diameter of the telescope mirror in meters. We know the size of our object in degrees, so we want to find D. When we do, we find that the diameter of our telescope should be 3.2 x 10.16 meters (32 quadrillion meters).
That’s about 3.4 light years, which would make, uh, a very large telescope. It’s a mirror that would cover three-quarters of the distance to Alpha Centauri!
Needless to say we don’t have the technology enough I haven’t built such a thing yet. Even if we had the know-how to build this mirror, obtaining the necessary construction materials would be a significant challenge: given the density of mirror glass typical of a telescope and assuming a mirror thickness of only one millimeter, our T. rex–the resolving mirror would have a mass of around 1030 (one million tons) of metric tons. It turns out that it is more than 100 million times the mass of Earth. You’d probably need to plunder, destroy, and remix a good portion of a large galaxy’s rocky planets to build a mirror like that.
If our peeping aliens are particularly intelligent, they could get around this problem by building an astronomical interferometer instead. This is a set of smaller telescopes spread over a certain area; Using sophisticated mathematical techniques, their observations can be combined to mimic the resolution of a single telescope with a size equal to the separation between the two smallest telescopes that are furthest apart. But even with the material savings from this feat of divine engineering, we’d still be talking about a billion billion tons of mirror, a decent fraction of Earth’s mass. I would love to see the face of the alien contractor when he receives this mission. (Assuming they have a face, of course.)
Just for fun, let’s say our curious alien friends have built a suitable telescope. Other questions would still arise, such as how to steer it in the right direction. Just moving it would be a monumental task. Worse yet, they’d have to keep it locked on our long-dead dinosaur for a while to get decent exposure. The need to track a target is no small problem because everything is in motion: the Earth revolves around the sun; the sun moves through the galaxy; the galaxy moves through the universe; and the galaxy of aliens is flying too. This apparent movement is incredibly small over such large distances, but remember how absurdly small the movement is. T. rex appears! At 66 million light years, a T. rex is quite weak; at this distance, even the sun would be too faint to see using something like the Hubble Space Telescope. Myriad celestial movements would tarnish the image unless corrected somehow – and I admit I have no idea how to deal with that. Whether a monolithic mirror or a sophisticated interferometric array, the telescope would be so large that relativistic effects would come into play.
This is all a bit gimmicky and fun to manipulate, but it has real astronomical ramifications. One of the goals of astronomy is to build a telescope powerful enough to observe details such as surface features and cloud patterns on distant exoplanets, those distant worlds orbiting other stars. Such a telescope would have to be hugeeven if it was an interferometer, but it is technically It’s possible: Resolving such details visually on an Earth-sized planet 10 light-years away, for example, would require an array of telescopes spanning a few hundred kilometers across. We are not ready to build this now, but maybe in a few decades.
Would it be surprising to see continents on a planet in another star system? We just need the will to do it; we already have the intellectual capacities. We’re not dinosaurs, after all.
