In last week’s The Universe column, I asked a reader’s question about galaxy collisions in an expanding universe. The answer has to do with vast distances, mysterious forces, and the ultimate fate of the universe.
Not all questions extremely so serious. For example, reader David Erickson had this in mind: “If there were aliens 66 million light years from Earth, how big a telescope would they need to see dinosaurs?”
Ha! I like this question. I’ve thought about it myself but never worked out the math – except to think, “possibly very large”, which dramatically underestimates the real answer. But what’s really beautiful is that tackling this bizarre thought experiment has some real-life 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 Chicxulub asteroid impact that wiped out the nonavian dinosaurs occurred about 66 million years ago. The light from that event would now be reaching a galaxy more or less 66 million light years away. At that distance, observers there could still (at last) see the dinosaurs, assuming they felt like building a really big telescope.
Now the question needs to be broken into two parts: how big is the dinosaur from this distance, and how big must the telescope be to see something of that size?
Since the sky looks like a giant sphere around us, astronomers use angles to measure apparent size. The basic unit for him is a degree; For example, the angle from the horizon to the point directly above the observer, called the zenith, is 90 degrees. The Moon’s apparent size is about 0.5 degrees.
How big an object appears depends on its physical size and its distance from the viewer. There’s a lovely little formula called small angle approximation Which is related to both. There are several different ways to represent this equation, depending on the units you use. For degrees, you take the physical size of the object, multiply it by 57.3 and divide by the distance. So a one meter wide object, such as a small wide screen TV, will have an apparent size of one degree at a distance of 57.3 meters.
Let’s choose everyone’s favorite terrifying carnivore, for your dinosaur Tyrannosaurus Rex. T. rex Vary in size, but let’s say the one the aliens want to see is 10 meters tall.
The distance is 66 million light-years, which is a slight increase. We need this in meters, so after converting (“let’s see, multiply by 10 trillion, take away 2,” and so on), we get a distance of a staggering 6.6×1023 meter.
Adding this to our formula, we get that a T. Rex The apparent size as seen from that distant galaxy would be about 10-21 degree. If you like fun math prefixes, it’s one-sixth of a degree, or a zeptodegree. He is small beyond comprehension. But to be honest, it is very far.
Great, this is one of the two main questions answered! Now, how big a telescope would you need to see something so Lilliputian?
You might think that we need magnification to see our animal from that far away, but that’s actually not the case. In short, something small and very far away will appear like a dimensionless dot. If you enlarge that point in an image, you are only enlarging the pixel. To see it as more than a point, you have to solve it. So what do we really need to look at T. rex And not a single point is higher Resolution.
Resolution is an inherent property of all telescopes and depends mostly on the size of the telescope’s mirror. There is another formula for that, which is called dawes range. This can also be expressed in many 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 telescopic mirror in meters. We know the size of our object in degrees, so we want to solve for D. When we do this, we find that the diameter of our telescope should be 3.2 x 10.16 meters (32 quadrillion metres).
It’s about 3.4 light years across, which, um, would make a mighty large telescope. This is a mirror that would extend three-quarters the distance to Alpha Centauri!
Needless to say, we don’t have the technology extremely No such thing has been built yet. Even if we had the knowledge to make this mirror, it would still be a difficult task to obtain the necessary manufacturing materials: The density of specific telescopic mirror glass is given by And assuming that the thickness of the mirror is only one millimeter, our T. rexThe mass of the -resolution mirror will be about 1030 (a nonillion) metric ton. this is done 100 million times the mass of Earth. You would probably need to raid, destroy, and rebuild a good portion of a large galaxy’s rocky planets to create a mirror like that.
If our peeping aliens are particularly clever, they might avoid this by building an astronomical interferometer instead. It is a series of small telescopes spread over some area; Using sophisticated mathematical techniques, their observations can be combined to mimic the resolution of a single telescope, the size of which is equal to the separation between the two smaller telescopes that are furthest from each other. But even with the material savings from this godlike feat of engineering, we’d still be talking about a billion trillion metric tons of mirror—a decent fraction of the Earth’s mass. I would love to see the face of the foreign contractor when he gets that assignment. (Assuming they have a face, that is.)
Just for fun, let’s say our curious foreign friends somehow built a suitable telescope. Other issues will still arise, such as how to point it in the right direction. Just moving it would be a big task. Worse, they’ll have to keep it off for a while on our long-dead dinosaurs to get good performance. The need to track a target is no small problem because everything is in motion: the Earth is rotating and moving around the Sun; The Sun is moving in the galaxy; Galaxies are moving in the universe; And there’s also a galaxy of aliens flying around. That apparent motion is incredibly small over such vast distances, but remember how absurdly small it is T. rex Appears! From 66 million light years away, a T. rex is very pale; even at that distance Sun It would be too blurry to see using something like the Hubble Space Telescope. Unless corrected in some way, the myriad of celestial movements will blur the image – and I admit I don’t know how to manage this. Whether as a monolithic mirror or a fancy interferometric array, the telescope would be large enough that relativistic effects would come into play.
It’s all somewhat whimsical and amusing, but it has astronomical implications in the real world. One goal of astronomy is to build a telescope powerful enough to actually see details like surface features and cloud patterns on distant exoplanets, those distant worlds that orbit other stars. Such a telescope would be very large, even if it were an interferometer, but it is technically is possible—for example, to visually resolve such details on an Earth-sized planet 10 light years away would require a telescope array that spans a few hundred kilometers. We’re not ready to build it now, but maybe in a few decades.
How amazing would it be to see continents on a planet in another star system? We just need the will to do it; We already have brain power. After all, we’re not dinosaurs.
