In the early 2000s, when I I ran into people every week who thought the Apollo moon landings were fakeSuch people made what they thought was their trump card: If NASA's Hubble Space Telescope is powerful enough to see the intricate details of distant galaxies, why can't it see the Apollo astronauts' boot prints on our own moon?
Like most conspiracy theories, this argument seems convincing on the surface but falls apart under the slightest scrutiny. Those who buy into it misunderstand two things: how telescopes work, and how big there is space.
Many people think that the purpose of a telescope is to magnify images. Of course, manufacturers of inexpensive (read: cheap) telescopes like to advertise them as such: “150x magnification!” they print in huge letters on the box (along with highly misleading photos from much larger telescopes). While magnification is important, the real power of a telescope is its resolution. The difference is subtle, but important.
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Magnification is how close you can get to an object, making it appear larger. This is important because although astronomical objects are physically large, they are very far away, so they appear small in the sky. Magnification makes them more visible.
Resolution, on the other hand, is the ability to distinguish between two objects that are very close to each other. For example, you may perceive two stars orbiting each other—a double star—as a single star because they are too close together for your eye to separate. You can't decide them. However, looking through a higher resolution telescope, you can discern the separation between them, revealing that they are two separate stars.
But isn't that just magnification? No, because magnification only makes things bigger! This is easy to demonstrate in photography: you can zoom in on a photo as much as you want, but after a certain point you're just making pixels bigger and can't get more information out of them. To break through that wall, you need resolution, not magnification.
The problem is that the resolution inherent to the telescope itself, This means that to significantly improve resolution, you usually need to upgrade to a much larger telescope. But no matter how big your telescope gets, its resolution will still be limited. When light from an infinitesimally small point, such as a distant star, passes through a telescope, its light is scattered slightly inside the telescope's optics (mirrors or lenses). This is a fundamental property of light, called diffraction, and it cannot be avoided.
As I mentioned earlier, the resolution of a telescope depends in part on the size of its mirror or lens. The larger the light-collecting optics, the better the resolution. But how light travels through the optics depends on its wavelength, with shorter wavelengths giving better resolution. So two blue stars close together can be resolved in a telescope, while two red stars at the same distance cannot. When astronomers build telescopes with cameras on them, they must consider the wavelength they want to observe when deciding how big the camera's pixels will be. Otherwise, they're just increasing the noise, like in our earlier example of zooming in too much on a photograph.
All of this leads to a surprising result. The Hubble Space Telescope has a mirror 2.4 meters wide. NASA's James Webb Space Telescope (JWST) has mirror diameter 6.5 metersso one would expect JWST to have many higher resolution. And at some wavelengths it does: The shortest wavelength JWST can see is about 0.6 microns (what our eyes perceive as orange light), and there its resolution is technically much better than Hubble's.
But JWST is designed as an infrared telescope. At these wavelengths, say around two microns, its resolution is comparable to what Hubble can see at visible wavelengths. In the mid-infrared, 10 to 20 microns, JWST's resolution is even lower. Note that since it is the largest infrared telescope ever launched into space, it still provides some of the sharpest images we have ever taken at these wavelengths!
Astronomers measure resolution as an angle on the sky. There are 90 degrees from the horizon to the zenith, and we divide a degree into 60 arc minutes per degree and 60 arc seconds per arc minute. (An “arc” means it's an angle on the sky.) The Moon, for example, is half a degree wide on the sky, which is 30 arc minutes or 1,800 arc seconds. So the maximum resolution of a telescope is the smallest distance it can distinguish between two objects, expressed as an angle.
At best, Hubble's resolution is about 0.05 arc seconds — Very tiny angle! But how much detail it can see in real terms depends on the distance to the target and its physical size. For example, 0.05 arc seconds is equivalent to the apparent size of a dime seen from about 140 kilometers away.
Which brings us back to the conspiracy theorists and their complaints about bootprints on the moon. Galaxies are typically tens of millions or even billions of light years from Earth. At those distances, Hubble can resolve objects several light years across — tens of trillions kilometers, at best. So while we can see galaxies in great detail in these spectacular Hubble images, the smallest thing we can see is still incredibly huge.
Meanwhile, the Moon is only 380,000 km away from us and from Hubble. At that distance, Hubble's resolution is, oddly enough, limited to objects at least 90 meters across. So we can not only No Hubble images show the astronauts' boot prints, but we can't even see the Apollo lunar modules, which were only about four meters in diameter!
We can see the landing modules and boot prints. Images taken by NASA's Lunar Reconnaissance OrbiterAlthough the camera on this mission has a mirror only about 20 centimeters wide, the spacecraft is in lunar orbit and passed over the Apollo landing sites at an altitude of only 50 kilometers. Because it is much closer to the lunar surface, it can see much finer details on the moon than Hubble. That's why we send probes to planets: we get much better views. Sometimes there's no substitute for being there.
The lesson here is that how things actually work is often subtle and not what you expect. Claims that may seem reasonable fall apart when you know a little more about the underlying physics. And if you see a telescope that is advertised based on the magnification of the device, it is probably best to back off and look for another one. I know it can be difficult, but you just need a little determination.