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hubie [soylentnews.org] writes:

Even Earth's mightiest telescopes aren't up to the task of imaging Apollo lunar landing sites. A lack of resolution is the biggest reason why [scientificamerican.com]:

Back in the early 2000s, when I was butting heads seemingly every week with people who believed the Apollo moon landings were faked [scientificamerican.com], such individuals would pull out an argument they thought was their ace in the hole: If NASA's Hubble Space Telescope is powerful enough to see the intricate details of distant galaxies, why can't it see the Apollo astronaut boot prints on our own moon?

Like most conspiratorial thinking, this argument seems persuasive on its surface but falls apart under the slightest scrutiny. Those taken in by it have a misunderstanding of two things: how telescopes work and just how big space is.

Many people think a telescope's purpose is to magnify images. Certainly manufacturers of inexpensive (read: cheap) telescopes love to market them as such: "150x power!" they print in huge lettering on the box (along with highly misleading photographs from much bigger telescopes). While magnification is important, a telescope's real strength is in its resolution, however. The difference is subtle but critical.

Magnification is just how much you can zoom in on an object, making it look bigger. That's important because while astronomical objects are physically big, they're very far away, so they appear small in the sky. Magnifying them makes them easier to see.

Resolution, on the other hand, is the ability to distinguish two objects that are very close together. For example, you might perceive two stars orbiting each other—a binary star—as a single star because they're too closely spaced for your eye to separate. You can't resolve them. Looking through a telescope with higher resolution, however, you might be able to discern the separation between them, revealing that they are two individual stars.

But isn't that just magnification, then? No—because magnification only makes things bigger! This is easy to demonstrate with a photograph: you can zoom in on the photograph as much as you'd like, but past a certain limit, you're just magnifying the pixels, and you can't get any more information out of it. To break through that wall, you have to gain resolution rather than magnification.

[...] At its best, Hubble's resolution is about 0.05 arcsecond—a very tiny angle! But how much detail it can see in real terms depends on the target's distance and physical size. For example, 0.05 arcsecond is equivalent to the apparent size of a dime seen from about 140 kilometers away.

That brings us back to the conspiracy theorists and their gripe about spotting boot prints on the moon. Galaxies are typically tens of millions or even billions of light-years from Earth. At those distances, Hubble can resolve objects a few light-years across—tens of trillions of kilometers—at best. So while it looks like we're seeing galaxies in great detail in those spectacular Hubble images, the smallest thing we can see is still tremendously huge.

Meanwhile the moon is only about 380,000 km from us—and from Hubble. At that distance, Hubble's resolution surprisingly limits it to resolving objects no smaller than about 90 meters across. So not only can we not see the astronauts' boot prints in Hubble images but we also can't even see the Apollo lunar landers, which were only about four meters across!

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