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The difference here however is, anyone can *prove* those sites are wrong. First their analysis of the photos is either misguided (i've seen one pointing at a light reflected on Armstrong's helmet as a stage light, though it was the flag...) or plain wrong (edited photos, or "look those crosshairs ! they show it's a made up photo"). Second one can easily check NASA archives, people who actually got there, people who worked for the NASA then, or even pick up a (good) telescope and scan the landing site for the hardware they left there.
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Telescopes
You'd think that telescopes were the surest way of proving we went to the moon. Right? Er, wrong.
The Trouble With Hubble
Why don't we just point Hubble or some other big telescope at the moon to show the moon landing sites? Wouldn't that settle the argument once and for all?
If only it was that easy! The biggest problem with this is that they simply are not powerful enough. The lunar landers are very,very,very small in astronomical terms and they're pretty far away as well. There isn't a telescope in existence that could take a picture of one.
The're lots of mathematics we could show to demonstrate this, but's it's very complicated and we don't fully understand it anway. But here's our abridged dumbed-down version.
Size of Lunar Module. Let's be really generous and say 10m square.
Distance between Hubble and Moon. About 350, 000km.
This works out as an visual angle of (10m)/(3.5 x 10^8m) * (180/PI) = 1.6 x 10^-6 degrees = 6 milliarcseconds.
The WFPC2 'telescope' on Hubble has the following resolution: 800x800 pixels of a 35 arcseconds field of view with a pixel scale of 46 milliarcseconds. Actually resolution in practice is a little below this.
So what does this all mean? Well, roughly speaking, it means that the LM would have to be 15 times larger before it would even cause a dot on a Hubble picture.
(We have to thank Terry Hancock for helping us out with this info. You didn't think we worked it out ourselves, did you? If there's any errors in it, they almost certainly lie with our interpretation of his explanation.)
Or, to look at it another way....
We stole the following off a NASA discussion board. We would usually just link to it, but discussion messages have a habit of expiring and this was too good to lose. Ed Cheng explains there's a law of physics that would prevent Hubble seeing the Lunar Module, and it's to do with the size of its light collecting mirror.
The wavelength of visible light is around 550x10^-9m (i.e. very very small).
The diameter of Hubble's mirror is 2.4m.
Highest ever physically possible resolution = 1.4 x 550 x 10^-9 /2.4 m = 3.2 x 10^-7 radians
At a distance of 350,000km this works out as about 124 metres. As Ed says, roughly the size of a football field.
So even if Hubble's camera had a greater resolution, it still couldn't see the Lunar Module.
But doesn't this same Hubble take photos of things billions of light years away? Yup. Makes you feel very very very small, doesn't it?
Spies
But doesn't the military have spy satellites that can see a pimple on your nose from orbit? Why can't we use those?
The military may well have satellites that do that, but they are in low orbit a whole lot closer to Earth than they are to the moon. They swoop down to just above the atmosphere over the desired target, take the photos, then return to a safer, more stable orbit. They are nowhere near as close to the moon and don't have the power to get out there even if we wanted them to.
http://www.redzero.demon.co.uk/moonhoax/