A few days ago we briefly mentioned the chemtrail conspiracy theory in the context of water vapor in the atmosphere. Chemtrails are one of those conspiracy theories where belief is pretty much diagnostic of actual your-brain-is-defective crazy. Belief that NASA faked the moon landings is sadly more widespread, but adherents of that theory don’t even have the benefit of being able to blame their dumb on wonky neurochemicals.
Though we’ll never be able to send a little floating helicopter camera back in time to the grassy knoll, there is occasionally a conspiracy theory or two that actually becomes testable via advancing technology. And while the moon landing has been tested to death (retroreflectors, telemetry, site samples, etc), nothing beats a good old fashioned picture. Thus far no one can just take a picture of Tranquility Base, as it’s simply too far. Even Hubble is not even close to the required level of resolution (even if it could take pictures of something as bright as the moon, which it can’t). Why is this?
Well, light is a wave. When a wave passes through an opening like a telescope lens or mirror, it spreads. This spread is called diffraction, and it produces blurring. The bigger the opening of your telescope, the less diffraction and the less blurring. It’s possible to estimate the maximum resolving power of your telescope with a formula known as the Rayleigh criterion. While it’s not a hard and fast limit, by the time you’re looking at features near the size of the Rayleigh limit they’re going to be very blurry. Try to resolve features much smaller than the criterion allows and all you see is uniform fuzz. The criterion:
Really that should be a sine theta, but at the small angles we’re discussing it makes no difference. Lambda is the wavelength of the light, D is the aperture of the telescope. That’ll get you the smallest angular size you can resolve. Multiply that by the distance to your target and you’ll get the smallest linear size you can resolve. Now plug in some numbers:
My telescope is an 8″ reflector. Assuming a generously small 400nm for the light incoming from the moon, and we get an angular size of 2.4×10-6. Multiplied by the distance to the moon, and I can resolve features as small as roughly 870 meters. In other words I couldn’t even see the Superdome if you plopped it down in Mare Tranquillitatis.
The Hubble has an aperture of 2.4 meters. Cruncing the numbers gives a resolution of about 70 meters. It could pick out the Superdome as not much more than a blob of fuzz, but something the size of the lunar lander is not nearly going to be visible in the uniform haze of blur.
The largest earthbound telescopes are a lot larger, reaching around 10 meter mirror size, translating into a resolution in the 18 meter range. Still not going to work, and that’s leaving aside the fact that the Rayleigh criterion is a “perfect world” sort of idealization. In practice the turbulent atmosphere doesn’t let you even remotely approach this kind of resolution from the ground. Some newer technologies like adaptive optics can help, but even if they were perfect they couldn’t beat that 18 meter limit.
Or you could just get closer to the moon.
NASA is doing just that with their Lunar Reconnaissance Orbiter. Its scientific mission has exactly squat to do with looking at the Apollo sites, but in the process of photographing the whole moon up close it will do just that. It will do so with enough resolution to actually see the debris left behind.
And that will end the conspiracy theories.
Ha! Well, it should. I’m sure it won’t, as we’ll hear accusations of everything from faked pictures to unmanned dummy vehicles having been launched to whatever else an ingenious-but-misguided person might think up. But for those reasonable people who just might have been badly informed, I’m hopeful that some of them will come around. Then or when tourists finally start arriving at the inevitable Moon Disney.