Built on Facts

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.

Comments

#1 Paolo Amoroso
July 14, 2009

The Hubble Space Telescope did image the Moon, see http://www.nasa.gov/vision/universe/solarsystem/hubble_moon.html
#2 Russell
July 14, 2009

The obvious extension of the conspiracy theory is that the Lunar Reconnaisance Orbiter will be as fake as the moon landing.
#3 Matt Springer
July 14, 2009

Interesting. I had been told it couldn’t due to the brightness. That may have been with the older instrument sets though, over the years a lot of them have been upgraded significantly.
#4 MikeMa
July 14, 2009

As you say, the orbiter pics ought to end the conspiracies but they wont of course. It will only make the conspiracies more complex and sinister. Some of these loons have been spinning these tales for over 40 years. No way they are going to give up now.
#5 Uncle Al
July 14, 2009

(physical reality) – (empirical reality) = faith

Would Allah tolerate Christian trespass upon the face of the Muslim demigod? Either Americans did not go to the moon or there must be jihad! Lunar laser ranging is studied for the sake of acquiring theoretical knowledge internal to its Zwinglian contemplation of faith, but not in essence or reality.

Faith aspirates.
#6 Alex Metrakos
July 14, 2009

I bet a lot of people who believe the moon landing conspiracy do so because they once heard a compelling argument that makes sense to a laymen. These pictures will do a lot to set that group straight.
#7 Max Fagin
July 14, 2009

“(even if it could take pictures of something as bright as the moon, which it can’t).”

Not true, but a common misperception. See Phil Plaits first book “Bad Astronomy” for details on how the Hubble actually CAN take images of the moon.
#8 btet
July 15, 2009

This article does not exist. It’s a conspiracy, made up by the Moon. I am the Moon.

Goo-goo g’joob. ;-p
#9 Roland Chapman
July 15, 2009

Can not the I.S.S. take pictures of the landing site on the moon?If we can have high resoultion pictures of any city in the world why can we not turn those same cmeras to the moon?
Another point also with so many satellites buzzing around up there unhindered by the earths atmosphere surely to goodness many a good clear picture could have and were probably taken.If true about the noon landing why have we waited so very long for final verification.With todays technology far surpassing what passed for high tech way back when,the government can do it.The government does not tell us anything about what is really out there.Beliveve me they know far more than they’ll ever tell us common folk.
#10 tcmJOE
July 16, 2009

On the chance that Roland isn’t simply yanking our chains:

Distance from ISS to Earth: ~ 350 km
Distance from moon to Earth: ~ 380,000 km

Then apply the Rayleigh criterion.
#11 tcmJOE
July 16, 2009

Addendum (and apologies for the double post):

You COULD get a massive “aperture” on the ISS by placing a reflector mirror on each end and combining the light (for an effectively > 100 m aperture telescope) but that requires combining the light sources to within one wavelength of each other. Ask the fine folk at the Large Binocular Telescope how easy that is (punchline: it’s a bitch).
#12 CS
July 17, 2009

Just because you cannot resolve the locations of two distinct sources below some angular distance does not mean that you cannot determine that there is a source smaller than this size if its spectrum is different from the background.

For instance, suppose on a dark night you look towards a house 3 blocks away (~0.5km) that has an exterior light on. Assuming your eyes have adjusted to the dark with the pupils 1cm wide and taking the optimal end of the visible spectrum (wavelengths of 400nm), the best you can do is resolve objects at a scale of an inch or more at the distance of the house, which is far larger than the size of the filament in the light bulb. The wave properties of light prevent us from being able to distinguish features of the filament, but you would still be able to tell that there is a light shining!

The same is true with stars. The resolution of objects many light-years away is absolutely terrible compared with the actual size of the stars. By eye, there is not a single binary or triple star system for which we can distinguish the individual stars. Yet, if you take a photograph at night, you would still consider it to be a picture of the stars (even if we are unable to distinguish features of each star).

In the same line, could we do the same with the moon landing site? Whatever objects were left at the landing site may not be emitting their own light, but they would be reflecting sunlight differently than the regolith. The question would be, what resolution would you need to distinguish that some unique source of light exists at that point? Could Hubble look at that region and be able to say “this ~70m region exhibits a spectrum of light completely unlike any comparable region on the moon”?

Of course, the processing necessary to bring out the spectrum differences would be more than enough for the conspiracy theorists to cry, “This image was doctored!” Still, an interesting question for those of us who drink the Koolaid (as long as The Shadow Government continues to hand out the red kind, I am OK with it).
#13 Melvin W.
July 18, 2009

I love the Misdirection you use. The same as any sleight of hand con artist. You would have me believe that water is NOT wet simply because it is made of two gasses. You can look ONLY at the evidence available.The retro rockets NOT disturbing dust from a camera that is already on the surface,or extended STEADILY from the LLM. Technologically impossible at that time. Yet the Lunar Rover clearly kicks up dust.You put down others faith,yet are blinded by your own,How hypocritical!You place so much faith in the supposed fact of a lunar landing that you aren’t even looking at the slip ups you are presented with. Forget the flag waving and others that are easily explained away. Science is about Repeated results from experiments.Yet you won’t even let your own eyes sway your belief.You Are No scientist then.If you say the retro rockets couldn’t disturb the dust because there is a Vacuum,then how can the Rover?
#14 CCPhysicist
July 19, 2009

Melvin@13 gives me a chuckle.

The retro rockets (descent engine) did kick up dust during the landing. You can hear it mentioned in the pilot’s call during the landing sequence and see the dust in the film shot out of the window of the lander. The dust settles quickly because (a) the engine was turned off when the probe made contact with the surface so the lander dropped the last meter or so and (b) there is no atmospheric drag to keep small dust particles from falling at g/6 and (c) there wasn’t as much dust as they had expected, as seen in the photos of the surface.

By the way, item (b) is one of the bits of evidence it was not faked.

Since there were no TV images of the landing, I don’t know what “TV camera already on the surface” this person is blathering about. Similarly, I have no idea what was technologically impossible about any part of the mission.

Now if he was talking about video shot from the Lunar Rover on much later missions, those clearly show dust being kicked up by the ascent engine even though the landing module is still between it and the surface.

Finally, all of these experiments were repeated several times with consistent results and we still collect data from the retroreflector left up there. How did it get there if travel to the moon is impossible?
#15 Mike
July 21, 2009

If lead is needed to shield from radiation…how did their visors protect them?
#16 loan
February 20, 2012

I think that to get the loan from creditors you must present a great motivation. However, one time I’ve got a sba loan, because I wanted to buy a building.