Interestingly, one thing we DID do that's observable from earth is to put an array of retroreflectors onto the moon, so that we can bounce a laser off of it.
My sample size of moon landing skeptics (1) didn't dispute that we've been to the moon, he just didn't believe that we did it in 1969, but if you do run into a skeptic this is pretty good evidence that we made it there eventually, or at least requires the conspiracy to be much more involved =).
".... but if you do run into a skeptic this is pretty good evidence that we made it there eventually, or at least requires the conspiracy to be much more involved =) ..."
There is another conspiracy buster.
Get the skeptic to explain why the CDSCC [0] - the prime receiving station for the moon landing dish in Parkes, NSW, AUS, received the signal directly from the moon via the 3m S-band antenna during the Apollo 11 EVA? [1]
The kind of loon that's going to insist the entire thing was an elaborate soundstage production isn't exactly going to be swayed by claims that the signal, which they think was fake anyway, was received at a given location.
The laser retroreflectors are at least observable now, which is a pretty big distinction.
Minor correction: Canberra and the CDSCC are in the ACT (Australian Capital Territory), not New South Wales. It's OK though, everyone forgets about the ACT.
Yeah, I had to get a German to lookup what "ᵊ" really means in the International Phonetic Alphabet. It was only then I found out that of the two listed pronunciations on Wikipedia[1], the first actually is the usual Australian pronunciation that my ill-fated attempt at self-deprecating humour hinged upon.
You can measure the distance by modulating the laser and checking how time shifted the reflection is. The moon is pretty close for light but it's measurable.
The gist of the story is: Use a large telescope to not only increase your collecting area, but focus your beam onto that surface: turn that measly 1 milliradian divergence laser into a 1 microradian divergence laser.
If someone say honestly that they receive the photons coming from the moon, then they must get a number of photons that is bigger than the error margin, preferably a few times bigger than the error margin. If it is smaller they can't be sure that it is not some noise.
There are three sets of three graphs. They are very similar, so let's see only the first one.
In the first graph there is a dark line in the center that shows that there are more photons coming at the expected time, than before or after that time. The signal is easy to see, but it is difficult to get any numerical values from this graph.
From the second graph it is possible to read some numerical values. Each bar shows the number of photons that arrive in a 100 ps interval. They have probably a Poisson distribution, but for simplicity let's approximate that by a Normal distribution.
Before the peak, there are approximately 10 +/- 10 photons coming every 100 ps. (These values are estimated from the graph with a lot of zoom, I can't be very sure about them. The values seem to be scattered between 0 an 20, so I assume that the average is ~10 and the standard deviation is ~10.) These are the photons that come from others sources. So if no mirror is present in the moon, or the laser dos not have enough power, then this is the expected value during all the experiment.
At the peak, there are approximately 400 photons in the same time interval. The difference between this value and the average of the first values is like 40 times the standard deviation. So it is almost impossible that they get these peaks by a random chance. For example, the probability to get a value that is bigger than 5 standard deviation is less than 1E-6, for 10 standard deviation it is less than 1E-23, and for 40 standard deviation it is almost almost 0. And they get not only one, but 8 intervals with more than 100 photons.
After the peak, they get more photons than before the peak for technical problems. I see something like 20 +/- 20. Whit these numbers, the chance of a 400 photons peak is bigger, but still almost 0, but I think that the correct way to do the estimations is using the first values.
The third graph is an auxiliary measure with an earth based mirror to get the dispersion caused by the system.
The analysis in the web page is more elaborated. They estimate the shape of the mirror and use the data from the third graph to explain the shape of the peak.
1. The 3.5 mile figure is for resolving the stripes on the flag, not for seeing the flag. If you just want to see the flag, an aperture diameter of around 400 m is required.
2. The "Dawes Limit" is just presented with no explanation. It ultimately comes from the fact that the achievable angular resolution of an aperture of size D, using light with wavelength lambda is lambda/D. So if you were willing to work at 10 nm, then the aperture size goes down by a factor of 50 (of course working at 10 nm has it's own set of problems).
I was concerned by the lack of Wiki-fu about the Dawes Limit on this forum, but it turns out that the wikipedia page is very sparse. This is a more detailed page on the subject and explains where the Dawes Limit comes from.
http://en.wikipedia.org/wiki/Angular_resolution
> What could Hubble see on Earth if it were to be aimed at the Earth?
...
> it can be shown that Hubble could just make out something that is 5.56 inches wide on Earth.
I found that quite odd. I've always heard that spy satellites could read the headline on a newspaper. Why would the Hubble be so much worse? That makes the math in the article a little suspect.
The claims about what spy satellites can see have been exaggerations at least since the 1960s. They are still exaggerations today. I hope everybody knows that the "satellite" view on Google Maps is from conventional aerial photos (taken from airplanes) as you zoom in.
I would guess things have changed a little with the newest technology?
The correct answer might now be "not with the naked human eye" (through an optical telescope).
It is only recently possible to correct atmospheric distortion by having a computer project a laser through the atmosphere and measure the change in realtime and adapt for it (adaptive optics).
Also, the increase in CCD densities have become enormous in the past few years. So it might be possible to make a matrix that could resolve the flag in the near future.
The stereo telescope method they mention at the end has also been improved recently if I remember reading correctly and they have robotic telescopes that can pull this off.
ps. the James Webb Telescope that's going up in 2014 will have 6 times the collection area of the Hubble, so maybe that will be able to do it ! It looks like it's right out of Star Trek:
Even with adaptive optics you still won't get close to the diffraction limit.
> Also, the increase in CCD densities have become enormous in the past few years. So it might be possible to make a matrix that could resolve the flag in the near future.
You can't work around the diffraction limit. There's no CCD that could compensate for the lack of the 5 km aperture required. You must have at least 2 (more like 3 or 4) pieces of glass separated by 5 km or more, otherwise nothing would work.
No you are still constrained by the limit, super resolution only works with the information that is captured.
The diffraction limit isn't a hard line limit rather the information disappears into noise as you go past the limit. So what SR does is use multiple images to remove the noise for details close to the limit using some neat algorithms. But noise quickly overcomes the information as you push against the limit.
Thanks for asking this, I had the same question about high density CCDs, space telescopes, and signal processing. I think it is a reasonable question to bring up.
it just isn't physically possible to resolve a flag on the surface of the moon with anything less than 3.5 mile diameter telescope. The technology used can't help much with physically impossible things!
It is perfectly possible to resolve a (6-foot) flag with a telescope.
The article states "the Earth's atmosphere is never steady enough to allow resolution below about one arc second for most locations". But according to the European Southern Observatory one can do 1000x better:
"With AMBER on the Very Large Telescope Interferometer (VLTI), the astronomers were able to see details on the scale of one milli-arcsecond, corresponding to being able to distinguish, from the Earth, the headlights of a car on the Moon."
-- http://amber.obs.ujf-grenoble.fr/spip.php?article154
Therefore a 6-foot-wide flag ("headlights of a car") would be visible as 1 or 2 pixels with the VLTI, which is made of four 8.2 meter reflectors.
I presume the actual flag left by the astronomers was somewhat smaller, so one would need a tad better telescope, but certainly not something with a "3.5 mile diameter".
yes, but the article explicitly defines "flag being visible" as stripes of the US flag being visible. for that you would need a tad better than 6-foot resolution.
On a side node, the VLTI should be able to produce a 2x2 or 3x3 pixel image of one of the russian or american lunar landers (14-foot wide). It would be a cool thing to accomplish to demonstrate the resolution of the VLTI...
I don't know much about this topic, but I did RTFA, so permit me to ask a stupid question:
1. if this impossibility is related to noise overwhelming the image signal (thereby causing it to be an unresolved blur)
2. and if we assume that this 3.5-mile diameter is for a naked eye looking through a telescope (i.e. we're talking about a single exposure)
3. isn't there some statistical process that could enable a reduction of the diameter of the lens, which would reconstruct a less-noisy image based on multiple exposures?
The article throws numbers, it explains nothing about the Dawes number, which it explicitly describes as being discovered "A long time ago".
Asking if things discovered "a long time ago" have changed in light of modern development isn't un-called for. Especially given the vague statements.
>And, it would only be just visible as a small dot, it would not "look" like a flag at all.
Is similarly vague, and probably part of the reason for the question. We can build optical hardware with resolutions far in excess of our eyes per square unit. What we can see by looking through the scope directly has little to do with how we use more powerful modern telescopes, which appears to be how this is calculated. 20 years ago it would've been hard to predict high-density CCDs, how much more unlikely is it that something "A long time ago" took such things into account?
Lets ask another:
>The only method that could be used to (in theory) see something as small as the Flag on the Moon would be to use two optical telescopes set (for example) 1000 miles apart. This would easily provide the required resolution...
How does this help? Are they talking two Hubbles? Two 1.75 mile wide telescopes? There's zero explanation, despite such an absolute claim.
I didn't realize you didn't understand the article, and I thought you were just posting without reading it first.
There is an upper limit to how much detail you can see. It doesn't matter what you use to do the viewing, the eye, a ccd, anything. The information is simply not there, no matter how you magnify it.
That limit is called the diffraction limit, and it's related to the size of the lens used to collect the light. It sort of has to do with the fact that photons passing near the edge of the lens get distorted.
Dawes number is simply a calculation of the diffraction limit.
So that "small dot" that is really a flag, no matter how well you magnify it, will just look like a blur. The photons that used to show details about it have been scrambled enough that those details are lost.
Regarding the two collectors.
They are talking about two small telescopes placed far apart. They compare the image collected by both telescopes and using that they are able to synthesize information about the object that is not visible using just one telescope. But it's no longer a matter of just looking at it.
I'm sorry that I don't understand it well enough to give a simpler explanation of how that works.
I don't know if you read lord of the rings, but there is a scene where Legolas looks at riders at a great distance and can see details that the humans can't. Supposedly because of his keen eyesight. But actually it's impossible. Assuming that his eyes were about the same size as human eyes, he simply can not see those details, no matter how good of a retina he had. Here's the link: http://scienceblogs.com/principles/2009/06/the_limits_of_elv...
The only method that could be used to (in theory) see something as small as the Flag on the Moon would be to use two optical telescopes set (for example) 1000 miles apart. This would easily provide the required resolution, the huge problem however is combining the images from both telescopes in such a way to realize the resolution. As far as I know right now that technology is not available. Even if the technology was available, the unsteadiness of the Earth's atmosphere would likely render the method useless.
I've read about this method being used a lot in radioastronomy. But how does one proceed to use it in optical astronomy?
And surely if it is possible to algorithmize this it wouldn't be a problem to write a program that will take care of such "technology"?
The telescopes are in the two shed-like white buildings (one in the foreground, the other in shadows in the background).
The collected light is bounced through the white pipes into the large building in the middle, where it is combined and interference fringes are collected. (It has to be combined optically to preserve phase.)
To work, the distances between the two collectors must be maintained very precisely. Besides the obvious optical issues, the technical challenge becomes to measure the separation of the collectors very precisely ("metrology").
I can't speak for the interferometry side, but when it comes to reducing distortion caused by the atmosphere, a lot of advances have been built into the latest generation of big terrestrial telescopes that go a long way towards solving the problem. I have no idea what sort of improvement over the status quo you might need for such a system as described, but it's not unreasonable to think that at least that part of it would be feasible one day.
The method you're referring to is called optical interferometry [1] (well, interferometry in general but optical for visible light obviously). Great strides have been made in this department in recent years and I believe it's been used for exoplanet detection [2].
I don't consider myself a conspiracy theorist but in my opinion the demeanor of Armstrong and crew during the Apollo 11 press conference is indicative of deception.
Fair enough. To clarify, I don't subscribe to really any of the doctrine or ideas presented by the conspiracy "mainstream." I do believe American astronauts have walked on the moon during six individual Apollo missions. I also believe in the instance I referenced previously, that those three men are lying about something.
"Also a little regret knowing they will never go back."
Wow, I had never thought of that aspect of the Apollo program. It's a little sad that of the 22 people to orbit the moon, land on the moon, or both, it appears just four of them ever made a subsequent space flight.
"In March 1972, Aldrin retired from active duty after 21 years of service, and returned to the Air Force in a managerial role, but his career was blighted by personal problems. His autobiographies Return To Earth, published in 1973, and Magnificent Desolation, published in June 2009, both provide accounts of his struggles with clinical depression and alcoholism in the years following his NASA career."
https://secure.wikimedia.org/wikipedia/en/wiki/Lunar_Laser_R...
My sample size of moon landing skeptics (1) didn't dispute that we've been to the moon, he just didn't believe that we did it in 1969, but if you do run into a skeptic this is pretty good evidence that we made it there eventually, or at least requires the conspiracy to be much more involved =).