Earth-based telescopes to solve the mystery...
This is the classic claim of people who know nothing about how a telescope works! The fact that these instruments can detect and photograph objects billions of light-years away, huge and very bright, does not mean that they can also detect objects left on the lunar surface during the Apollo missions, which are small and faint.
It would be wonderful to have optical instruments that let us take a stroll among the rocks and dust of the Moon, perhaps while sitting comfortably in an armchair here on Earth, but unfortunately they do not exist. It may sound incredible, but at the moment no telescope ever built, not even the largest, could detect the objects left on the Moon during the Apollo missions.
But why is that currently impossible? The logical answer comes, as always, from physics and, specifically, from an insurmountable law of optics and geometry. When you consider a telescope's objective, you cannot avoid reckoning with a fundamental parameter: angular optical resolution. Expressed in fractions of a degree or in arcseconds, it gives the size of the smallest details that can be "resolved" by any instrument, large or small...
Every telescope has a physical limit called the diffraction limit: light, behaving as a wave, tends to "smear out" when it passes through a telescope's circular aperture. The smaller the diameter of the mirror, the less detailed the image. The angular resolution θ is calculated with the Rayleigh criterion:
θ = 1.22 (λ / D)
where λ is the wavelength of the light and D is the diameter of the mirror. The smaller the value of θ, the finer the detail we can capture.
Suppose we point the Hubble Space Telescope (HST) at the Moon, with its 2.4 meter diameter objective and its maximum resolution of about 0.1 arcseconds. According to the calculations, this instrument could detect the cap of a ballpoint pen 50 km away from its objective. This comparison helps us understand that if we pointed it at the Moon, which is on average 384,400 km from Earth, the largest object we could make out on its surface would have a diameter of about 100 meters. What does this mean? It means that one pixel of our hypothetical photo, taken with the CCD sensor of HST's digital camera, would correspond to a patch of lunar ground 100 by 100 meters. The pixel-to-meter ratio is therefore dramatically insufficient: a single point of the image covers an area as large as an entire city block.
The largest object left by the astronauts on the Moon is the LM descent stage, the gold one with four legs, which has a diameter of about 10 meters, that is, 10 times smaller than the smallest resolvable detail. This means that on our sensor it would literally be swallowed up by a single pixel, vanishing into the visual noise of the surrounding terrain. It would look the same to the human eye. If we could fit an eyepiece at HST's prime focus we would see the same thing! We could magnify the image, which would be sharp at first, but would then inevitably blur as it approached the theoretical resolution of the optics. A telescope, in fact, cannot show details finer than that physical limit. It is, unfortunately, an insurmountable barrier...
If you want to see for yourself what we have just said, visit the NASA web pages with a high-resolution photo of the Apollo 17 landing site, taken by Hubble and then processed on a computer to obtain a 3D version too. It shows the Taurus-Littrow valley on the edge of the Sea of Serenity imaged at the telescope's maximum possible optical resolution .
As you would expect, of the LEM descent stage, the Lunar Rover and the other equipment left behind during the mission there is no trace at all. These objects are immensely smaller than the smallest resolvable object. The red cross in the center of the photo marks the area where, in December 1972, the Challenger module landed with Eugene Cernan and Harrison Schmitt on board, but Hubble's eye can give us nothing but dust and rocks.
The principle of optical interferometry is to use the digital images provided by the cameras of many small telescopes to obtain a single image through computer processing. The end result is comparable to what could be obtained with a single telescope whose objective spans the combined area of the many small telescopes used.We could take the largest telescopes on Earth, but unlike Hubble, which is in space, they are further handicapped by the shimmering of Earth's atmosphere. Atmospheric turbulence, or seeing, distorts incoming light, limiting the effective resolution. To see the lunar module from the ground as an object of at least one pixel, we would need an optical telescope with a mirror more than 75 meters in diameter. If, on the other hand, we wanted to see the astronauts' footprints or the rover with acceptable detail, say 10 centimeters per pixel, we would need a telescope more than 2,000 meters in diameter. The only instruments on Earth that might achieve some result are those of the VLT group (Very Large Telescope), which, working together in interferometry, would make it possible to glimpse objects with a minimum size of about 4-5 meters. In fact, the theoretical resolution of this "giant eye" is estimated at around 0.002-0.003 arcseconds. But let us rein in our enthusiasm: we would still be talking about a handful of pixels that could only partly outline the shape of the hardware. Unfortunately this theoretical resolution has not yet been fully achieved, despite adaptive optics systems, although one test proposed by scientists is precisely to try pointing the array at the Apollo sites.
In conclusion, the only way to obtain direct photographic evidence is to shorten the distance between observer and target. We will have to wait for technological progress, although several robotic probes from various international space agencies, including NASA's LRO (Lunar Reconnaissance Orbiter), have already beaten the astronomers to it. Orbiting, in some cases, just 50 kilometers above the lunar surface, they have achieved a resolution of about 50 centimeters per pixel. Only at this close range was it possible to clearly capture the bases of the LM descent stages, the dark trails left by the astronauts' footsteps and even the rover's shadow, confirming with facts what the physics of telescopes had already told us long ago: from Earth, those historic space relics, witnesses of a wonderful and courageous era, will remain forever invisible to our eyes. And the conspiracy theorists will just have to accept it!
