Is there any concrete, solid proof of this space odyssey?
Is there a way that I personally have a look a it? Let's say, with a nice telescope ?
no we don't have any evidence ;-)
The artifacts of the mission have been seen by the Lunar Reconnaissance Orbiter and probably other satellites. They can't be seen from Earth.
I've spent a great deal of effort arguing about the moon landing, and done a great deal of research (the google kind, not the graduate kind) into the claims about the moon landing "hoax." The biggest struggle I've had is that I (obviously) don't possess all the knowledge from every scientist who worked on Apollo, and the person I'm arguing with will normally ask more and more detailed questions until I can't answer them, and they say something like "see? You find out it's a government cover-up if you dig deep enough."
Most of the claims I hear are technical in nature, and are easy to debunk if you can go read about the subject and then follow up with the person (and the person is willing to appeal to fact, which in many cases, is doubtful). Some of the technical claims I hear:
All of these are founded on a misunderstanding of some scientific discipline or the other. Most people don't know that the Van Allen belts aren't made of "radiation," but high energy charged particles. Or that the astronauts were plenty warm from being in direct sunlight the entire time, and had to keep cool.
These are supplemented with claims that the US would do anything to win the space race. Since the technical challenges are insurmountable, it follows that the landings were faked in order to win. Of course, the technical challenges aren't insurmountable -- and the evidence that the moon landings are real is overwhelming.
There's a few things that I think are very convincing evidence that the moon landings happened:
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