I don't have doubts that astronauts landed on the moon.
I watched documentaries, read about it and actual witnessed one of the landings as a kid watching the live news.
But what amazes me amongst all other obstacles, is the precision of the trajectories. I studied at university and am familiar with math and physics. But I would never ever even know how to start calculating orbits, angles, etc.
How did they know the gravity on the surface of the moon with enough precision so that the lunar lander would have enough trust to get back in orbit? How did they calculate the correct moment for it, so that the lunar lander would meet the Apollo capsule and attach to it?
Not to mention the launch itself with so many spins around the Earth to then activate some trust that propells the capsule heading to the moon. I mean this is not some aproximate calculation where you just assume some constants and ignore some facts: it had to be precise!
How did they do it? How did they know how to calculate all of this? Did they make constant corrections on their way to the moon?
I know that there are many more challenges like materials, oxigen, water, waste disposal, radiation, communication, batteries/electricity, enough fuel, etc.
But calculating the orbits is to me the biggest mystery! Also, how did they manage to not "forget" anything? Like compensating for something that influences the math? How did they know which parameters to take into account?
Indeed, putting a man on the moon is without question man's biggest feat (close to nuclear fission/fusion and being able to f### up the whole planet in less than 100 years).
Was it of any particular use? I don't think so, apart from already mentioned marketing reasons.
I don't believe in space exploration: once we have completely wasted our planet, we're doomed. Or, else, when the sun burns down. Space is simply to big for any useful space exploration. And it is less challenging to do something to prevent destroying our planet than to colonize another one.
Even Mars is completely off to us: it does not feature an iron core and hence does not provide a shield against cosmic radiation.
Regards,
Vitor