Admittingly not simple, as then NOD would have the Ion Cannon.

There is your answer!

To avoid NASA and other muggles from seeing it, the satilliete could also produce strong muggle reppellant charms, so when they scan the area in which space is in the cannon is in, they think they have something more important to do.

Now then about how to avoid people seeing a giant blue beam of death falling from the sky, as you put, I shall resort to illusion charms or repellant charms. Or the Imperius curse on a large basis, telling them to ignore it.

On sec0nd thoughts maybe it should be about the big crater casued as well? I think that this idera is being stuck in the mud.

 

You're forgetting that the Imperius curse is one of the three UNFORGIVABLE curses and lands you a life sentence in Azkaban. And an illusion isn't very believable if you fall into the crater. And another thing, where would you aim? There's nothing to shoot.

 

Err.... We are taking about scanning through scientific instruments, not merely visual. And how exactly with a charm, spell, whatever, transmit it's effects over the enormous distances?

Magical Portraits would already have been invented.
Muggleborns would have made some progress at least.

If you really want some good ideas, try to find some inventions invented After 95, and adapt them.