"Invisible" isn't quite correct. They won't be visible as white spots, they'll be black spots blocking out the things behind them. Not a big deal for human eyes. Quite a big deal for astronomers.
It'll block a star for ~1/2500th of a second (assuming a three meter blocking radius, and 7500m/s) - I wouldn't be surprised if that went undetected 99% of the time. At most it would read as a minor brightness fluctuation, right?
Not only that, but it first has to actually pass in front of the star. This gets increasingly likely as you look at fainter and fainter stars, but the sky is still mostly empty and is not as common as you might think. (Olber's paradox and all that.)
The satellites are not only small, they are also fast. A fast moving satellite can only occlude a 100 light years away object for a couple of microseconds before it passes. This is absolutely negligible for an astronomical observation lasting seconds to minutes. And even if you launched billions of opaque satellites they couldn't come close to blocking a big enough percentage of the sky for this to matter at all.
It'd be in front of an object 100 light years away for an absurdly tiny amount of time. The percentage of the sky occluded by these satellites is absolutely minuscule. This is not a rational notion.
These are not geosynchronous satellites, but instead are 200-500 miles above the Earth, moving many, many thousands of mph. No, it isn't blocking anything 100 light years away unless your shutter speed is in the single-digit nanoseconds.
The relative (apparent) motion differences and the fact that the locations of the satellites are known should take care of that, no? It’s unlikely that the motions are going to track each other exactly in most cases.
In fact if, as you believe, these satellites would actually occlude things beyond them, they sound very useful for calibration and education.
