Well, a net isn't really accurate, a net is just string with holes, the holes are to allow water and air through, two things that aren't in space. Instead you would need something like that stuff in bullet proof jackets to catch the objects.
As for size, big yes, but if there is enough time and it can reposition, it could be smaller.
500 miles? I check online, it seems people consider space to be between 62 and 220 mile. Apparently the space station is about 220 miles away. So if you wanted to catch debris that could be a danger, a decent guess could be the 158 miles of space.
at 220 miles the space station orbits completely every 92 minutes. A "net" we could assume would travel the same speed at the high orbit, and faster at the low orbit (or it would fall).
Assume we had a "net" that was about a square 1/4 mile in size (Dunno who we would get it up there) .
That should be enough information to calculate, but my brain just stalled, someone else do it please.
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