satellites and black holes

[primitive]

Yes, the sats would move.

If you have the QR, you could try to put a sat layer ship on repeat orders and make it pick up and replace the sats each turn. It will take a couple of moves of each turn to replace them though, so the warppoint will be undefended early each turn.
This might work on the AI, but I don�t think any human players would fall for it