That’s why somebody needs to send out a sequence of prime numbers
xx xxx xxxxx xxxxxxx
So they just go around and around, including the light, from the point of view of a far away perspective
As a method to communicate with people you don’t know exist, it’s not very good because chances are they won’t be viewing your satellites edge on. For people you know are there, it’s needlessly complicated and expensive.
If you’re going to go to the trouble, you’d be better off making a Dyson swarm and cloaking your star completely. You’d get energy back and be just as detectable for a civilization that thought to compare visible and IR sources (which some Earth scientists have done, with negative results).