My understanding was that in a gravitationally bound system like that, the orbits would be slightly larger (or slower for the same distance) based on the rate of expansion and the distance, but not grow any unless the rate of expansion increases. Like maybe the earth is a few angstroms farther from the sun than in a not expanding universe, but that number doesn’t change as long as the expansion keeps going the same. Same for galaxies and clusters.
My understanding was that in a gravitationally bound system like that, the orbits would be slightly larger (or slower for the same distance) based on the rate of expansion and the distance, but not grow any unless the rate of expansion increases. Like maybe the earth is a few angstroms farther from the sun than in a not expanding universe, but that number doesn’t change as long as the expansion keeps going the same. Same for galaxies and clusters.