I totally missed this one. It is called a Niven Ring (or a Polyakov Ring for a non-rigid arrangement of tethered structures https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19780010146.pdf). Such structures are, famously, unstable. https://www.popularmechanics.com/space/deep-space/a11183/could-we-build-a-ringworld-17166651/ also https://en.wikipedia.org/wiki/The_Ringworld_Engineers#Plot_summary Your choices for locating a mirror in solar orbit so that it is always in the same position with respect to the other thing in solar orbit that you want to illuminate are -- really -- only the trojan points L4 and L5 (the antipodal point L3 is stable, but the sun would always be in the way). For a mirror in orbit around the earth, if you want to keep the mirror in the same place in the sky, you've only got the geostationary orbit.