Low Earth Orbit (LEO) satellite mega-constellations promise ubiquitous network services to "unconnected" users. But their upcoming global routing for Earth will be unstable due to exhaustive topology updates between satellites and Earth, inside an orbital shell, and across heterogeneous orbital shells. In real LEO networks, these multi-dimensional dynamics are interleaved and complicated by chaotic orbital maneuvers and random failures. They are less predictable than most satellite routing proposals expect and threaten these proposals' availability, efficiency, or resiliency at scale.