We don't know whether it's possible to fully predict the long-term stability of any mathematical system describing three or more interacting bodies under gravity.
open
Global / Unspecified, Global
WS01313
The three-body problem famously resists the same clean, closed-form solutions available for two-body systems, and general long-term predictability for all such systems remains incompletely understood. This unresolved question connects pure mathematics directly to astrophysics.