Horseshoe Orbit
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
As the amplitude of libration orbits near the triangular points grows toward L3, the orbit eventually encompasses both L4 and L5: these are horseshoe orbits, more precisely librating about L3, L4, and L5 (Murray & Dermott 1999, §3.9/3.11). Horseshoe orbits are separated from tadpole orbits by the Jacobi constant C = C_L3; their zero-velocity curves take the eponymous horseshoe shape in the rotating frame.
Note that horseshoe orbits are large-scale co-orbital motions and do not inherit the linear stability of the equilibrium points: the inference that L4/L5 are stable and therefore horseshoe orbits are relatively stable does not hold.
Examples
The best-known natural horseshoe orbits are Saturn's co-orbital moons Janus and Epimetheus, which exchange orbits (Murray & Dermott 1999, §3.12). The near-Earth asteroid Cruithne is also commonly cited as a horseshoe-orbit example.
Related Concepts
References
- Murray & Dermott, 1999, Solar System Dynamics (§3.9, §3.11, §3.12)