Horseshoe orbit

A co-orbital trajectory in which an object moves relative to another along a horseshoe-shaped path in a rotating frame, reversing direction near close approaches.

Co-orbital motion: Orbital motion in which two bodies share the same or nearly the same mean orbital period. Horseshoe trajectories are one form of motion in the 1:1 orbital resonance.
Cruithne: Near-Earth asteroid 3753 Cruithne, which follows a complex co-orbital trajectory with Earth. Its motion is often depicted as a horseshoe in a frame rotating with Earth, though its full path is more complex.
Restricted three-body problem: A model of two massive bodies and a third body whose mass is negligible by comparison. It supplies the standard framework for describing a small object’s horseshoe motion around two primaries.
Quasi-satellite orbit: A co-orbital trajectory in which an object appears to circle its host planet in a rotating frame while orbiting the star. It is another 1:1-resonant state, but the relative path loops around the host rather than forming a horseshoe.
1:1 mean-motion resonance: An orbital resonance in which two bodies complete one orbit in approximately the same time. The shared orbital period lets their relative positions evolve slowly around the central body.
2010 TK7: An asteroid that librates around Earth's leading triangular Lagrange point. It provides a well-known Earth co-orbital example with tadpole motion rather than a horseshoe path.
Hill sphere: The region around an astronomical body where its gravity dominates the attraction of a more distant primary. Close encounters and orbital reversals depend on the scale of each co-orbital body's gravitational influence.
Orbit: The path of an object moving under the influence of gravity or another force. Horseshoe motion is a specific orbital pattern within the broader concept of an orbit.
Rotating reference frame: A coordinate system that rotates at a chosen angular velocity relative to an inertial frame. In this frame, the relative path appears as a horseshoe around the stable orbital regions.
Janus: A small moon of Saturn that shares a nearly identical orbit with Epimetheus. Its orbital exchanges with Epimetheus are a prominent natural example of horseshoe-like co-orbital dynamics.

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