3753 Cruithne is a Q-type, Aten asteroid in orbit around the Sun in 1:1 orbital resonance with Earth, making it a co-orbital object. It is an asteroid that, relative to Earth, orbits the Sun in a bean-shaped orbit that effectively describes a horseshoe, and that can change into a quasi-satellite orbit. Cruithne does not orbit Earth and at times it is on the other side of the Sun, placing Cruithne well outside of Earth's Hill sphere. Its orbit takes it near the orbit of Mercury and outside the orbit of Mars. Cruithne orbits the Sun in about one Earth year, but it takes 770 years for the series to complete a horseshoe-shaped movement around Earth.
3753 Cruithne
Cruithne's distance to Earth (blue) and the Sun (yellow) plotted over 500 years (top) and 10 years (bottom)
Plan showing possible orbits along gravitational contours (not to scale)
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Neptune and Pluto. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large planetary system bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.
Spiral density waves in Saturn's A Ring excited by resonances with inner moons. Such waves propagate away from the planet (towards upper left). The large set of waves just below center is due to the 6:5 resonance with Janus.
The eccentric Titan Ringlet in the Columbo Gap of Saturn's C Ring (center) and the inclined orbits of resonant particles in the bending wave just inside it have apsidal and nodal precessions, respectively, commensurate with Titan's mean motion.
Depiction of the resonance between Neptune's moons Naiad (whose orbital motion is shown in red) and Thalassa, in a view that co-rotates with the latter