Singular case of lane jumping Moon Janus and Epimetheus of Saturn 

When  Sir Issac Newton defined Laws of Motion and Gravity, the Solar system had become a very ordered place.  Celestial mechanics is derived from these simple laws of motions and gravity.  Mediaeval philosophers imagined these planets either as gods or demigods moving forward and retrograde at their whims to make life earthly humans mostly  difficult but rewarding if one appeases these heavenly wanderers, the planets. Newtonian physics demoted these planets from magisterial role to lump of rock or gases orbiting the Sun and Moons to their respective planets in neat and well defined orbits. Very early on Newton realised when there this only Sun and a Planet alone system will remain stable forever. But as soon as three or more planets or their moons enter the calculation system become ‘unstable’ and over a long period of time planets or moons will either fall into each other or escape the system altogether.  The great Newton at this point had to introduce an outside entity, the ‘Master’  mechanic making small periodic adjustments to keep the system going. Pierre Simon  Laplace, a French scholar developed Newtonian Celestial dynamics further and suggested these systems self correcting remain dynamically stable over a long period of time. One interesting example of such a changing but stable system are  lane jumping moons of the ring planet Saturn.

Janus and Epimetheus 5th and 6th moons of Saturn are typical phase locked moons, keeping the same side towards Saturn. These small potato shaped moons have a mean diameter of 117 km  and 178 km respectively. These co orbital moons complete their orbit in less than 17 hours with the inner moon completing orbit in 30 seconds less than the outer one. Their respective orbits are separated only by 50 km. Every time the inner moon takes over the outer one gravitational pull of each other  causes them to switch over their orbit and the outer moon becomes the inner moon and the moon that was in the inner orbit earlier now becomes the outer one. But during these ‘encounters’ with each other they are never closer than 10,000 km. At each crossing over Janus’s orbit is changed by 20 km and Epimethi’s 80 km. This lane jumping occurs every four years. Last one was in the year 2022 and the next one is due in the year 2026. This bizarre orbital relationship is unique in the Solar system and is an example of circular  three body problems involving Saturn Janus and Epimetheus.