Orbital resonance
Imagine a child on a swing. The motion has a natural frequency, and if you push at just the right moment in each cycle, the swing goes higher with every push. Orbital resonance works the same way. When orbiting bodies exert regular, periodic gravitational influence on each other, their orbital periods relate by ratios of small integers. Most commonly this relationship exists between a pair of objects known as binary resonance. The physical principle behind orbital resonance is similar to pushing a child on a swing. The body doing the pushing acts in periodic repetition to have a cumulative effect on the motion. These resonances greatly enhance the mutual gravitational influence of the bodies. In most cases this results in an unstable interaction where 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 near 28:14:7:3 resonance of Jupiter's moons Io, Europa, Ganymede and Callisto. Another example is the 3:2 resonance between Neptune and Pluto.
Pierre-Simon Laplace began studying the stability of the Solar System after Newton published his law of universal gravitation in the 17th century. Before Newton there was consideration of ratios and proportions in orbital motions called musica universalis or the music of the spheres. It was Laplace who found the first answers explaining the linked orbits of the Galilean moons. The stable orbits that arise in a two-body approximation ignore the influence of other bodies. The effect of these added interactions on the stability of the Solar System is very small but at first it was not known whether they might add up over longer periods to significantly change the orbital parameters. Mathematicians wondered if some other stabilizing effects might maintain the configuration of the orbits of the planets. A primary result from the study of dynamical systems is the discovery and description of a highly simplified model of mode-locking. This is an oscillator that receives periodic kicks via a weak coupling to some driving motor. The analog here would be that a more massive body provides a periodic gravitational kick to a smaller body as it passes by. The mode-locking regions are named Arnold tongues.
The dwarf planet Pluto follows an orbit trapped in a web of resonances with Neptune including a mean-motion resonance of 2:3. The resonance ensures that when Pluto approaches perihelion and Neptune's orbit, Neptune is consistently distant averaging a quarter of its orbit away. Other much more numerous Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune. There are also smaller but significant groups of resonant trans-Neptunian objects occupying the 1:1 Neptune trojans, 3:5, 4:7, 1:2 twotinos and 2:5 resonances among others with respect to Neptune. In the asteroid belt beyond 3.5 AU from the Sun the 3:2, 4:3 and 1:1 resonances with Jupiter are populated by clumps of asteroids known as the Hilda family, the few Thule asteroids, and the numerous Trojan asteroids respectively. A binary resonance ratio should be interpreted as the ratio of number of orbits completed in the same time interval rather than as the ratio of orbital periods which would be the inverse ratio. Thus the 2:3 ratio above means that Pluto completes two orbits in the time it takes Neptune to complete three.
In the rings of Saturn the Cassini Division is a gap between the inner B Ring and the outer A Ring that has been cleared by a 2:1 resonance with the moon Mimas. More specifically the site of the resonance is the Huygens Gap which bounds the outer edge of the B Ring. In the asteroid belt within 3.5 AU from the Sun the major mean-motion resonances with Jupiter are locations of gaps in the asteroid distribution called Kirkwood gaps most notably at the 4:1, 3:1, 5:2, 7:3 and 2:1 resonances. Asteroids have been ejected from these almost empty lanes by repeated perturbations. However there are still populations of asteroids temporarily present in or near these resonances. For example asteroids of the Alinda family are in or close to the 3:1 resonance with their orbital eccentricity steadily increased by interactions with Jupiter until they eventually have a close encounter with an inner planet that ejects them from the resonance. The Encke and Keeler gaps within the A Ring are cleared by 1:1 resonances with the embedded moonlets Pan and Daphnis respectively. The A Ring's outer edge is maintained by a destabilizing 7:6 resonance with the moon Janus.
TRAPPIST-1 has seven approximately Earth-sized planets in a chain of near resonances forming the longest such chain known. They have an orbit ratio of approximately 24, 15, 9, 6, 4, 3 and 2 or nearest-neighbor period ratios proceeding outward of about 8/5, 5/3, 3/2, 3/2, 4/3 and 3/2. Each triple of adjacent planets is in a Laplace configuration such as b, c and d in one such Laplace configuration and c, d and e in another. Kepler-223 has four planets in a resonance with an 8:6:4:3 orbit ratio and a 3:4:6:8 ratio of periods. This represents the first confirmed 4-body orbital resonance. Simulations indicate that this system of resonances must have formed via planetary migration. TOI-178 has six confirmed planets of which the outer five planets form a similar resonant chain in a rotating frame of reference expressed as 2:4:6:9:12 in period ratios. The innermost planet b orbits close to where it would also be part of the same Laplace resonance chain.
A past resonance between Jupiter and Saturn may have played a dramatic role in early Solar System history. A 2004 computer model by Alessandro Morbidelli of the Observatoire de la Côte d'Azur in Nice suggested the formation of a 1:2 resonance between Jupiter and Saturn due to interactions with planetesimals that caused them to migrate inward and outward respectively. In the model this created a gravitational push that propelled both Uranus and Neptune into higher orbits. The resultant expulsion of objects from the proto-Kuiper belt as Neptune moved outwards could explain the Late Heavy Bombardment 600 million years after the Solar System's formation. While Saturn's mid-sized moons Dione and Tethys are not close to an exact resonance now they may have been in a 2:3 resonance early in the Solar System's history. This would have led to orbital eccentricity and tidal heating that may have warmed Tethys's interior enough to form a subsurface ocean. Subsequent freezing of the ocean after the moons escaped from the resonance may have generated the extensional stresses that created the enormous graben system of Ithaca Chasma on Tethys.
Common questions
What is orbital resonance and how does it work?
Orbital resonance occurs when orbiting bodies exert regular periodic gravitational influence on each other so their orbital periods relate by ratios of small integers. This physical principle works like pushing a child on a swing where the body doing the push acts in periodic repetition to have a cumulative effect on the motion.
Who discovered the stability of linked orbits for Jupiter's moons Io Europa Ganymede and Callisto?
Pierre-Simon Laplace found the first answers explaining the linked orbits of the Galilean moons after Newton published his law of universal gravitation in the 17th century. Before Newton there was consideration of ratios and proportions in orbital motions called musica universalis or the music of the spheres but Laplace provided the explanation for these stable orbits.
How does Pluto maintain its orbit relative to Neptune despite crossing its path?
The dwarf planet Pluto follows an orbit trapped in a web of resonances with Neptune including a mean-motion resonance of 2:3 that ensures when Pluto approaches perihelion Neptune is consistently distant averaging a quarter of its orbit away. Other much more numerous Neptune-crossing bodies that were not in resonance were ejected from that region by strong perturbations due to Neptune.
What causes gaps in Saturn's rings and which moon creates them?
In the rings of Saturn the Cassini Division is a gap between the inner B Ring and the outer A Ring that has been cleared by a 2:1 resonance with the moon Mimas. The Encke and Keeler gaps within the A Ring are cleared by 1:1 resonances with the embedded moonlets Pan and Daphnis respectively while the A Ring's outer edge is maintained by a destabilizing 7:6 resonance with the moon Janus.
Which exoplanet system has the longest known chain of near resonances?
TRAPPIST-1 has seven approximately Earth-sized planets in a chain of near resonances forming the longest such chain known with nearest-neighbor period ratios proceeding outward of about 8/5, 5/3, 3/2, 3/2, 4/3 and 3/2. Each triple of adjacent planets is in a Laplace configuration such as b c and d in one such Laplace configuration and c d and e in another.