Orbital resonance

1:1 resonanceresonancemean-motion resonancemean motion resonanceresonancesLaplace resonanceresonantmean-motion resonancesresonant orbitresonant orbits
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.wikipedia
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Ganymede (moon)

GanymedeNicholson RegioAtmosphere of Ganymede
Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune.
Ganymede orbits Jupiter in roughly seven days and is in a 1:2:4 orbital resonance with the moons Europa and Io, respectively.

Pluto

134340 Pluto(134340) Plutoescaped moon of Neptune
Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune.
This means that Pluto periodically comes closer to the Sun than Neptune, but a stable orbital resonance with Neptune prevents them from colliding.

Rings of Saturn

Cassini DivisionA Ringrings
Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. A Lindblad resonance drives spiral density waves both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in Saturn's rings (where ring particles are subject to forcing by Saturn's moons).
The rings have numerous gaps where particle density drops sharply: two opened by known moons embedded within them, and many others at locations of known destabilizing orbital resonances with the moons of Saturn.

Secular resonance

secularν 6 resonanceresonant alignment
A secular resonance occurs when the precession of two orbits is synchronised (usually a precession of the perihelion or ascending node).
A secular resonance is a type of orbital resonance between two bodies with synchronized precessional frequencies.

Galilean moons

Galilean satellitesGalilean moonmoons of Jupiter
It was Laplace who found the first answers explaining the linked orbits of the Galilean moons (see below).
The three inner moons—Io, Europa, and Ganymede—are in a 4:2:1 orbital resonance with each other.

Moons of Saturn

moon of Saturnmoonmoons
A Lindblad resonance drives spiral density waves both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in Saturn's rings (where ring particles are subject to forcing by Saturn's moons).
The relatively large Hyperion is locked in a resonance with Titan.

Musica universalis

music of the spheresharmony of the spheresthe music of the spheres
Before Newton, there was also consideration of ratios and proportions in orbital motions, in what was called "the music of the spheres", or Musica universalis.
Further scientific exploration discovered orbital resonance in specific proportions in some orbital motion.

Europa (moon)

EuropaEuropanLife on Europa
Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune.
The orbital eccentricity of Europa is continuously pumped by its mean-motion resonance with Io.

Stability of the Solar System

Digital Orrerychaotic behavior
Since the discovery of Newton's law of universal gravitation in the 17th century, the stability of the Solar System has preoccupied many mathematicians, starting with Pierre-Simon Laplace.
Orbital resonance happens when any two periods have a simple numerical ratio.

Lindblad resonance

Lindblad resonancesOuter Lindblad Resonance
A Lindblad resonance drives spiral density waves both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in Saturn's rings (where ring particles are subject to forcing by Saturn's moons).
A Lindblad resonance, named for the Swedish galactic astronomer Bertil Lindblad, is an orbital resonance in which an object's epicyclic frequency (the rate at which one periapse follows another) is a simple multiple of some forcing frequency.

Gliese 876

confirmedGl 876
It is now also often applied to other 3-body resonances with the same ratios, such as that between the extrasolar planets Gliese 876 c, b, and e. Three-body resonances involving other simple integer ratios have been termed "Laplace-like" or "Laplace-type".
It is the only known system of orbital companions to exhibit a triple conjunction in the rare phenomenon of Laplace resonance (a type of resonance first noted in Jupiter's inner three Galilean moons).

Io (moon)

IoAtmosphere of IoIo torus
Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune.
Based on ephemerides produced by astronomer Giovanni Cassini and others, Pierre-Simon Laplace created a mathematical theory to explain the resonant orbits of Io, Europa, and Ganymede.

Mercury (planet)

MercuryMercurioplanet Mercury
Numerical simulations have suggested that the eventual formation of a perihelion secular resonance between Mercury and Jupiter (g 1 = g 5 ) has the potential to greatly increase Mercury's eccentricity and possibly destabilize the inner Solar System several billion years from now.
It is tidally locked with the Sun in a 3:2 spin-orbit resonance, meaning that relative to the fixed stars, it rotates on its axis exactly three times for every two revolutions it makes around the Sun.

514107 Kaʻepaokaʻawela

Kaʻepaokaʻawela
Most bodies that are in resonance orbit in the same direction; however, the retrograde asteroid 514107 Kaʻepaokaʻawela appears to be in a stable (for a period of at least a million years) 1:−1 resonance with Jupiter.
The unusual object is the first example of an asteroid in a 1:1 resonance with any of the planets.

Jupiter

JovianGioveplanet Jupiter
Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune.
This is approximately two-fifths the orbital period of Saturn, forming a near orbital resonance between the two largest planets in the Solar System.

Asteroid belt

main-beltMain beltmain-belt asteroid
Asteroids which approach it have their eccentricity slowly increased until they become Mars-crossers, at which point they are usually ejected from the asteroid belt by a close pass to Mars.
Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter.

Resonant trans-Neptunian object

restwotinoresonance
In astronomy, a resonant trans-Neptunian object is a trans-Neptunian object (TNO) in mean-motion orbital resonance with Neptune.

Saturn

Atmosphere of SaturnOrbit of SaturnPhainon
Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn.
As a consequence, it forms a near 5:2 mean-motion resonance with Jupiter.

Plutino

plutinos2:3 resonance with Neptune2:3 resonant
The next largest body in a similar 2:3 resonance with Neptune, called a plutino, is the probable dwarf planet Orcus.
In astronomy, the plutinos are a dynamical group of trans-Neptunian objects that orbit in 2:3 mean-motion resonance with Neptune.

Clearing the neighbourhood

cleared the neighborhoodcleared its neighborhoodcleared their neighbourhoods
The special case of 1:1 resonance between bodies with similar orbital radii causes large Solar 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.
Over many orbital cycles, a large body will tend to cause small bodies either to accrete with it, or to be disturbed to another orbit, or to be captured either as a satellite or into a resonant orbit.

Titan (moon)

TitanSaturn's moon Titanatmosphere
The outer end of this eccentric ringlet always points towards Saturn's major moon Titan.
The small, irregularly shaped satellite Hyperion is locked in a 3:4 orbital resonance with Titan.

Hilda asteroid

3:2Hilda familyHilda group
Hildian) are a dynamical group of more than 4000 asteroids located beyond the asteroid belt in a 3:2 orbital resonance with Jupiter.

N-body problem

n''-body problemthree-body problemN-body
The stable orbits that arise in a two-body approximation ignore the influence of other bodies.
Perturbative approximation works well as long as there are no orbital resonances in the system, that is none of the ratios of unperturbed Kepler frequencies is a rational number.

Solar System

outer Solar Systeminner Solar Systemouter planets
The special case of 1:1 resonance between bodies with similar orbital radii causes large Solar 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.
Hilda asteroids are in a 2:3 resonance with Jupiter; that is, they go around the Sun three times for every two Jupiter orbits.

Alinda asteroid

Alinda familyAlinda groupAlinda
These objects are held in this region by the 1:3 orbital resonance with Jupiter, which results in their being close to a 4:1 resonance with Earth.