
related topics 
{math, energy, light} 
{math, number, function} 
{day, year, event} 
{rate, high, increase} 

In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each others' orbits). 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 stable and self correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Pluto and Neptune. 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 Solar System bodies to clear the neighborhood around their orbits by ejecting nearly everything else around them; this effect is used in the current definition of a planet.
Except as noted in the Laplace resonance figure (below), a resonance ratio in this article 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). The 2:3 ratio above means Pluto completes 2 orbits in the time it takes Neptune to complete 3.
Contents
History
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 Laplace. The stable orbits that arise in a twobody 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 and lead to a completely different configuration, or whether some other stabilising effects might maintain the configuration of the orbits of the planets.
Full article ▸


related documents 
Holographic principle 
Electromagnetic field 
Event horizon 
Eclipse 
Brown dwarf 
Quark 
Uranus 
Corona 
Tau Ceti 
Oort cloud 
Gamma ray burst 
Proxima Centauri 
Neutron star 
Comet ShoemakerLevy 9 
Kinetic energy 
Twin paradox 
Newton's laws of motion 
Correspondence principle 
Wave 
Variable star 
Precession (astronomy) 
Planets beyond Neptune 
Nonlinear optics 
Phonon 
Second law of thermodynamics 
Chaos theory 
Continuum mechanics 
Shape of the Universe 
List of relativistic equations 
Electric field 
