Orbital resonance

In celestial mechanics, there is an orbital resonance ( or short- resonance), when two or more celestial bodies are subject to recurring gravitational influences. Causes of railway resonances are the orbital periods of the celestial bodies involved, their relationship to each other can be described by low natural numbers, for example by 2:1 or a 3:2.

• 2.1 Secular resonance
• 2.2 Kozai mechanism
• 2.3 Laplace resonance

Effects

Resonances can be both disruptive as also have a stabilizing effect on the orbits of the heavenly bodies. This is dependent on the geometric constellation of the celestial bodies involved. Track changes by periodic disturbances (see resonance), which are always applied to the same orbit position, cumulative in the case of an unstable, disturbing resonance or compensate each other in the case of a stable resonance.

Interfering resonances

In the case of interfering resonances, the recurring disturbances prolonged periods to dramatic changes in web form. The most common result is the growth of eccentricity, to the celestial body falls on a collision course with another object or is ejected at a nearby passage from the system.

Examples of interfering resonances are caused by the moons of Saturn division of Saturn's rings and the Kirkwood gaps in the asteroid belt. The latter is considered as the most likely origin of near-Earth asteroids.

Stabilizing resonances

In stabilizing resonances, the locations of the perturbations are evenly distributed on the path of the perturbed object so that their effects cancel each other.

Examples

• The Dwarf Planet Pluto and numerous smaller Kuiper Belt objects, which are called Plutinos, are in a 3:2 resonance with Neptune, ie during three Neptunumläufe they orbit the sun twice. Further afield there are more resonant Kuiper belt objects that are in 2:1 resonance with Neptune's orbit. There are also objects with other resonances such as 5:2 and 3:1.
• A special form of orbital resonance with the ratio of 1:1 form the co-orbital objects. The best known example is the so-called Trojan. You are in a Lagrange point with respect to the sun and a planet (usually Jupiter).
• A large number of smaller asteroids groups outside the main belt between Mars and Jupiter are stabilized by resonance to Jupiter's orbit. Among the Hilda group at 3:2 and the Cybele group at 7:4.
• The extrasolar planet Gliese 876b and Gliese 876c are in a 2:1 resonance.

Other types

Secular resonance

A secular resonance occurs when the movement of the perihel or the node of two or more celestial body is synchronized with each other. The precession frequency of smaller body adapts to this case, the disturbing of the massive body.

Kozai mechanism

Kozai mechanism when there is a periodic and synchronous change of eccentricity and orbital inclination of a celestial body as a result of resonance effects.

Laplace resonance

In a Laplace resonance, the orbital periods of three or more celestial bodies in a low whole-number ratio to each other. Currently, the only known system is that of the three inner Galilean moons of Jupiter, Io, Europa and Ganymede. Their orbital frequencies are in resonance 4:2:1 - Io - four rounds on two Europa and Ganymede rounds circulation.