Secular resonance
Encyclopedia
A secular resonance is a type of orbital resonance
.
Secular resonances occur when the precession of two orbits is synchronised (a precession of the perihelion, with frequency g, of the ascending node, with frequency s, or both). A small body in secular resonance with a much larger one (e.g. a planet
) will precess at the same rate as the large body. Over relatively short time periods (a million years, or so) a secular resonance will change the eccentricity and inclination
of the small body.
The effects of secular resonances are most studied in the context of the long-time evolution (millions of years or more) of minor planet
orbits within the asteroid belt
.
One can distinguish between
s and Saturn
. 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
due to a close pass to Mars
. This resonance forms the inner and "side" boundaries of the main asteroid belt around 2 AU
, and at inclination
s of about 20°.
Orbital resonance
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...
.
Secular resonances occur when the precession of two orbits is synchronised (a precession of the perihelion, with frequency g, of the ascending node, with frequency s, or both). A small body in secular resonance with a much larger one (e.g. a planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
) will precess at the same rate as the large body. Over relatively short time periods (a million years, or so) a secular resonance will change the eccentricity and inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
of the small body.
The effects of secular resonances are most studied in the context of the long-time evolution (millions of years or more) of minor planet
Minor planet
An asteroid group or minor-planet group is a population of minor planets that have a share broadly similar orbits. Members are generally unrelated to each other, unlike in an asteroid family, which often results from the break-up of a single asteroid...
orbits within the asteroid belt
Asteroid belt
The asteroid belt is the region of the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets...
.
One can distinguish between
- linear secular resonances between a body and a single other large perturbing body (e.g. a planet), such as the ν6 = g -g6 secular resonance between asteroidAsteroidAsteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
s and SaturnSaturnSaturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...
; and - nonlinear secular resonances, which are higher order resonances, usually combination of linear resonanaces such as the z1 = (g -g6) +(s-s6), or the ν6+ν5 =2g -g6-g;5 resonances.
ν6 resonance
A prominent example of a linear resonance is the ν6 secular resonance between asteroidAsteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
s and Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...
. 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
Asteroid belt
The asteroid belt is the region of the Solar System located roughly between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called asteroids or minor planets...
due to a close pass to Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...
. This resonance forms the inner and "side" boundaries of the main asteroid belt around 2 AU
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
, and at inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
s of about 20°.