A secular resonance is a type of

orbital resonance 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. Most commonly, this relationsh ...

between two bodies with synchronized precessional frequencies. In

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

secular Secularity, also the secular or secularness (from Latin ''saeculum'', "worldly" or "of a generation"), is the state of being unrelated or neutral in regards to religion. Anything that does not have an explicit reference to religion, either negativ ...

refers to the long-term motion of a system, and

resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...

is periods or frequencies being a simple numerical

ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

of small

integers An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

. Typically, the synchronized precessions in secular resonances are between the rates of change of the argument of the periapses or the rates of change of the longitude of the ascending nodes of two system bodies. Secular resonances can be used to study the long-term orbital evolution of

asteroids An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

and their

families Family (from la, familia) is a group of people related either by consanguinity (by recognized birth) or affinity (by marriage or other relationship). The purpose of the family is to maintain the well-being of its members and of society. Ideal ...

within the

asteroid belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, c ...

Description

Secular resonances occur when the

precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In oth ...

of two orbits is synchronised (a precession of the

perihelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elli ...

, with frequency g, or the

ascending node An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes. Planes of reference Common planes of refere ...

, with frequency s, or both). A small

body Body may refer to: In science * Physical body, an object in physics that represents a large amount, has mass or takes up space * Body (biology), the physical material of an organism * Body plan, the physical features shared by a group of anima ...

(such as a

small Solar System body A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first defined in 2006 by the International Astronomical Union (IAU) as follows: "All other objects, ...

) in secular resonance with a much larger one (such as a

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...

) 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 Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-Centre (geometry), center, in geometry * Eccentricity (g ...

and the

inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Eart ...

of the small body. One can distinguish between: *''linear secular resonances'' between a body (no subscript) and a single other large perturbing body (e.g. a planet, subscript as numbered from the Sun), such as the ''ν₆ = g − g₆ secular resonance'' between asteroids and Saturn; and *''nonlinear secular resonances'', which are higher-order resonances, usually combination of linear resonances such as the z₁ = (g − g₆) + (s − s₆), or the ν₆ + ν₅ = 2g − g₆ − g₅ resonances.

ν₆ resonance

A prominent example of a linear resonance is the ''ν₆ secular resonance'' between

and Saturn. Asteroids that approach Saturn have their eccentricity slowly increased until they become Mars-crossers, when they are usually ejected from the

by a close encounter with

Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...

. The resonance forms the inner and "side" boundaries of the asteroid belt around 2 AU and at inclinations of about 20°.

References

Orbital perturbations Orbital resonance {{scattering-stub

Description

ν6 resonance

See also

References

ν₆ resonance