Mean Motion Resonances in the Asteroid Belt

Mean orbital elements are obtained from their instantaneous, osculating counterparts by removal of the short periodic perturbations. They can be computed by means of different theories, analytical or numerical, depending on the problem and accuracy required. The most advanced contemporary analytical theory (Knežević 1988) accounts only for the perturbing effects due to Jupiter and Saturn, to the first order in their masses and to degree four in eccentricity and inclination. Nevertheless, the mean elements obtained by means of this theory are of satisfactory accuracy for majority of the asteroids in the main belt (Knežević et al. 1988), for the purpose of producing large catalogues of mean and proper elements, to identify asteroid families, to assess their age, to study the dynamical structure of the asteroid belt and chaotic phenomena of diffusion over very long time spans. In the vicinity of the main mean motion resonances, however, especially 2:1 mean motion resonance with Jupiter, these mean elements are of somewhat degraded accuracy.

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Mean Motion Resonances in The Asteroid Belt

International Astronomical Union Colloquium ◽

10.1017/s025292110007281x ◽

1999 ◽

Vol 172 ◽

pp. 381-382

Author(s):

D. Nesvorný ◽

A. Morbidelli

Keyword(s):

Asteroid Belt ◽

Mean Motion Resonances ◽

Mean Motion ◽

Lyapunov Time ◽

Asteroidal Belt ◽

Kirkwood Gaps ◽

The Mean ◽

Three Body

The Kirkwood gaps in the main asteroidal belt (2 – 3.5 AU) coincide with the mean motion resonances with Jupiter (4/1, 3/1, 5/2, 7/3, 2/1). Similarly, several narrower gaps are observed in the outer asteroid belt (3.5 – 4 AU) at places of 11/6, 9/5, 7/4 and 5/3 Jovian resonances (Holman and Murray 1996). As it is now generally accepted, the formation and preservation of these gaps is due to the chaos of the resonant space and efficient ejection of the primordial and collisionaly injected bodies towards high eccentricities and planet-crossing orbits.The Jovian mean motion resonances are not the most important in what concerns the chaos of the observed (i.e. remaining) asteroid population. It was estimated by Šidlichovský and Nesvorný (1998) that about 40% of known objects have the Lyapunov time less than 105 years. It was later found (Nesvorný and Morbidelli 1998, 1999; Morbidelli and Nesvorný 1999) that the resonances responsible for this chaos are, in decreasing order of importance: 1) three-body resonances with Jupiter and Saturn, 2) exterior resonances with Mars, 3) moderate order Jovian resonances, and 4) three-body resonances with Mars and Jupiter.

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Dynamical transport mechanisms of planet-crossing bodies

International Astronomical Union Colloquium ◽

10.1017/s0252921100031274 ◽

1999 ◽

Vol 173 ◽

pp. 87-96

Author(s):

Ch. Froeschlé ◽

P. Michel ◽

C. Froeschlé

Keyword(s):

Large Diameter ◽

Asteroid Belt ◽

Transport Mechanisms ◽

Mean Motion Resonances ◽

Mean Motion ◽

Numerical Integrations ◽

Quantitative Results

AbstractIn this paper we review the most important dynamical mechanisms for transporting material from the asteroid belt to the vicinity of the inner planets. Most of these mechanisms are associated with secular or/and mean motion resonances. From numerical integrations on timescales of hundreds Myr, new quantitative results on the dynamical lifetimes of bodies injected in the main resonances have been obtained. These new results are not consistent with the observed population of Earth-crossers of large diameter. At the light of these results a new scenario for the origin of large Earth-crossers has recently been proposed.

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Stable Chaos versus Kirkwood Gaps in the Asteroid Belt: A Comparative Study of Mean Motion Resonances

Icarus ◽

10.1006/icar.2002.6927 ◽

2002 ◽

Vol 159 (2) ◽

pp. 284-299 ◽

Cited By ~ 17

Author(s):

Kleomenis Tsiganis ◽

Harry Varvoglis ◽

John D. Hadjidemetriou

Keyword(s):

Comparative Study ◽

Asteroid Belt ◽

Mean Motion Resonances ◽

Mean Motion ◽

Kirkwood Gaps

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On a possibility of transfer of asteroids from the 2:1 mean motion resonance with Jupiter to the Centaur zone

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab1078 ◽

2021 ◽

Author(s):

Kazantsev Anatolii ◽

Kazantseva Lilia

Keyword(s):

Terrestrial Planet ◽

Numerical Calculations ◽

Asteroid Belt ◽

Time Interval ◽

Transfer Time ◽

Mean Motion ◽

Resonant Orbits ◽

Main Asteroid Belt ◽

Absolute Magnitudes ◽

Mean Motion Resonance

ABSTRACT The paper analyses possible transfers of bodies from the main asteroid belt (MBA) to the Centaur region. The orbits of asteroids in the 2:1 mean motion resonance (MMR) with Jupiter are analysed. We selected the asteroids that are in resonant orbits with e > 0.3 whose absolute magnitudes H do not exceed 16 m. The total number of the orbits amounts to 152. Numerical calculations were performed to evaluate the evolution of the orbits over 100,000-year time interval with projects for the future. Six bodies are found to have moved from the 2:1 commensurability zone to the Centaur population. The transfer time of these bodies to the Centaur zone ranges from 4,600 to 70,000 yr. Such transfers occur after orbits leave the resonance and the bodies approach Jupiter Where after reaching sufficient orbital eccentricities bodies approach a terrestrial planet, their orbits go out of the MMR. Accuracy estimations are carried out to confirm the possible asteroid transfers to the Centaur region.

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