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

Icarus ◽  
2002 ◽  
Vol 159 (2) ◽  
pp. 284-299 ◽  
Author(s):  
Kleomenis Tsiganis ◽  
Harry Varvoglis ◽  
John D. Hadjidemetriou
Keyword(s):  
Comparative Study ◽  
Asteroid Belt ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Kirkwood Gaps

scholarly journals Mean Motion Resonances in The Asteroid Belt

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.

scholarly journals Higher Order and Iterative Theories to Compute Asteroid Mean Elements

1999 ◽  
Vol 172 ◽  
pp. 359-360 ◽  
Author(s):  
Z. Knežević ◽  
A. Milani
Keyword(s):  
Asteroid Belt ◽  
Dynamical Structure ◽  
Orbital Elements ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Long Time ◽  
The Mean ◽  
Mean Elements ◽  
Asteroid Families

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.

scholarly journals Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem

2016 ◽  
Vol 18 (10) ◽  
pp. 2315-2403 ◽  
Author(s):  
Jacques Féjoz ◽  
Marcel Guàrdia ◽  
Vadim Kaloshin ◽  
Pablo Roldán
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Kirkwood Gaps ◽  
Three Body ◽  
And Diffusion

Dynamical transport mechanisms of planet-crossing bodies

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.

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

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.

scholarly journals Motion of dust in mean motion resonances with planets

2009 ◽  
Vol 103 (4) ◽  
pp. 343-364 ◽  
Author(s):  
Pavol Pástor ◽  
Jozef Klačka ◽  
Ladislav Kómar
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion
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