scholarly journals Three-Body Mean Motion Resonances and the Chaotic Structure of the Asteroid Belt

1998 ◽  
Vol 116 (6) ◽  
pp. 3029-3037 ◽  
Author(s):  
D. Nesvorný ◽  
A. Morbidelli
Keyword(s):  
Asteroid Belt ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Three Body

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 Planetary and satellite three body mean motion resonances

Icarus ◽  
2016 ◽  
Vol 274 ◽  
pp. 83-98 ◽  
Author(s):  
Tabaré Gallardo ◽  
Leonardo Coito ◽  
Luciana Badano
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion ◽  
Three Body

Asteroids in three-body mean motion resonances with planets

Icarus ◽  
2018 ◽  
Vol 304 ◽  
pp. 24-30 ◽  
Author(s):  
Evgeny A. Smirnov ◽  
Ilya S. Dovgalev ◽  
Elena A. Popova
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion ◽  
Three Body

scholarly journals An integrable model for first-order three-planet mean motion resonances

2021 ◽  
Vol 133 (8) ◽  
Author(s):  
Antoine C. Petit
Keyword(s):  
Integrable Model ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Zeroth Order ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Formation And Evolution ◽  
The Stability ◽  
Three Body

AbstractRecent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one-degree-of-freedom Hamiltonian, little is known of the exact dynamics of three-body resonances besides the cases of zeroth-order MMRs or when one of the bodies is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one-degree-of-freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application, I show how this model could improve our understanding of the capture into MMRs as well as their role in the stability of planetary systems.

The functional relation between three-body mean motion resonances and Yarkovsky drift speeds

2021 ◽  
Vol 507 (4) ◽  
pp. 5796-5803
Author(s):  
I Milić Žitnik
Keyword(s):  
Time Delays ◽  
Semimajor Axis ◽  
Functional Relation ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Drift Speed ◽  
Functional Relations ◽  
Numerical Integrations ◽  
Three Body ◽  
Good Agreement

ABSTRACT We examined the motion of asteroids across the three-body mean motion resonances (MMRs) with Jupiter and Saturn and with the Yarkovsky drift speed in the semimajor axis of the asteroids. The research was conducted using numerical integrations performed using the Orbit9 integrator with 84 000 test asteroids. We calculated time delays, dtr, caused by the seven three-body MMRs on the mobility of test asteroids with 10 positive and 10 negative Yarkovsky drift speeds, which are reliable for Main Belt asteroids. Our final results considered only test asteroids that successfully crossed over the MMRs without close approaches to the planets. We have devised two equations that approximately describe the functional relation between the average time 〈dtr〉 spent in the resonance, the strength of the resonance SR, and the semimajor axis drift speed da/dt (positive and negative) with the orbital eccentricities of asteroids in the range (0, 0.1). Comparing the values of 〈dtr〉 obtained from the numerical integrations and from the derived functional relations, we analysed average values of 〈dtr〉 in all three-body MMRs for every da/dt. The main conclusion is that the analytical and numerical estimates of the average time 〈dtr〉 are in very good agreement, for both positive and negative da/dt. Finally, this study shows that the functional relation we obtain for three-body MMRs is analogous to that previously obtained for two-body MMRs.

Kozai mechanism inside mean motion resonances in the three-dimensional phase space

2020 ◽  
Vol 493 (4) ◽  
pp. 5816-5824 ◽  
Author(s):  
Yi Qi ◽  
Anton de Ruiter
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Necessary Condition ◽  
Resonant Coupling ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
3D Space ◽  
Test Particles ◽  
Dimensional Phase Space ◽  
Three Body

ABSTRACT In this paper, we investigate the Kozai mechanism inside the inclined mean motion resonance (MMR) through a three-dimensional (3D) phase space. The Hamiltonian approximation for both prograde and retrograde MMRs is established by a semi-analytical method. We pick Jupiter as the disturber and study the Kozai mechanism in the Sun–Jupiter circular restricted three-body problem. Kozai islands of the prograde and retrograde MMRs are found in the 3D phase space. Numerical integration demonstrates that the locus of the orbit on the Kozai island is bounded by the Kozai island in the 3D phase space, so the orbit is locked in the Kozai+MMR state. The study of the Kozai dynamics inside a retrograde 1:1 MMR indicates that Kozai islands in the 3D phase space are just a sufficient condition for the Kozai+MMR mechanism rather than a necessary condition. There is no Kozai island in the 3D space for the retrograde 1:1 MMR, but the resonant coupling of Kozai with the retrograde 1:1 MMR appears in the phase space. Finally, dynamical behaviours of the two test particles located on Kozai islands are demonstrated in the ephemeris model.

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
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