scholarly journals The orbital stability of planets trapped in the first-order mean-motion resonances

Icarus ◽  
2012 ◽  
Vol 221 (2) ◽  
pp. 624-631 ◽  
Author(s):  
Yuji Matsumoto ◽  
Makiko Nagasawa ◽  
Shigeru Ida
Keyword(s):  
Orbital Stability ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion

scholarly journals Orbital evolution of Saturn’s satellites due to the interaction between the moons and the massive rings

2020 ◽  
Vol 640 ◽  
pp. L15
Author(s):  
Ayano Nakajima ◽  
Shigeru Ida ◽  
Yota Ishigaki
Keyword(s):  
Orbital Evolution ◽  
The Self ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Saturn’S Satellites ◽  
Orbital Configuration ◽  
Self Gravity ◽  
Spiral Arm ◽  
Orbital Migration

Context. Saturn’s mid-sized moons (satellites) have a puzzling orbital configuration with trapping in mean-motion resonances with every-other pairs (Mimas-Tethys 4:2 and Enceladus-Dione 2:1). To reproduce their current orbital configuration on the basis of a recent model of satellite formation from a hypothetical ancient massive ring, adjacent pairs must pass first-order mean-motion resonances without being trapped. Aims. The trapping could be avoided by fast orbital migration and/or excitation of the satellite’s eccentricity caused by gravitational interactions between the satellites and the rings (the disk), which are still unknown. In our research we investigate the satellite orbital evolution due to interactions with the disk through full N-body simulations. Methods. We performed global high-resolution N-body simulations of a self-gravitating particle disk interacting with a single satellite. We used N ∼ 105 particles for the disk. Gravitational forces of all the particles and their inelastic collisions are taken into account. Results. Dense short-wavelength wake structure is created by the disk self-gravity and a few global spiral arms are induced by the satellite. The self-gravity wakes regulate the orbital evolution of the satellite, which has been considered as a disk spreading mechanism, but not as a driver for the orbital evolution. Conclusions. The self-gravity wake torque to the satellite is so effective that the satellite migration is much faster than was predicted with the spiral arm torque. It provides a possible model to avoid the resonance capture of adjacent satellite pairs and establish the current orbital configuration of Saturn’s mid-sized satellites.

scholarly journals Four-billion year stability of the Earth–Mars belt

2020 ◽  
Vol 500 (1) ◽  
pp. 1151-1157
Author(s):  
Yukun Huang (黄宇坤) ◽  
Brett Gladman
Keyword(s):  
Semimajor Axis ◽  
Orbital Stability ◽  
Terrestrial Planet ◽  
Small Bodies ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
The Earth ◽  
Steady State Model ◽  
Near Earth Objects

ABSTRACT Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the ‘Earth–Mars belt’ from 1.08 < a < 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04–1.30 au for the age of the Solar system. We show that on this time-scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower ‘Earth–Mars belt’ covering a ∼ (1.09, 1.17) au, e < 0.04, and I < 1° has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν3, ν4, and ν6 secular resonances contribute to long-term instability in the outer (1.17–1.30 au) region on Gyr time-scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth–Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200 m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis and use these to estimate that a diameter of ∼100 km or larger would allow primordial asteroids in the Earth–Mars belt to likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.

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.

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 On the divergence of first-order resonance widths at low eccentricities

2020 ◽  
Vol 496 (3) ◽  
pp. 3152-3160 ◽  
Author(s):  
Renu Malhotra ◽  
Nan Zhang
Keyword(s):  
Planetary Systems ◽  
Circular Orbits ◽  
Mean Motion Resonances ◽  
Order Resonance ◽  
First Order ◽  
Resonance Zone ◽  
Mean Motion ◽  
Orbital Resonances ◽  
Theoretical Analyses

ABSTRACT Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.

Primordial Stability of the Earth–Mars Belt

2020 ◽  
Author(s):  
Yukun Huang ◽  
Brett Gladman
Keyword(s):  
Semimajor Axis ◽  
Orbital Stability ◽  
Terrestrial Planet ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Yarkovsky Effect ◽  
The Earth ◽  
Steady State Model ◽  
Near Earth Objects

<p>Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the 'Earth–Mars belt' from 1.08 au<a<1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04–1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower 'Earth–Mars belt' covering a∼(1.09,1.17) au, e<0.04, and I<1◦ has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν3, ν4, and ν6 secular resonances contribute to long-term instability in the outer (1.17–1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth–Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200m scale of these NEOs, we estimated the Yarkovsky effect drift rates in semimajor axis, and use these to estimate that a diameter of ∼100km or larger would allow primordial asteroids in the Earth–Mars belt to likely survive. We conclude that only a few 100 km scale asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.</p>

scholarly journals Long-term evolution of asteroids in the 2:1 Mean Motion Resonance

2014 ◽  
Vol 9 (S310) ◽  
pp. 178-179
Author(s):  
Despoina K. Skoulidou ◽  
Kleomenis Tsiganis ◽  
Harry Varvoglis
Keyword(s):  
Giant Planets ◽  
Dynamical Models ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
System A ◽  
Term Evolution ◽  
Approximate Treatment ◽  
Mean Motion Resonance

AbstractThe problem of the origin of asteroids residing in the Jovian first-order mean motion resonances is still open. Is the observed population survivors of a much larger population formed in the resonance in primordial times? Here, we study the evolution of 182 long-lived asteroids in the 2:1 Mean Motion Resonance, identified in Brož & Vokrouhlické (2008). We numerically integrate their trajectories in two different dynamical models of the solar system: (a) accounting for the gravitational effects of the four giant planets (i.e. 4-pl) and (b) adding the terrestrial planets from Venus to Mars (i.e. 7-pl). We also include an approximate treatment of the Yarkovksy effect (as in Tsiganis et al.2003), assuming appropriate values for the asteroid diameters.

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