scholarly journals A study of the high-inclination population in the Kuiper belt – III. The 4:7 mean-motion resonance

2020 ◽  
Vol 492 (3) ◽  
pp. 3566-3579
Author(s):  
Jian Li ◽  
S M Lawler ◽  
Li-Yong Zhou ◽  
Yi-Sui Sun
Keyword(s):  
Kuiper Belt ◽  
Resonant Mode ◽  
Long Term Stability ◽  
Mean Motion ◽  
High Order Resonance ◽  
Eccentric Orbits ◽  
Resonant Modes ◽  
Type Mode ◽  
Mean Motion Resonance

ABSTRACT The high-inclination population in the 4:7 mean-motion resonance (MMR) with Neptune has also substantial eccentricities (e ≳ 0.1), with more inclined objects tending to occupy more eccentric orbits. For this high-order resonance, there are two different resonant modes. The principal one is the eccentricity-type mode, and we find that libration is permissible for orbits with $e\ge e_\mathrm{ c}^0$, where the critical eccentricity $e_\mathrm{ c}^0$ increases as a function of increasing inclination i. Correspondingly, we introduce a limiting curve $e_\mathrm{ c}^0(i)$, which puts constraints on the (e, i) distribution of possible 4:7 resonators. We then perform numerical simulations on the sweep-up capture and long-term stability of the 4:7 MMR, and the results show that the simulated resonators are well constrained by this theoretical limiting curve. The other 4:7 resonant mode is the mixed-(e, i)-type, and we show that stable resonators should exist at i ≳ 20○. We predict that the intrinsic number of these mixed-(e, i)-type resonators may provide a new clue into the Solar system’s evolution, but, so far, only one real object has been observed resonating in this mode.

scholarly journals Impactor Flux on the Pluto-Charon System

2009 ◽  
Vol 5 (S263) ◽  
pp. 98-101 ◽  
Author(s):  
Gonzalo C. de Elía ◽  
Romina P. Di Sisto ◽  
Adrián Brunini
Keyword(s):  
Size Distribution ◽  
Kuiper Belt ◽  
Primary Source ◽  
Mean Motion ◽  
Stability And Instability ◽  
The Stability ◽  
Mean Motion Resonance ◽  
Collisional Evolution

AbstractIn this work, we study the impactor flux on Pluto and Charon due to the collisional evolution of Plutinos.To do this, we develop a statistical code that includes catastrophic collisions and cratering events, and takes into account the stability and instability zones of the 3:2 mean motion resonance with Neptune. Our results suggest that if 1 Pluto-sized object is in this resonance, the flux of D = 2 km Plutinos on Pluto is ~4–24 percent of the flux of D = 2 km Kuiper Belt projectiles on Pluto. However, with 5 Pluto-sized objects in the resonance, the contribution of the Plutino population to the impactor flux on Pluto may be comparable to that of the Kuiper Belt. As for Charon, if 1 Pluto-sized object is in the 3:2 resonance, the flux of D = 2 km Plutinos is ~10–63 percent of the flux of D = 2 km impactors coming from the Kuiper Belt. However, with 5 Pluto-sized objects, the Plutino population may be a primary source of the impactor flux on Charon. We conclude that it is necessary to specify the Plutino size distribution and the number of Pluto-sized objects in the 3:2 Neptune resonance in order to determine if the Plutino population is a primary source of impactors on the Pluto-Charon system.

scholarly journals Spin evolution of Earth-sized exoplanets, including atmospheric tides and core–mantle friction

2014 ◽  
Vol 14 (2) ◽  
pp. 233-254 ◽  
Author(s):  
Diana Cunha ◽  
Alexandre C.M. Correia ◽  
Jacques Laskar
Keyword(s):  
Atmospheric Tides ◽  
Mean Motion ◽  
Eccentric Orbits ◽  
Spin Evolution ◽  
Restricted Number ◽  
Habitable Zones ◽  
Equilibrium Configurations

AbstractPlanets with masses between 0.1 and 10 M⊕ are believed to host dense atmospheres. These atmospheres can play an important role on the planet's spin evolution, since thermal atmospheric tides, driven by the host star, may counterbalance gravitational tides. In this work, we study the long-term spin evolution of Earth-sized exoplanets. We generalize previous works by including the effect of eccentric orbits and obliquity. We show that under the effect of tides and core–mantle friction, the obliquity of the planets evolves either to 0° or 180°. The rotation of these planets is also expected to evolve into a very restricted number of equilibrium configurations. In general, none of these equilibria is synchronous with the orbital mean motion. The role of thermal atmospheric tides becomes more important for Earth-sized planets in the habitable zones of their systems; so they cannot be neglected when we search for their potential habitability.

scholarly journals The chaotic nature of TRAPPIST-1 planetary spin states

2019 ◽  
Vol 488 (4) ◽  
pp. 5739-5747 ◽  
Author(s):  
Alec M Vinson ◽  
Daniel Tamayo ◽  
Brad M S Hansen
Keyword(s):  
Central Star ◽  
Spin States ◽  
Habitable Zone ◽  
Long Term Stability ◽  
Mean Motion ◽  
Stable Attractor ◽  
The Mean ◽  
Orbital Periods ◽  
Chaotic Nature

ABSTRACT The TRAPPIST-1 system has seven known terrestrial planets arranged compactly in a mean motion resonant chain around an ultracool central star, some within the estimated habitable zone. Given their short orbital periods of just a few days, it is often presumed that the planets are tidally locked such that the spin rate is equal to that of the orbital mean motion. However, the compact, and resonant, nature of the system implies that there can be significant variations in the mean motion of these planets due to their mutual interactions. We show that such fluctuations can then have significant effects on the spin states of these planets. In this paper, we analyse, using detailed numerical simulations, the mean motion histories of the three planets that are thought to lie within or close to the habitable zone of the system: planets d, e, and f. We demonstrate that, depending on the strength of the mutual interactions within the system, these planets can be pushed into spin states which are effectively non-synchronous. We find that it can produce significant libration of the spin state, if not complete circulation in the frame co-rotating with the orbit. We also show that these spin states are likely to be unable to sustain long-term stability, with many of our simulations suggesting that the spin evolves, under the influence of tidal synchronization forces, into quasi-stable attractor states, which last on time-scales of thousands of years.

scholarly journals Fomalhaut b could be massive and sculpting the narrow, eccentric debris disc, if in mean-motion resonance with it

2021 ◽  
Vol 503 (4) ◽  
pp. 4767-4786
Author(s):  
Tim D Pearce ◽  
Hervé Beust ◽  
Virginie Faramaz ◽  
Mark Booth ◽  
Alexander V Krivov ◽  
...  
Keyword(s):  
Dynamical Interaction ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Resonant Interactions ◽  
Significant Mass ◽  
Mean Motion Resonance

ABSTRACT The star Fomalhaut hosts a narrow, eccentric debris disc, plus a highly eccentric companion Fomalhaut b. It is often argued that Fomalhaut b cannot have significant mass, otherwise it would quickly perturb the disc. We show that material in internal mean-motion resonances with a massive, coplanar Fomalhaut b would actually be long-term stable, and occupy orbits similar to the observed debris. Furthermore, millimetre dust released in collisions between resonant bodies could reproduce the width, shape, and orientation of the observed disc. We first re-examine the possible orbits of Fomalhaut b, assuming that it moves under gravity alone. If Fomalhaut b orbits close to the disc mid-plane then its orbit crosses the disc, and the two are apsidally aligned. This alignment may hint at an ongoing dynamical interaction. Using the observationally allowed orbits, we then model the interaction between a massive Fomalhaut b and debris. While most debris is unstable in such an extreme configuration, we identify several resonant populations that remain stable for the stellar lifetime, despite crossing the orbit of Fomalhaut b. This debris occupies low-eccentricity orbits similar to the observed debris ring. These resonant bodies would have a clumpy distribution, but dust released in collisions between them would form a narrow, relatively smooth ring similar to observations. We show that if Fomalhaut b has a mass between those of Earth and Jupiter then, far from removing the observed debris, it could actually be sculpting it through resonant interactions.

scholarly journals Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

2020 ◽  
Vol 640 ◽  
pp. A55
Author(s):  
Kyriaki I. Antoniadou ◽  
Anne-Sophie Libert
Keyword(s):  
Periodic Orbits ◽  
Intrinsic Property ◽  
Orbital Elements ◽  
Orbital Parameters ◽  
Mean Motion ◽  
Extrasolar Systems ◽  
Resonant Systems ◽  
Three Body ◽  
Mean Motion Resonance

Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.

scholarly journals Long-term orbital stability of exosolar planetary systems with highly eccentric orbits

2015 ◽  
Vol 11 (A29A) ◽  
pp. 38-39
Author(s):  
Kyriaki I. Antoniadou ◽  
George Voyatzis
Keyword(s):  
Phase Space ◽  
Orbital Stability ◽  
Planetary Systems ◽  
Dynamical Analysis ◽  
Hill Stability ◽  
Mean Motion Resonances ◽  
Term Stability ◽  
Long Term Stability ◽  
Eccentric Orbits

AbstractNowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem as our model. Highly eccentric orbits are out of the Hill stability regions. However, mean motion resonances can provide phase protection and orbits with long-term stability exist. We construct maps of dynamical stability based on the computation of chaotic indicators and we figure out regions in phase space, where the long-term stability is guaranteed. We focus on regions where at least one planet is highly eccentric and attempt to associate them with the existence of stable periodic orbits. The values of the orbital elements, which are derived from observational data, are often given with very large deviations. Generally, phase space regions of high eccentricities are narrow and thus, our dynamical analysis may restrict considerably the valid domain of the system's location.

scholarly journals Small Bodies in The Outer Solar System

1999 ◽  
Vol 172 ◽  
pp. 51-54
Author(s):  
Brian G. Marsden
Keyword(s):  
Solar System ◽  
Kuiper Belt ◽  
Absolute Magnitude ◽  
Outer Solar System ◽  
Small Bodies ◽  
Mean Values ◽  
Mean Motion ◽  
Minimum Distances ◽  
The Absolute ◽  
Mean Motion Resonance

This report is a continuation of three earlier reviews (Marsden 1996a, 1996b, 1998) that included a summary of our orbital knowledge of the Kuiper Belt. Presented at conferences held in the middle of 1994, 1995 and 1996, respectively, these reviews showed the steadily developing picture of a system dominated by the platinos, librating in the 2:3 mean-motion resonance with Neptune, and the cubewanos, a somewhat more distant population of nonlibrating objects with low orbital eccentricities. The existence of a 3:4 Neptune librator and a 3:5 Neptune librator was also suspected. These librators have now been confirmed, and a possible 4:7 librator and possible second 3:5 librator have also been found. The known and suspected multiple-opposition librators are listed in Table 1. Here it is important to note that the orbital semimajor axes a (in AU), eccentricities e and inclinations i (in degrees with respect to the 2000.0 ecliptic) are mean values that eliminate the large 12-year and 30-year periodicities arising from the indirect perturbations by Jupiter and Satum on sun-centered orbits. The numbers in parentheses are the semimajor axes (in AU) corresponding to the resonances. Following the absolute magnitude H, the entries “Nep.” and “Ura.” show the minimum distances (in AU) from Neptune and Uranus (the latter being of course quite small for the most eccentric 2:3 Neptune librators) within several millennia of the present time.

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.

scholarly journals The motion of Pluto over the age of the solar system

1996 ◽  
Vol 172 ◽  
pp. 61-70 ◽  
Author(s):  
Hiroshi Kinoshita ◽  
Hiroshi Nakai
Keyword(s):  
Lyapunov Exponent ◽  
Solar System ◽  
Kuiper Belt ◽  
Stable State ◽  
Orbital Plane ◽  
Maximum Lyapunov Exponent ◽  
List Type ◽  
Mean Motion ◽  
Lyapunov Time ◽  
Mean Motion Resonance

Pluto's motion is chaotic in the sense that the maximum Lyapunov exponent is positive and the Lyapunov time (the inverse of the Lyapunov exponent) is about 20 million years (Myr). We have carried out the numerical integration of Pluto over the age of the solar system (5.7 billion years towards the past and 5.5 billion years towards the future), which is about 280 times of the Lyapunov time. Our integration does not show any indication of gross instability in the motion of Pluto. The time evolution of Keplerian elements of a nearby trajectory of Pluto at first grow linearly with the time and then start to increase exponentially. These exponential divergences stop at about 420 Myr and saturate. The exponential divergences are suppressed by the following three resonances that Pluto has: (1)Pluto is in the 3:2 mean motion resonance with Neptune and the libration period of the critical argument is about 20000 years.(2)The argument of perihelion librates around 90 degrees and its period is 3.8 Myr.(3)The motion of the Pluto's orbital plane referred to the Neptune's orbital plane is synchronized with the libration of the argument of perihelion (a secondary resonance). The libration period associated with the second resonance is 34.5 Myr.We briefly discuss the motions of Kuiper belt objects in a 3:2 mean motion resonance with Neptune and several possible scenarios how Pluto evolves to the present stable state.

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