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 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 Dynamical interactions in the planetary system GJ4276

2019 ◽  
Vol 490 (2) ◽  
pp. 2732-2739
Author(s):  
Fergus Horrobin ◽  
Hanno Rein
Keyword(s):  
Planetary System ◽  
Stable Region ◽  
Mean Motion Resonances ◽  
Orbital Parameters ◽  
First Order ◽  
Mean Motion ◽  
The Mean ◽  
The Stability ◽  
The One ◽  
Mean Motion Resonance

ABSTRACT GJ4276 is an M4.0 dwarf star with an inferred Neptune mass planet from radial velocity (RV) observations. We re-analyse the RV data for this system and focus on the possibility of a second, super-Earth mass, planet. We compute the time-scale for fast resonant librations in the eccentricity to be $\sim \!2000 \, \mathrm{d}$. Given that the observations were taken over $700\, \mathrm{d}$, we expect to see the effect of these librations in the observations. We perform a fully dynamical fit to test this hypothesis. Similar to previous results, we determine that the data could be fit by two planets in a 2:1 mean motion resonance. However, we also find solutions near the 5:4 mean motion resonance that are not present when planet–planet interactions are ignored. Using the mean exponential growth of nearby orbits indicator, we analyse the stability of the system and find that our solutions lie in a stable region of parameter space. We also find that though out-of-resonance solutions are possible, the system favours a configuration that is in a first-order mean motion resonance. The existence of mean motion resonances has important implications in many planet formation theories. Although we do not attempt to distinguish between the one- and two-planet models in this work, in either case, the predicted orbital parameters are interesting enough to merit further study. Future observations should be able to distinguish between the different scenarios within the next 5 yr.

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 A resonant pair of warm giant planets revealed by TESS

2019 ◽  
Vol 486 (4) ◽  
pp. 4980-4986 ◽  
Author(s):  
David Kipping ◽  
David Nesvorný ◽  
Joel Hartman ◽  
Guillermo Torres ◽  
Gaspar Bakos ◽  
...  
Keyword(s):  
Giant Planets ◽  
Dynamical Model ◽  
First Year ◽  
Mean Motion ◽  
M Dwarf ◽  
Mean Motion Resonance ◽  
Dynamical Masses

ABSTRACT We present the discovery of a pair of transiting giant planets using four sectors of TESS photometry. TOI-216 is a 0.87 M⊙ dwarf orbited by two transiters with radii of 8.2 and 11.3 R⊕, and periods of 17.01 and 34.57 d, respectively. Anticorrelated TTVs are clearly evident indicating that the transiters orbit the same star and interact via a near 2:1 mean motion resonance. By fitting the TTVs with a dynamical model, we infer masses of $30_{-14}^{+20}$ and $200_{-100}^{+170}$ M⊕, establishing that the objects are planetary in nature and have likely sub-Kronian and Kronian densities. TOI-216 lies close to the southern ecliptic pole and thus will be observed by TESS throughout the first year, providing an opportunity for continuous dynamical monitoring and considerable refinement of the dynamical masses presented here. TOI-216 closely resembles Kepler-9 in architecture, and we hypothesize that in such systems these Saturn analogues failed to fully open a gap and thus migrated far deeper into the system before becoming trapped into resonance, which would imply that future detections of new analogues may also have sub-Jupiter masses.

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 The long-term evolution of photoevaporating transition discs with giant planets

2015 ◽  
Vol 454 (2) ◽  
pp. 2173-2182 ◽  
Author(s):  
Giovanni P. Rosotti ◽  
Barbara Ercolano ◽  
James E. Owen
Keyword(s):  
Long Term Evolution ◽  
Giant Planets ◽  
Term Evolution

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 Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems

1989 ◽  
Vol 31 (1) ◽  
pp. 48-75 ◽  
Author(s):  
A. J. Roberts
Keyword(s):  
Dynamical System ◽  
Invariant Manifold ◽  
Initial Conditions ◽  
Long Term Evolution ◽  
Equation Model ◽  
Starting Position ◽  
System A ◽  
Term Evolution ◽  
Shear Dispersion

AbstractA centre manifold or invariant manifold description of the evolution of a dynamical system provides a simplified view of the long term evolution of the system. In this work, I describe a procedure to estimate the appropriate starting position on the manifold which best matches an initial condition off the manifold. I apply the procedure to three examples: a simple dynamical system, a five-equation model of quasi-geostrophic flow, and shear dispersion in a channel. The analysis is also relevant to determining how best to account, within the invariant manifold description, for a small forcing in the full system.

scholarly journals Design of a Compact MIMO Antenna Using Coupled Feed for LTE Mobile Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xing Zhao ◽  
Youngki Lee ◽  
Jaehoon Choi
Keyword(s):  
Correlation Coefficient ◽  
Mobile Applications ◽  
Return Loss ◽  
Impedance Matching ◽  
Antenna Element ◽  
Mimo Antenna ◽  
First Order ◽  
Term Evolution ◽  
Radiating Element

A compact multi-input multi-output (MIMO) antenna with a coupled feed structure for 4th generation (4G) handsets is proposed for operation in long-term evolution (LTE) band 13 (0.746 GHz–0.787 GHz). The MIMO antenna consists of two symmetrically distributed identical antenna elements. The size of each element is limited to 20 mm × 10 mm × 5 mm (λ0=392 mm at 0.765 GHz), and the separation between different elements is minimized to 15 mm. Each antenna element contains a Z-shaped coupled feed strip and a simple folded monopole-type radiating element. The simple folded radiating element supports two monopole modes (first order) excited at adjacent frequencies to achieve broadband performance. The coupled feed strip effectively modifies impedance matching and maintains good isolation. The proposed antenna has a 6 dB return loss bandwidth of 55 MHz (0.735 GHz–0.79 GHz) and isolation above 12 dB without the use of an additional isolation enhancement element. Moreover, the envelope correlation coefficient (ECC) is maintained below 0.5 over the designed frequency band.

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