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 Analysis of near-separatrix motion in planetary systems

2007 ◽  
Vol 3 (S249) ◽  
pp. 491-498
Author(s):  
Su Wang ◽  
Ji-Lin Zhou
Keyword(s):  
Planetary Systems ◽  
Scattering Model ◽  
High Occurrence ◽  
Mean Motion ◽  
Accretion Process ◽  
Three Body ◽  
Mean Motion Resonance

AbstractNear-separatrix motion is a kind of motion of two planets with their relative apsidal longitude near the boundary between libration and circulation. Observed multiple planetary systems seem to favor near-separatrix motions between neighboring planets. In this report, we study the probability that near-separatrix motion occurs with both the linear secular system and full three-body systems. We find that generally the ratio of near-separatrix motion is small unless the eccentricities of the two planets differ from each other by an order of magintude, or they are in mean motion resonance. To explore the dynamical procedures causing the near-separatrix motion, we suppose a modification to scattering model by adding a mass-accretion process during the protoplanet growth. Statistics on the modified scattering model indicate that the probability of the final planet pairs in near-separatrix motion is high (∼ 85%), which may explain the high occurrence of near-separatrix motions in observed planetary systems.

scholarly journals Measuring the Orbital Parameters of Radial Velocity Systems in Mean-motion Resonance: A Case Study of HD 200964

2019 ◽  
Vol 158 (4) ◽  
pp. 136
Author(s):  
M. M. Rosenthal ◽  
W. Jacobson-Galan ◽  
B. Nelson ◽  
R. A. Murray-Clay ◽  
J. A. Burt ◽  
...  
Keyword(s):  
Radial Velocity ◽  
Orbital Parameters ◽  
Mean Motion ◽  
Mean Motion Resonance

scholarly journals The Configuration Formation of Planetary Systems Observed by Kepler

2012 ◽  
Vol 8 (S293) ◽  
pp. 106-109
Author(s):  
Su Wang ◽  
Jianghui Ji
Keyword(s):  
Star Formation ◽  
Late Stage ◽  
Early Stage ◽  
Planetary Systems ◽  
High Rate ◽  
Mean Motion ◽  
Star Evolution ◽  
Kepler Mission ◽  
Resonant Systems ◽  
Mean Motion Resonance

AbstractThe Kepler mission has found many planetary systems, among them more than 80 systems host three planet candidates which reveal a configuration of near 4:2:1 mean motion resonance. In this paper, we focus on the configuration formation of resonant systems. As shown from our model and N-body simulations, we find that 3:2 mean motion resonance always forms at the early stage of star evolution and planets undergo high rate of migration, while 2:1 mean motion resonance happens at the late stage of the star formation, more often.

scholarly journals A first analysis of the mean motion of CHAMP

2003 ◽  
Vol 1 ◽  
pp. 95-101
Author(s):  
F. Deleflie ◽  
P. Exertier ◽  
P. Berio ◽  
G. Metris ◽  
O. Laurain ◽  
...  
Keyword(s):  
Orbital Motion ◽  
Surface Forces ◽  
The Moon ◽  
Orbital Elements ◽  
Champ Satellite ◽  
Mean Motion ◽  
The Earth ◽  
The Mean ◽  
Low Altitude

Abstract. The present study consists in studying the mean orbital motion of the CHAMP satellite, through a single long arc on a period of time of 200 days in 2001. We actually investigate the sensibility of its mean motion to its accelerometric data, as measures of the surface forces, over that period. In order to accurately determine the mean motion of CHAMP, we use “observed" mean orbital elements computed, by filtering, from 1-day GPS orbits. On the other hand, we use a semi-analytical model to compute the arc. It consists in numerically integrating the effects of the mean potentials (due to the Earth and the Moon and Sun), and the effects of mean surfaces forces acting on the satellite. These later are, in case of CHAMP, provided by an averaging of the Gauss system of equations. Results of the fit of the long arc give a relative sensibility of about 10-3, although our gravitational mean model is not well suited to describe very low altitude orbits. This technique, which is purely dynamical, enables us to control the decreasing of the trajectory altitude, as a possibility to validate accelerometric data on a long term basis.Key words. Mean orbital motion, accelerometric data

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 Survivability of moon systems around ejected gas giants

2018 ◽  
Vol 489 (2) ◽  
pp. 2323-2329
Author(s):  
Ian Rabago ◽  
Jason H Steffen
Keyword(s):  
Large Fraction ◽  
Giant Planets ◽  
The Moon ◽  
Orbital Elements ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Subsurface Ocean ◽  
Gas Giant ◽  
The Stability ◽  
Three Body

ABSTRACT We examine the effects that planetary encounters have on the moon systems of ejected gas giant planets. We conduct a suite of numerical simulations of planetary systems containing three Jupiter-mass planets (with the innermost planet at 3 au) up to the point where a planet is ejected from the system. The ejected planet has an initial system of 100 test-particle moons. We determine the survival probability of moons at different distances from their host planet, measure the final distribution of orbital elements, examine the stability of resonant configurations, and characterize the properties of moons that are stripped from the planets. We find that moons are likely to survive in orbits with semi-major axes out beyond 200 planetary radii (0.1 au in our case). The orbital inclinations and eccentricities of the surviving moons are broadly distributed and include nearly hyperbolic orbits and retrograde orbits. We find that a large fraction of moons in two-body and three-body mean-motion resonances also survive planetary ejection with the resonance intact. The moon–planet interactions, especially in the presence of mean-motion resonance, can keep the interior of the moons molten for billions of years via tidal flexing, as is seen in the moons of the gas giant planets in the solar system. Given the possibility that life may exist in the subsurface ocean of the Galilean satellite Europa, these results have implications for life on the moons of rogue planets – planets that drift through our Galaxy with no host star.

scholarly journals Revisiting The Averaged Problem in The Case of Mean-Motion Resonances of The Restricted Three-Body Problem. Global Rigorous Treatment and Application To The Co-Orbital Motion.

2021 ◽  
Author(s):  
Alexandre Pousse ◽  
Elisa Maria Alessi
Keyword(s):  
Reference Frame ◽  
Body Problem ◽  
Orbital Motion ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Mean Motion ◽  
Rigorous Treatment ◽  
Three Body ◽  
Suitable Approximation ◽  
Mean Motion Resonance

Abstract A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem of a mean-motion resonance allows to investigate the long-term behavior of the solutions through a suitable approximation that focuses on a particular region of the phase space. In this paper, we intend to bridge a gap between the two approaches in the specific case of mean-motion resonant dynamics, establish the limit of validity of the averaged problem, and take advantage of its results in order to compute trajectories in the synodic reference frame. After the description of each approach, we develop a rigorous treatment of the averaging process, estimate the size of the transformation and prove that the averaged problem is a suitable approximation of the restricted three-body problem as long as the solutions are located outside the Hill's sphere of the secondary. In such a case, a rigorous theorem of stability over finite but large timescales can be proven. We establish that a solution of the averaged problem provides an accurate approximation of the trajectories on the synodic reference frame within a finite time that depend on the minimal distance to the Hill's sphere of the secondary. The last part of this work is devoted to the co-orbital motion (i.e., the dynamics in 1:1 mean-motion resonance) in the circular-planar case. In this case, an interpretation of the solutions of the averaged problem in the synodic reference frame is detailed and a method that allows to compute co-orbital trajectories is displayed.

scholarly journals TESS exoplanet candidates validated with HARPS archival data

2019 ◽  
Vol 622 ◽  
pp. L7 ◽  
Author(s):  
Trifon Trifonov ◽  
Jan Rybizki ◽  
Martin Kürster
Keyword(s):  
Light Curve ◽  
Radial Velocity ◽  
Planetary Systems ◽  
Archival Data ◽  
Velocity Analysis ◽  
Orbital Parameters ◽  
Mean Motion ◽  
Two Systems ◽  
Made In ◽  
Mean Motion Resonance

Aims. We aim at the discovery of new planetary systems by exploiting the transit light-curve results from observations made in TESS orbital observatory Sectors 1 and 2 and validating them with precise Doppler measurements obtained from archival HARPS data. Methods. Taking advantage of the reported TESS transit events around GJ 143 (TOI 186) and HD 23472 (TOI 174), we modeled their HARPS precise Doppler measurements and derived orbital parameters for these two systems. Results. For the GJ 143 system, TESS has reported only a single transit, and thus its period is unconstrained from photometry. Our radial velocity analysis of GJ 143 reveals the full Keplerian solution of the system, which is consistent with an eccentric planet with a mass almost twice that of Neptune and a period of Pb = 35.59−0.1+0.1 days. Our estimates of the GJ 143 b planet are fully consistent with the transit timing from TESS. We confirm the two-planet system around HD 23472, which according to our analysis is composed of two Neptune-mass planets in a possible 5:3 mean motion resonance.

scholarly journals The onset of instability in resonant chains

2020 ◽  
Vol 494 (4) ◽  
pp. 4950-4968 ◽  
Author(s):  
Gabriele Pichierri ◽  
Alessandro Morbidelli
Keyword(s):  
Dynamical Mechanism ◽  
Mean Motion Resonances ◽  
Secondary Resonances ◽  
Mean Motion ◽  
Large N ◽  
Excited System ◽  
Resonant Systems ◽  
The Mean ◽  
The Stability ◽  
Mean Motion Resonance

ABSTRACT There is evidence that most chains of mean motion resonances of type k:k − 1 among exoplanets become unstable once the dissipative action from the gas is removed from the system, particularly for large N (the number of planets) and k (indicating how compact the chain is). We present a novel dynamical mechanism that can explain the origin of these instabilities and thus the dearth of resonant systems in the exoplanet sample. It relies on the emergence of secondary resonances between a fraction of the synodic frequency 2π(1/P1 − 1/P2) and the libration frequencies in the mean motion resonance. These secondary resonances excite the amplitudes of libration of the mean motion resonances, thus leading to an instability. We detail the emergence of these secondary resonances by carrying out an explicit perturbative scheme to second order in the planetary masses and isolating the harmonic terms that are associated with them. Focusing on the case of three planets in the 3:2–3:2 mean motion resonance as an example, a simple but general analytical model of one of these resonances is obtained, which describes the initial phase of the activation of one such secondary resonance. The dynamics of the excited system is also briefly described. Finally, a generalization of this dynamical mechanism is obtained for arbitrary N and k. This leads to an explanation of previous numerical experiments on the stability of resonant chains, showing why the critical planetary mass allowed for stability decreases with increasing N and k.

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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