Analysis of near-separatrix motion in planetary systems

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.

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The Configuration Formation of Planetary Systems Observed by Kepler

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313012635 ◽

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.

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Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

Astronomy and Astrophysics ◽

10.1051/0004-6361/202037779 ◽

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.

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TESS exoplanet candidates validated with HARPS archival data

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834817 ◽

2019 ◽

Vol 622 ◽

pp. L7 ◽

Cited By ~ 16

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.

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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.

10.21203/rs.3.rs-614015/v1 ◽

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.

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On a possibility of transfer of asteroids from the 2:1 mean motion resonance with Jupiter to the Centaur zone

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab1078 ◽

2021 ◽

Author(s):

Kazantsev Anatolii ◽

Kazantseva Lilia

Keyword(s):

Terrestrial Planet ◽

Numerical Calculations ◽

Asteroid Belt ◽

Time Interval ◽

Transfer Time ◽

Mean Motion ◽

Resonant Orbits ◽

Main Asteroid Belt ◽

Absolute Magnitudes ◽

Mean Motion Resonance

ABSTRACT The paper analyses possible transfers of bodies from the main asteroid belt (MBA) to the Centaur region. The orbits of asteroids in the 2:1 mean motion resonance (MMR) with Jupiter are analysed. We selected the asteroids that are in resonant orbits with e > 0.3 whose absolute magnitudes H do not exceed 16 m. The total number of the orbits amounts to 152. Numerical calculations were performed to evaluate the evolution of the orbits over 100,000-year time interval with projects for the future. Six bodies are found to have moved from the 2:1 commensurability zone to the Centaur population. The transfer time of these bodies to the Centaur zone ranges from 4,600 to 70,000 yr. Such transfers occur after orbits leave the resonance and the bodies approach Jupiter Where after reaching sufficient orbital eccentricities bodies approach a terrestrial planet, their orbits go out of the MMR. Accuracy estimations are carried out to confirm the possible asteroid transfers to the Centaur region.

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