scholarly journals Stability Mechanism of Planetary System of ν Andromedae

2004 ◽  
Vol 202 ◽  
pp. 202-204 ◽  
Author(s):  
Hiroshi Kinoshita ◽  
Hiroshi Nakai
Keyword(s):  
Perturbation Theory ◽  
Planetary System ◽  
Secular Resonance ◽  
Secular Perturbation ◽  
Outer Planets ◽  
The Stability

Three planets are detected around ν Andromedae. The stability of Upsilon Andromedae Planetary system is maintained by the co rotation of the pericenters of the two outer planets. If the pericenters of the two outer planets move independently, the planetary system becomes unstable. The corotation of the pericenters is explained by the secular perturbation theory. This corotation is not a secular resonance.

scholarly journals An unusually low density ultra-short period super-Earth and three mini-Neptunes around the old star TOI-561

2020 ◽  
Author(s):  
G Lacedelli ◽  
L Malavolta ◽  
L Borsato ◽  
G Piotto ◽  
D Nardiello ◽  
...  
Keyword(s):  
Transit Time ◽  
Time Variation ◽  
Planetary System ◽  
Radial Velocities ◽  
Low Density ◽  
Outer Planets ◽  
Short Period ◽  
The Stability

Abstract Based on HARPS-N radial velocities (RVs) and TESS photometry, we present a full characterisation of the planetary system orbiting the late G dwarf After the identification of three transiting candidates by TESS, we discovered two additional external planets from RV analysis. RVs cannot confirm the outer TESS transiting candidate, which would also make the system dynamically unstable. We demonstrate that the two transits initially associated with this candidate are instead due to single transits of the two planets discovered using RVs. The four planets orbiting TOI-561 include an ultra-short period (USP) super-Earth (TOI-561 b) with period Pb = 0.45 d, mass Mb = 1.59 ± 0.36 M⊕ and radius Rb = 1.42 ± 0.07 R⊕, and three mini-Neptunes: TOI-561 c, with Pc = 10.78 d, Mc = 5.40 ± 0.98 M⊕, Rc = 2.88 ± 0.09 R⊕; TOI-561 d, with Pd = 25.6 d, Md = 11.9 ± 1.3 M⊕, Rd = 2.53 ± 0.13 R⊕; and TOI-561 e, with Pe = 77.2 d, Me = 16.0 ± 2.3 M⊕, Re = 2.67 ± 0.11 R⊕. Having a density of 3.0 ± 0.8 g cm−3, TOI-561 b is the lowest density USP planet known to date. Our N-body simulations confirm the stability of the system and predict a strong, anti-correlated, long-term transit time variation signal between planets d and e. The unusual density of the inner super-Earth and the dynamical interactions between the outer planets make TOI-561 an interesting follow-up target.

scholarly journals The stability of charged-particle motion in sheared magnetic reversals

2001 ◽  
Vol 65 (4) ◽  
pp. 331-352 ◽  
Author(s):  
M. TSALAS ◽  
S. C. CHAPMAN ◽  
G. ROWLANDS
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Phase Space ◽  
Solar Flares ◽  
Resonance Effect ◽  
Charged Particles ◽  
Magnetic Reversal ◽  
Shear Component ◽  
The Stability ◽  
Multiple Timescale

We consider the motion of charged particles in a static magnetic reversal with a shear component, which has application for the stability of current sheets, such as in the Earth's geotail and in solar flares. We examine how the topology of the phase space changes as a function of the shear component by. At zero by, the phase space may be characterized by regions of stochastic and regular orbits (KAM surfaces). Numerically, we find that as we vary by, the position of the periodic orbit at the centre of the KAM surfaces changes. We use multiple-timescale perturbation theory to predict this variation analytically. We also find that for some values of by, all the KAM surfaces are destroyed owing to a resonance effect between two timescales, making the phase space globally chaotic. By investigating the stability of the solutions in the vicinity of the fixed point, we are able to predict for what values of by this happens and when the KAM surfaces reappear.

Stability of spiral flow between concentric circular cylinders at low axial Reynolds number

1965 ◽  
Vol 21 (4) ◽  
pp. 635-640 ◽  
Author(s):  
Subhendu K. Datta
Keyword(s):  
Reynolds Number ◽  
Perturbation Theory ◽  
Viscous Liquid ◽  
Axial Flow ◽  
Circular Cylinders ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
The Stability

The stability of a viscous liquid between two concentric rotating cylinders with an axial flow has been investigated. Attention has been confined to the case when the cylinders are rotating in the same direction, the gap between the cylinders is small and the axial flow is small. A perturbation theory valid in the limit when the axial Reynolds number R → 0 has been developed and corrections have been obtained for Chandrasekhar's earlier results.

scholarly journals On the divergence difficulty of quantized field theories and the rigorous treatment of radiation reaction

1946 ◽  
Vol 186 (1004) ◽  
pp. 119-147 ◽  
Keyword(s):  
Perturbation Theory ◽  
Expansion Method ◽  
Radiation Reaction ◽  
Field Theories ◽  
Unperturbed System ◽  
Secular Perturbation ◽  
Rigorous Treatment ◽  
Quantized Field

By an orthodox application of the perturbation theory to the general case of a quantized field, it is shown th at the divergence difficulty hitherto encountered arises from a faulty application of the expansion method. The difficulty, in certain cases, disappears if the degeneracy of the unperturbed system is properly treated by the method of secular perturbation. Physically, this amounts to a rigorous treatm ent of the radiation reaction, in such cases where its effect is strong.

scholarly journals The Chaotic Motion of the Solar System

1993 ◽  
Vol 132 ◽  
pp. 21-21
Author(s):  
J. Laskar
Keyword(s):  
Lyapunov Exponent ◽  
Solar System ◽  
Initial Conditions ◽  
Maximum Lyapunov Exponent ◽  
Secular Resonance ◽  
Critical Argument ◽  
Outer Planets ◽  
Fundamental Frequencies ◽  
Chaotic Nature ◽  
Evolution With Time

AbstractIn a previous paper (Laskar, Nature, 338, 237-238), the chaotic nature of the solar system excluding Pluto was established by the numerical computation of the maximum Lyapunov exponent of its secular system over 200 Myr. In the present an explanation is given for the exponential divergence of the orbits: it is due to the transition from libration to circulation of the critical argument of the secular resonance 2(g4−g3)−(s4−s3) related to the motions of perihelions and nodes of the Birth and Mars. An other important secular resonance is identified: (g1−g5)−(s1−s2). Its critical argument stays in libration over 200 Myr with a period of about 10 Myr and amplitude from 85° to 135°. The main features of the solutions of the inner planets are now identified when taking these resonances into account. Estimates of the size of the chaotic regions are determined by a new numerical method using the evolution with time of the fundamental frequencies. The size of the chaotic regions in the inner solar system are large and correspond to variations of about 0.2 arcsec/year in the fundamental frequencies. The chaotic nature of the inner solar system can thus be considered as robust against small variations of the initial conditions or of the model. The chaotic regions related to the outer planets frequencies are very thin except for g6 which present variations sufficiently large to be significant over the age of the solar system.

scholarly journals The GAPS programme at TNG

2020 ◽  
Vol 641 ◽  
pp. A68
Author(s):  
D. Barbato ◽  
M. Pinamonti ◽  
A. Sozzetti ◽  
K. Biazzo ◽  
S. Benatti ◽  
...  
Keyword(s):  
Negative Impact ◽  
Semimajor Axis ◽  
Giant Planet ◽  
Habitable Zone ◽  
Lower Mass ◽  
Outer Planets ◽  
Long Period ◽  
Dynamical Simulations ◽  
The Stability ◽  
The Impact

Context. With the growth of comparative exoplanetology, it is becoming increasingly clear that investigating the relationships between inner and outer planets plays a key role in discriminating between competing formation and evolution models. To do so, it is important to probe the inner region of systems that host long-period giants in search of undetected lower-mass planetary companions. Aims. In this work, we present our results on the K-dwarf star BD-11 4672, which is already known to host a long-period giant planet, as the first output of a subsample of the GAPS programme specifically aimed at assessing the impact of inefficient migration of planets formed beyond the snowline by searching for Neptune-mass and super-Earth planetary companions of known longer-period giants. Methods. We used the high-precision HARPS-N observations of BD-11 4672 in conjunction with time series taken from the literature in order to search for additional inner planetary signals to be fitted using differential evolution Markov chain Monte Carlo. The long-term stability of the new orbital solutions was tested with N-body dynamical simulations. Results. We report the detection of BD-11 4672 c, a new Neptune-mass planet with an orbital period of 74.20−0.08+0.06 d, eccentricity of 0.40−0.15+0.13, semimajor axis of 0.30 ± 0.01 au, and minimum mass 15.37−2.81+2.97 M⊕, orbiting slightly outside the inner edge of the optimistic circumstellar habitable zone. In order to assess its impact on the dynamical stability of the habitable zone, we computed the angular momentum deficit of the system, showing that planet c has a severe negative impact on the stability of possible additional lower-mass temperate planets. The BD-11 4672 system is notable for its architecture, hosting both a long-period giant planet and an inner lower-mass planet, the latter being one of the most eccentric Neptune-mass planets known at similar periods.

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