Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

Invariant rotational curves in Sitnikov's Problem

The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.     

Non-linear stability of the equilibria in the gravity field of a finite straight segment

We study the non-linear stability of the equilibria corresponding to the motion of a particle orbiting around a finite straight segment. The potential is a logarithmic function and may be considered as an approximation to the one generated by elongated celestial bodies. By means of the Arnold's theorem for non-definite quadratic forms we determine the orbital stability of the equilibria, for all values of the parameter k of the problem, resonant cases included.     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

Oxidation of CO on surface hematite in high CO2 atmospheres

We propose a mechanism for the oxidation of gaseous CO into CO₂ occurring on the surface mineral hematite (Fe₂O₃(s)) in hot, CO₂-rich planetary atmospheres, such as Venus. This mechanism is likely to constitute an important source of tropospheric CO₂ on Venus and could at least partly address the CO₂ stability problem in Venus’ stratosphere, since our results suggest that atmospheric CO₂ is produced from CO oxidation via surface hematite at a rate of 0.4 petagrammes (Pg) CO₂ per (Earth) year on Venus which is about 45% of the mass loss of CO₂ via photolysis in the Venusian stratosphere. We also investigated CO oxidation via the hematite mechanism for a range of planetary scenarios and found that modern Earth and Mars are probably too cold for the mechanism to be important because the rate-limiting step, involving CO(g) reacting onto the hematite surface, proceeds much slower at lower temperatures. The mechanism may feature on extrasolar planets such as Gliese 581c or CoRoT-7b assuming they can maintain solid surface hematite which, e.g. starts to melt above about 1200 K. The mechanism may also be important for hot Hadean-type environments and for the emerging class of hot Super-Earths with planetary surface temperatures between about 600 and 900 K.     

Stability Regions and Quasi-Periodic Motion in the Vicinity of Triangular Equilibrium Points

The regions of quasi-periodic motion around non-symmetric periodic orbits in the vicinity of the triangular equilibrium points are studied numerically. First, for a value of the mass parameter less than Routh's critical value, the stability regions determined by quasi-periodic motion are examined around the existing families of short (L^s ₄) and long (L^l ₄) period solutions. Then, for two values of μ greater than the Routh value, the unified family L^sl ₄, to which, in these cases, L^s ₄ and L^l ₄ merge, is considered. It is found that such regions surround in general the linearly stable segments of the corresponding families and become smaller as the mass ratio increases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Planar Symmetric Periodic Orbits in Four Dipole Problem

We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines” such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn. For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families of three dimensional symmetric periodic orbits.     

镇江市运河滑坡机理分析

镇江市古运河边岸滑坡干扰了城市交通、航运和河道整治工程的正常运行。本文研究了城市边岸的工程环境、滑坡形态、特有的城市地质环境恶化所诱发的边岸破坏机制及其稳定性,它对我同城市水陆交通发展所导致的斜坡地质灾害及其治理有实用价值。     

金沙江下咱日堆积体的成因和稳定性初步分析

下咱日堆积体的稳定性对拟建的梨园水电站大坝和附近的水力设施有着重要的意义。利用下咱日堆积体的勘察资料,本文分析后认为下咱日堆积体经历了中更新世的金江冰期和晚更新世的丽江冰期两次冰期的作用,是由冰碛物、河流沉积物、湖相沉积物及崩积物组成的复杂成因堆积体;稳定性初步分析认为,下咱日堆积体局部有坍塌,但是整体稳定,以后稳定与否的关键是堆积体中湖相沉积层及坡脚的松散砾石层的稳定性。     

Finding the most suitable slope stability model for the assessment of the impact of climate change on a ­landslide in southeast France

The response of a landslide near Barcelonnette (southeast France) to climatic factors was simulated with three slope stability models: a fully empirical gross precipitation threshold, a semi‐empirical threshold model for net precipitation, and a fully conceptual slope stability model. The three models performed with similar levels in reproducing the present‐day temporal pattern of landslide reactivation, using dendrogeomorphological information as test data. The semi‐empirical and conceptual models were found to be overparameterized, because more than one parameter setting matching the test data was identified. In the case of the conceptual model, this resulted in strongly divergent scenarios of future landslide activity, using downscaled climate scenarios as inputs to the model. The uncertainty of the landslide scenarios obtained with the semi‐empirical model was much lower. In addition, the simulation of strongly different scenarios by the fully empirical threshold was attributed to its incomplete representation of the site‐specific landslide reactivation mechanism. It is concluded that the semi‐empirical model constitutes the best compromise between conceptual representation and model robustness. Copyright © 2000 John Wiley & Sons, Ltd.