scholarly journals Stability of the Solar System

1979 ◽  
Vol 81 ◽  
pp. 7-15
Author(s):  
Victor Szebehely
Keyword(s):  
Dynamical System ◽  
Solar System ◽  
Quantitative Measure ◽  
Marginal Stability ◽  
Actual Behavior ◽  
The Sun ◽  
Dynamical Models ◽  
Restricted Problems ◽  
Hill’S Method ◽  
The Stability

This paper reviews the present status of research on the problem of stability of satellite and planetary systems in general. In addition new results concerning the stability of the solar system are described. Hill's method is generalized and related to bifurcation (or catastrophe) theory. The general and the restricted problems of three bodies are used as dynamical models. A quantitative measure of stability is introduced by establishing the differences between the actual behavior of the dynamical system as given today and its critical state. The marginal stability of the lunar orbit is discussed as well as the behavior of the Sun-Jupiter-Saturn system. Numerical values representing the measure of stability of several components of the solar system are given, indicating in the majority of cases bounded behavior.

scholarly journals Planets in Double Stars: The ϒ Cephei System

2004 ◽  
Vol 191 ◽  
pp. 222-226 ◽  
Author(s):  
R. Dvorak ◽  
E. Pilat-Lohinger ◽  
E. Bois ◽  
B. Funk ◽  
F. Freistetter ◽  
...  
Keyword(s):  
Solar System ◽  
The Sun ◽  
Stable Orbit ◽  
Orbital Parameters ◽  
Double Stars ◽  
The Stability

AbstractUp to now we have evidence for some 15 planets moving in double stars. They are all of the so-called S-type, which means that they are orbiting one of the primaries. Only two of the binaries have separations in the order of the distances where the planets in our Solar system orbit the Sun, namely Gliese 86 and ϒ Cep. In this study we investigate the stability of the recently discovered planet in ϒ Cep with respect to the orbital parameters of the binary and of the planet. Additionally we check the region inside and outside the planet’s orbit (a = 2.1 AU). Even when the mass of an additional planet in 1 AU would be in the order of that of Jupiter, the discovered planet would be in a stable orbit.

scholarly journals The orbital stability of the Sun-Jupiter-Saturn system

1996 ◽  
Vol 172 ◽  
pp. 53-56
Author(s):  
J. R. Donnison ◽  
D. F. Mikulskis
Keyword(s):  
Solar System ◽  
Orbital Stability ◽  
The Sun ◽  
Numerical Investigations ◽  
The Stability ◽  
The Masses ◽  
Mass Enhancement

Kuiper(1973) suggested that the stability of the Solar System may be meaningfully investigated by studying the stability of the Sun-Jupiter-Saturn system. Numerical investigations by Nacozy(1976) showed that mass enhancement of the two planets beyond a factor of 29.25 led to instabilities in the system. In this new investigation similar mass enhancements were studied in detail numerically and compared with the analytical values derived from the c2H method. In addition, the eccentricities of the two planets were varied as well as their masses. It was found that the system soon showed signs of instability for the increased eccentricities when the masses of the planets were enhanced by fairly small factors.

scholarly journals Velocity dispersion and the stability of galactic disks

1985 ◽  
Vol 106 ◽  
pp. 541-542
Author(s):  
John Kormendy
Keyword(s):  
Global Stability ◽  
Velocity Dispersion ◽  
Spiral Structure ◽  
Marginal Stability ◽  
The Sun ◽  
Stellar Kinematics ◽  
Local Modes ◽  
Stellar Velocity ◽  
The Stability ◽  
Estimated Error

This paper estimates the effect of the stellar velocity dispersion on local and global instabilities in galaxy disks. Measurements of rotation velocities and velocity dispersions are illustrated for the disks of NGC 488 (Illingworth and Kormendy, in preparation), NGC 936 and NGC 1553. These are used to derive the Toomre stability parameter Q, i.e. the ratio of the observed dispersion to that needed for marginal stability against local modes. In both NGC 488 and 1553, Q = 2.5 − 4, depending on the assumed mass-to-light ratio. These values larger than 2 imply that the stellar disks are stable, although the gas in NGC 488 may remain unstable. This is consistent with the observation that both galaxies largely lack coherent spiral structure: NGC 1553 is an SO and NGC 488 a flocculent spiral. The SBO galaxy NGC 936 is more extreme: Q = 5 (estimated error is a factor of two). This is consistent with Sellwood's suggestion that a bar heats the disk until it is too hot to support spiral structure. In contrast to the above galaxies, Toomre has shown that our Galaxy has Q = 1.6 ± 0.5 near the Sun. It is therefore responsive enough to make spiral structure, as observed.We also explore the stellar kinematics of the disk of NGC 1553 as a function of radius. The exceptionally strong lens component in this galaxy is very hot. At half of the radius of the lens the velocity dispersion appears to be large enough to have an effect even on global stability.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

Assessing the temporal reliability of rhythm metrics

2011 ◽  
Vol 41 (3) ◽  
pp. 271-281 ◽  
Author(s):  
Rachael-Anne Knight
Keyword(s):  
Current Paper ◽  
Empirical Measure ◽  
The Sun ◽  
British English ◽  
The North ◽  
North Wind ◽  
The Stability ◽  
Current Popularity ◽  
Temporal Reliability

Despite the current popularity of rhythm metrics, there has been relatively little work aimed at establishing their validity or reliability, important characteristics of any empirical measure. The current paper focuses on the stability, or temporal reliability, of rhythm metrics by establishing if they give consistent results for the same speakers, in the same task, on successive occasions. Four speakers of Southern British English were recorded reading ‘The North Wind and the Sun’ (NWS) passage on three consecutive days. Results indicated that some measures correlate more highly across time than others, and the choice of a measure that is both reliable and valid is discussed. It is suggested that the metric that best fits these criteria is formulated in terms of the proportion of vowels within an utterance (%V).

scholarly journals Astrometry of the solar system: the ground-based observations

2007 ◽  
Vol 3 (S248) ◽  
pp. 66-73
Author(s):  
J.-E. Arlot
Keyword(s):  
Solar System ◽  
Space Missions ◽  
Physical Characteristics ◽  
Physical Parameters ◽  
Dynamical Models ◽  
Long Period ◽  
Solar System Objects ◽  
Different Characteristics

AbstractThe main goal of the astrometry of solar system objects is to build dynamical models of their motions to understand their evolution, to determine physical parameters and to build accurate ephemerides for the preparation and the exploitation of space missions. For many objects, the ground-based observations are still very important because radar or observations from space probes are not available. More, the need of observations on a long period of time makes the ground-based observations necessary. The solar system objects have very different characteristics and the increase of the astrometric accuracy will depend on the objects and on their physical characteristics. The purpose of this communication is to show how to get the best astrometric accuracy.

scholarly journals Stability-preserving model order reduction for linear stochastic Galerkin systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Roland Pulch
Keyword(s):  
Dynamical System ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Electric Circuit ◽  
Physical Parameters ◽  
Science And Engineering ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Stochastic Galerkin ◽  
The Stability

Abstract Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a larger linear dynamical system, whose solution represents an approximation of random processes. A model order reduction (MOR) of the Galerkin system is advantageous due to the high dimensionality. However, asymptotic stability may be lost in some MOR techniques. In Galerkin-type MOR methods, the stability can be guaranteed by a transformation to a dissipative form. Either the original dynamical system or the stochastic Galerkin system can be transformed. We investigate the two variants of this stability-preserving approach. Both techniques are feasible, while featuring different properties in numerical methods. Results of numerical computations are demonstrated for two test examples modeling a mechanical application and an electric circuit, respectively.

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