A note on weak stability boundaries

This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L ₁ and L ₂, as boundary of the weak stability region, is shown.     

Connection between Hill stability and weak stability in the elliptic restricted three-body problem

This paper provides a study on the connection between Hill stability and weak stability in the framework of the spatial elliptic restricted three-body problem. We determine a necessary condition for weak stability by giving an upper and a lower bound of qualitative measure of the Hill stability. The sufficient condition for weak stability and the symmetry of weak stable regions around the planets of the Solar System is also investigated.     

Lunar color boundaries and their relationship to topographic features: A preliminary survey

By combining UV negatives with IR positives of the full Moon, it is possible to suppress albedo differences and to enhance color differences between various lunar regions. Areas within the lunar maria exhibit the greatest color variations, and many have sharp boundaries. In contrast, the terrae in general show only feeble color variations, although small terra regions situated near or surrounded by maria sometimes display enhanced redness. The mare color boundaries in some cases coincide with the edges of clear-cut lava flows, the bluer material overlying the redder. One wedge-shaped area of bluer material corresponds with a prominent sinuous rille, the rille source being situated precisely in the point of the wedge. This area has obliterated portions of two ray systems, showing that the bluer material was deposited later than both the surrounding redder material and the ray material. On the other hand, rays from the crater Olbers A cross both colored areas impartially. Other examples of ray obliteration by bluer deposits are found elsewhere. From Apollo and Surveyor analyses, it is found that there is an apparent correlation between degree of blueness and titanium content of the surface materials. The following conclusions may be drawn:

1. The various maria were deposited over considerable lengths of time; this does not support the fusion-through-impact hypothesis.
2. The bluer materials, which appear to be those of high Ti content, are the more recent.
3. The hypothesis that sinuous rilles are lava drainage channels is supported.
4. The terrae covered by this study are mostly monotonous, suggesting constant composition, but a few anomalously red isolated regions may be of substantially different composition.

     

Diversity and validity of stable-unstable transitions in the algorithmic weak stability boundary

This paper is devoted to verify the consistency of the algorithmic Weak Stability Boundary definition concerning the achievement of capture-escape detection, through examining the transitions produced by the implementation of this definition. Our main goal is to show that many types of spurious transitions concerning capture-escape behavior are found besides the expected transitions due to the separatrix role of the hyperbolic invariant manifolds of the central manifold of the collinear equilibria of the Planar Circular Restricted Three-Body Problem. We identify and characterize authentic and spurious transitions and discuss their spatial distribution along the boundary for sets of initial conditions with high eccentricity, showing the frequent occurrence of spurious transitions and of collisional trajectories. Also, we investigate smooth and fractal-like portions of the boundary. Finally, we propose an alternative stability boundary definition based on the effective detection of capture-escape transitions.     

A re-determination of the boundaries of the cusp

Ariel 4 data (Goodallet al., 1973) of February 4 to May 5 1972 have been used to investigate the cusp boundaries. Data with the same local time (LT) and magnetic local time (MLT) around noontime and at high invariant latitudes (INL) have been used to represent the cusp area. (1) For noontime hours (MLT=1200 and LT=1200) high electron density values are observed. (2) the boundary towards the equator of the high density region starts at 76°–77° INL and the poleward boundary is at about 82° INL. Therefore, high electron densities are observed along an INL interval of 5°–6° at the Ariel 4 heights of 500–600 km, agreeing with other investigations.     

Thermal stability of a layer with permeable boundaries and variable gravitational field

The aim of this paper is to investigate the thermal stability of a fluid layer with permeable boundaries and a variable gravitational field. It is observed that the principle of exchange of stabilities is valid when the layer is heated form below and the complex growth rate of an arbitrary oscillatory mode exists outside of a circle whose radius depends upon the permeability parameter, Prandtl number and wavelength of the mode. In the case of a layer heated from below, gravity increasing upward has a destabilizing effect whereas the permeability parameter has a stabilizing effect.     

A remarkable configuration of sector boundaries

A study of all the observed and well-defined sector boundaries from January 1957 to February 1975, published by Svalgaard (1974, 1975a, b), indicated that sector boundary key-dates, transformed into Bartels' days, have a significant preference to occur on certain days of the solar rotation. The eclectic distribution of these sector boundaries give some Bartels' days that are empty of cases, while on other days there is a significant excess over the average. Using this effect, we can predict, in high levels of significance, the possible occurrence of a (+,–) or (–,+) boundary within particular days of the solar rotation.     

Applicability and dynamical characterization of the associated sets of the algorithmic weak stability boundary in the lunar sphere of influence

The present contribution investigates the applicability of the associated initial condition sets generated by the algorithmic definition of the weak stability boundary in the lunar sphere of influence in the context of Earth-to-Moon low-energy capture transfers. First, we test the applicability of the initial condition sets in view of two mission strategies, namely, direct inner transfers in the Planar Circular Restricted Three-Body Problem and external transfers based in the Patched Three-Body approach. Then, we check the consistency of the stability classification regarding the selection of captured solutions, identifying the stable subsets which provide temporary capture solutions. Additionally, we show the diversity of behaviors classified as stable by the current stability criteria of the algorithmic definition, which indicates that the algorithmic criteria must be reviewed in order to guarantee that the stable solutions correspond solely to low-energy capture orbits. The combination of our analyses allows the detection of the subsets of stable initial conditions that provide feasible Earth-to-Moon transfer solutions. Specifically, we show an external low-energy Earth- to-Moon transfer with zero midcourse correction at the patching section.     

Restricted problem stability and the solar system

Reference periodic orbits are determined accurately for the planets of the solar system, using a restricted problem model with the Sun and Jupiter as the two primaries. The prediction is verified that stability of the planetary orbits should imply stability of those reference orbits that are simple-periodic.     

The stability and evolution of the solar system

The known history of the solar system is discussed, also the types of dynamical problems exhibited by members of the solar system and the solutions suggested for a number of such problems. The recent work of Walker, Emslie and Roy, on Empirical Stability Criteria in Many Body Problems is also mentioned.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Metal-line system survey: characterizing the low-redshift IGM

The low-redshift IGM probes the last ten billion years of metal enrichment from galactic feedback processes. We present preliminary results from a survey of intergalactic metal-line absorption systems in archival HST STIS, GHRS, and FUSE spectra of ≈50 z?2 UV-bright objects. We summarize the detailed analysis of one sightline (PKS1302–102, z _QSO =0.2784) with which we set the methodology for the larger survey. We use simple CLOUDY models to constrain the ionizing mechanism(s) and metallicities for the metal-line systems. For about 15 sightlines, including PKS1302–102, we have a complementary galaxy survey, and we look for correlations between galaxies and absorption systems in order to understand the large-scale distribution of the metal-enriched IGM.     

A study of weak molecular and atomic lines in the photospheric spectrum

An attempt is made to detect the lines of Mg²⁵H and Mg²⁶H in the photospheric spectrum, using calculated isotope shifts. From comparisons with the Mg²⁴H lines of the ² –² transition in the (0, 0) band the ratios Mg²⁵/Mg²⁴ = 0.12 ± 0.04 and Mg²⁶/Mg²⁴ = 0.12 ± 0.02 are derived. These are essentially the same as the terrestrial ratios. The profile of one line of Mgi confirms these values.The wavelengths of MgH and C₂ lines, when corrected for the gravitational red shift, indicate that macroturbulent (or streaming) velocities die out near log ₀ = – 1.0. From the equivalent widths of the MgH lines a rotational temperature of 5132 ± 200 K is obtained and compared to predictions from various model atmospheres. The band oscillator strength is found to be 0.024 ± 0.002, in serious disagreement with the single laboratory determination.The profiles of MgH, C₂, CN and some weak atomic lines are used to derive the variation of the radial component of microturbulence with optical depth, on the assumption of streaming velocities of 2.5–3.0 km/sec. A slow increase with increasing height in the photosphere is found, over the range –1.5 < log₀< 0.2.The center-limb variation of the equivalent widths of MgH and C₂ lines for a wholly inhomogeneous model is found to be the same as for a model which is homogeneous above log ₀ = - 1.0. With such a model as the latter, the center-limb variation of the profiles of the selected molecular and atomic lines is moderately-well reproduced by an anisotropic microturbulent velocity with a tangential component of 3 km/sec which seems to be constant with height over the range considered.     

Large scale chaos and marginal stability in the solar system

Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994     

The stability of our solar system

Most investigations of the stability of the solar system have been concerned with the question as to whether the very long term effect of the gravitational attractions of the planets on each other will be to alter the nearly coplanar, nearly circular nature of the orbits in which they move. Analytical investigations in the traditions of Laplace, Lagrange, Poisson and Poincaré strongly indicate stability, though rely on asymptotic expansions with difficult analytical properties. The question is related to the existence of invariant tori, which have been proved to exist in certain motions. Numerical integration experiments have thrown considerable light on possible types of motions, especially in fictitious solar systems in which the planetary masses have been increased to enhance the perturbations, and in testing how critical are stability boundary estimates given by Hill surface type methods.     

Higher-order stability of the restricted problem and the solar system

A generalization is expressed of the Poisson theorem referring to the invariance of the planetary semi-major axes using the restricted problem model. In particular, it is shown that first and second approximation in terms of a change in the initial states of planets describing closed motions in the solar system remain invariant in modulus after any number of revolutions. But third-order terms contain secular parts and, thus, they undergo a secular change in their orbital motion. Such change would be apparent after ^-2 Jovian years, where is a constant and is the maximum initial deviation of each planet from its reference orbit.