Effect of perturbed potentials on the non-linear stability of libration pointL 4 in the restricted problem

The non-linear stability of the libration pointL ₄ in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL ₄ is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases:

Particle acceleration and the decay of soft X-ray non-thermal line broadening in solar flares

The relationship between the production of -ray emitting particles and non-thermal soft X-ray line broadening is investigated. A model of particle acceleration via the stochastic interaction with MHD turbulence is assumed and the time development of the wave energy density derived under the condition of energy conservation between waves and particles. The inferred numbers and energy distribution of accelerated protons for four -ray flares are used to define the wave energy density and its temporal development. The presence of Alfvén wave turbulence is considered as the source of the non-thermal motions in the ambient plasma. These motions are observed as excess widths in the soft X-ray line emission from these events. The decay of the waves via the particle acceleration process is compared with the observed decays of this non-thermal line broadening. Our results show that both the -ray emission and excess soft X-ray line widths in these flares can be explained by the single physical phenomenon of Alfvén wave turbulence.     

An integrable case of a rotational motion analogous to that of Lagrange and Poisson for a gyrostat in a Newtonian force field

The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV ⁽²⁾.We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t ₀)=₀, (t ₀)=₀, (t ₀)=(t ₀)=₀, ₁(t ₀)=0, ₂(t ₀)=0 and ₃(t ₀)= ₃ ⁰ .The problem is integrated when the third component of the total angular momentum is different from zero (B ₁ 0). There now appear equilibrium solutions that did not exist in the caseB ₁=0, which can be determined in function of the value ofl ₃ ^r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l ₃ ^r =0), the obtained solutions are valid for rigid bodies.     

LonGSp: A near infra-red spectrometer

We present a new cooled grating near infra-red spectrometer designed to acquire spectra at the TIRGO telescope in the 0.9÷2.5m region with a resolving power of 300÷4000, equipped with a Rockwell NICMOS 3 detector.     

Recreation on public lands in New Zealand — past,present and future

Since the turn of the century, recreation has grown as a motivating force in public land administration. Today, the Department of Conservation manages approximately one third of New Zealand's outdoor recreation resources and has the mandate to foster the use of natural and historic resources for recreation, and to allow their use for tourism (Conservation Act 1987:8). This paper traces the emergence of a recreation perspective within public land administration and examines the development of a recreation philosophy and policy within the Department of Conservation. It suggests future directions for outdoor recreation management in New Zealand.     

TEM imaging of polytypism in pseudowollastonite

A study of polytypism in synthetic polycrystalline pseudowollastonite has been made using conventional and high resolution transmission electron microscopy (TEM and HRTEM). Three polytypes of 2, 4 and 6-layers coexist in the one sample in the form of lamellae parallel to (001). From the electron microscopy images the lamellae are interpreted as combinations of the stacking fault vectors: 1/3 [010], 1/6 [310] and 1/6 [3 $\bar 1$ 0], which are probably all equivalent at high temperatures. The polytype lamellae are stable even after prolonged annealing at high temperatures greater than 1700K. These observations suggest that the most frequently reported 4-layer polytype is not the only high-temperature stable polytype. No evidence of melt is detected in samples annealed in the regime where premelting behaviour of pseudowollastonite has previously been reported (above 1600 K).     

An occurrence of ardennite in quartz veins in piemontite schist,Western Otago,New Zealand

Summary Ardennite of complex composition: (Mn²⁺ _3.488Ca_0.509Ba_0.002)₌₄(Mg_0.916916 Fe³⁺ _0.165 Mn³⁺ _0.099Cu_0.033Ni_0.009Zn_0.006 Ti_0.008Al_4.764)₌₆(As⁵⁺ _0.823V⁵⁺ _0.022P_0.005B_0.069Al_0.042Si_5.039)₌₆O_21.81(OH)_6.17 occurs in crack-seal quartz veins in quartz-albite-piemontite-spessartine-phengitehematite-chlorite-rutile-tourmaline ± calcite schist of the Haast Schist Group near Arrow Junction, western Otago, New Zealand. The Mn²⁺/Mn³⁺-ratio is sensitive to calculations and to accuracy of analyses. Boron is detected in ardennite for the first time. Other properties include = 1.734(3), = 1.735(3), = 1.751(3), 2V_Z = 30(2)°;a = 8.721(1),b = 5.816(1),c = 18.545(3) Å,V = 940.7(2) ų. Associated mineral phases are spessartine, hematite, piemontite containing 0.7% SrO and 0.06% PbO, and phengite. Later-stage vein minerals comprise chlorite, albite, and manganoan calcite which were deposited under less highly oxidizing conditions. Digenite with minor intergrown covellite occurs in small amount with manganoan calcite and quartz in a cross-cutting late-stage veina chalcopyrite and native copper occur in other late-stage veins. Arsenic and other components of the ardennite and associated minerals are derived from highly oxidized ferromanganese oxide- and hydroxide-bearing siliceous pelagic sediments that formed the protolith for the piemontite schist. The veins formed at a relatively early stage after metamorphism peaked in the chlorite zone of the greenschist facies under conditions that have been estimated at about 4.5 kbar, 390 °C.

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Vorkommen von Ardennit in Quarzgängen aus Piemontit-Schiefern, West-Otago, Neuseeland

Zusammenfassung Ardennit mit der Zusammensetzung (Mn²⁺ _3.488Ca_0.509Ba_0.002)₌₄(Mg_0.916Fe³⁺ _0.165Mn³⁺ _0.099Cu_0.033Ni_0.009Zn_0.006 Ti_0.008Al_4.764)₌₆(As⁵⁺ _0.823V⁵⁺ _0.022P_0.005B_0.069Al_0.042Si_5.039)₌₆O_21.81(OH)_6.17 tritt in Crack-seal-Quarzgängen in Quarz-Albit-Piemontit-Spessartin-Phengit-Hämatit-Chlorit-Rutil-Turmalin ± Calcit-Schiefern der Haast Schiefer-Gruppe nahe der Arrow Junction, West-Otago, Neuseeland, auf. Die Proportionen von Mn²⁺/Mn³⁺ hängen von der Kalkulation und der Genauigkeit der Analyse ab. Bor wird zum ersten Mal im Ardennit bestimmt. Andere Eigenschaften sind: = 1.734(3), = 1.735(3), = 1.751(3), 2Vz = 30(2)°; a = 8.721(1), b = 5.816(1), c = 18.545(3) Å, V = 940.7(2) Å3. Assoziierte Mineralphasen sind Spessartin, Hämatit, Piemontit, der 0.7% SrO und 0.06% PbO enthält und Phengit. Spät gebildete Gangmineralien, wie Chlorit, Albit und Mn-Calcit, sind unter geringer oxidierenden Bedingungen entstanden. Digenit mit etwas Covellin tritt in kleinen Mengen zusammen mit Mn-Calcit und Quartz in einem querschlägigen Gang auf, Chalcopyrit und gediegenes Kupfer kommen in anderen späten Gängen vor. Arsen und andere Komponenten des Ardennites and der assoziierten Minerale können von hochoxidierten, Fe-Mn-Oxid- und Hydroxyd-führenden, Sireichen, pelagischen Sedimenten hergeleitet werden, die das Ausgangsgestein für den Piemontit darstellen. Die Gänge wurden in einem relativ frühen Stadium, nach dem Metamorphosehöhepunkt, innerhalb der Chloritzone der Grünschiefer-Fazies, unter ungefähr 4.5 kbar und 390°C, gebildet.

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With 4 Figures     

The arrangement in mean elements space of the periodic orbits close to that of the Moon

In a simplified model of the Earth-Moon-Sun system based on the restricted circular 3-dimensional 3-body problem, it is possible to find numerically a set of 8 periodic orbits whose time evolutions closely resemble that of the Moon's orbit. These orbits have a period of 223 synodic months (i.e. the period of the Saros cycle known for more than two millennia as a means of predicting eclipses), and are characterized by a secular rotation of the argument of perigee . Periodic orbits of longer durations exhibiting this last feature are very abundant in Earth-Moon-Sun dynamical models. Their arrangement in the space of the mean orbital elements- for various values of the lunar mean motion is presented.     

A stability study of asteroid families near the 3:1 and 5:2 resonance with Jupiter

By using theD-criterion Lindblad (1992) has identified 14 asteroid families from a sample of 4100 numbered asteroids with proper elements from Milani and Kneevi (1990). Taxonomic types and other physical properties for a significant number of objects in five of the families show strong homogeneity within each family, further strengthening their internal relationship.To test the hypothesis of a common origin in, e.g., a catastrophic collision event, we have set out to integrate the orbits of the members of the Maria, Dora and Oppavia-Gefion families over some 10⁶ years. The mean distance for the Maria family is close to the 3:1 mean-motion resonance with Jupiter, while the other two families lie close to the 5:2 resonance.We used a simplified solar system model which included the perturbations by Jupiter and Saturn only and implemented Everhart's variable stepsize integrator RA15. All close encounters between the family members (within 0.1 AU) were recorded as well. Preliminary results from integrations over 4×10⁵ years are presented here.The statistics of close encounters show pronounced peaks for several members within each family, while for others no significant levels above the background of random encounters or even very low frequencies were found. This indicates a subclustering within the families. Quite a lot of very close (<0.005 AU) mutual encounters are found, which suggest that, at least for the larger members in a family, the mutual gravitational interactions could be of some importance for the real orbital evolutions.The encounter statistics between the Dora and Oppavia family members suggest a possible interrelationship between this two groups.     

Asteroid motion near the 3 : 1 resonance

A mapping model is constructed to describe asteroid motion near the 3 : 1 mean motion resonance with Jupiter, in the plane. The topology of the phase space of this mapping coincides with that of the real system, which is considered to be the elliptic restricted three body problem with the Sun and Jupiter as primaries. This model is valid for all values of the eccentricity. This is achieved by the introduction of a correcting term to the averaged Hamiltonian which is valid for small values of the ecentricity.We start with a two dimensional mapping which represents the circular restricted three body problem. This provides the basic framework for the complete model, but cannot explain the generation of a gap in the distribution of the asteroids at this resonance. The next approximation is a four dimensional mapping, corresponding to the elliptic restricted problem. It is found that chaotic regions exist near the 3 : 1 resonance, due to the interaction between the two degrees of freedom, for initial conditions close to a critical curve of the circular model. As a consequence of the chaotic motion, the eccentricity of the asteroid jumps to high values and close encounters with Mars and even Earth may occur, thus generating a gap. It is found that the generation of chaos depends also on the phase (i.e. the angles andv) and as a consequence, there exist islands of ordered motion inside the sea of chaotic motion near the 3 : 1 resonance. Thus, the model of the elliptic restricted three body problem cannot explain completely the generation of a gap, although the density in the distribution of the asteroids will be much less than far from the resonance. Finally, we take into account the effect of the gravitational attraction of Saturn on Jupiter's orbit, and in particular the variation of the eccentricity and the argument of perihelion. This generates a mixing of the phases and as a consequence the whole phase space near the 3 : 1 resonance becomes chaotic. This chaotic zone is in good agreement with the observations.