Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval ( _–, ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g. ₁₂) exceeds some fixed non-negative lower bound, for allt contained in ( _–, ₊), is considered. For given masses and initial data, the increasing sequences of the numbers _k , each of which provides the estimate ₊ > _k , are constructed. It appears that if ₊ = +, then .     

On transfer equation in a semi-infinite atmosphere with albedo ω>1

In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH ⁰-functionH ⁰() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases.     

Photoelectric study of the δ Scuti star HR 1225

The periodogram analysis of theV observations of the Scuti star HR 1225 has been carried out. Two frequencies of 6.415 cd (P ₀=0 _. ^d 1558) and 8.418 cd (P ₁=0 _. ^d 1188) have been determined. The period ratio ofP ₁/P ₀=0.762 indicates radial pulsation. The absolute magnitude, effective temperature and mass of the star are derived to be 1 _. ^m 05, 7600 K and 1.9M , respectively.     

The enigma of helium and anomalous xenon

Isotopically anomalous xenon in chondrites is closely associated with low-Z noble gases, but there is no helium (or neon) in the noble gas component with normal xenon. The correlation of elemental and isotopic heterogeneities in meteoritic noble gases places stringent limits on the origin of isotopically anomalous elements in meteorites and on the formation of the solar system.     

A history of the determination of Pluto's mass

Lowell's value for the mass of Planet X was about seven times that of the Earth. Postdiscovery determinations of the mass of Pluto from analysis of the observed motions of Uranus and Neptune reduced this value to about one Earth mass. More extended analyses in the past 10 years have lowered this value to about one-tenth of an Earth mass. The mass so derived, however, fails to agree by a factor of 50 with that determined from the motion of the newly discovered satellite Charon. The discrepancy may arise from unmodeled effects in the motions of the outer planets.     

Proton-cyclotron instabilities in non-uniform loss-cone magnetospheric plasma

The waves, propagating nearly transverse to the ambient magnetic field, with frequencies near the harmonics of the proton-cyclotron frequency are studied in an inhomogeneous plasma with protons having loss-cone distributions. Three types of drift cyclotron instabilities have been studied: (i) non-flute instability; (ii) B-resonant instability; and (iii) non-resonant instability. Increases of loss-cone and density gradient increase the growth rates of all three instabilities. Increases in the positive temperature gradient and _t (ratio of thermal pressure of trapped protons to magnetic field pressure) have a stabilizing effect on the non-flute and non-resonant instabilities and a destabilizing effect on the B-resonant instability. The non-resonant instability has an interesting feature: a particular harmonic can be excited in two separate bands of unstable wave numbers. These instabilities can play an important role in the dynamics of the ring current and the inner edge of the plasma sheet region of the magnetosphere. The discrete turbulence generated by them would give rise to precipitation of protons on the auroral field lines, which may contribute to the excitation of diffuse aurora. These instabilities may be relevant to the observation of harmonic waves at 6R _E by Perrautet al. (1978).     

Absolute dimensions of TT Hydrae

The photometric elements of the Algol type binary TT Hydrae derived by the authors from theirUBV observations during 1973–77 have been combined with the spectroscopic elements given by Sanford (1937) and Sahade and Cesco (1946) to obtain the absolute dimensions of the system. It is found that the spectroscopic orbital elements given by Sanford represent the evolutionary status of the secondary component better than those of Sahade and Cesco. The primary appears to be an Al v main sequence star of mass and radius ∼2.3R _⊙. The secondary fills its Roche lobe; it can be represented by a K0iii star of mass and radius ∼6.0R _⊙. Better spectroscopic data are needed for confirmation of these results.     

On the convective instability of finitely conducting viscous model chromosphere

The convective stability of a simple model chromosphere, consisting of protons, electrons and hydrogen atoms in the ground state, has been studied in the presence of a vertically upward uniform magnetic field to include the effects of FLR, Hall-currents, finite conductivity and ionization. The ionization in the chromosphere is collisional and the recombination is radiative. It is found that the Schwarzchild criterion should necessarily be satisfied for the stability together with the condition thatv > 2v ₀, where is kinematic viscosity andv ₀ is gyroviscosity. Some special cases have also been investigated.     

Morphology of Lonar Crater,India: Comparisons and implications

Lonar Crater is a young meteorite impact crater emplaced in Deccan basalt. Data from 5 drillholes, a gravity network, and field mapping are used to reconstruct its original dimensions, delineate the nature of the pre-impact target rocks, and interpret the emplacement mode of the ejecta. Our estimates of the pre-erosion dimensions are: average diameter of 1710 m; average rim height of 40 m (30–35 m of rim rock uplift, 5–10 m of ejected debris); depth of 230–245 m (from rim crest to crater floor). The crater's circularity index is 0.9 and is unlikely to have been lower in the past. There are minor irregularities in the original crater floor (present sediment-breccia boundary) possibly due to incipient rebound effects. A continuous ejecta blanket extends an average of 1410 m beyond the pre-erosion rim crest.In general, fresh terrestrial craters, less than 10 km in diameter, have smaller depth/diameter and larger rim height/diameter ratios than their lunar counterparts. Both ratios are intermediate for Mercurian craters, suggesting that crater shape is gravity dependent, all else being equal. Lonar demonstrates that all else is not always equal. Its depth/diameter ratio is normal but, because of less rim rock uplift, its rim height/diameter ratio is much smaller than both fresh terrestrial and lunar impact craters. The target rock column at Lonar consists of one or more layers of weathered, soft basalt capped by fresh, dense flows. Plastic deformation and/or compaction of this lower, incompetent material probably absorbed much of the energy normally available in the cratering process for rim rock uplift.A variety of features within the ejecta blanket and the immediately underlying substrate, plus the broad extent of the blanket boundaries, suggest that a fluidized debris surge was the dominant mechanism of ejecta transportation and deposition at Lonar. In these aspects, Lonar should be a good analog for the fluidized craters of Mars.     

40Ar39Ar ages of Allende

KAr and/or ⁴⁰Ar³⁹Ar plateau ages of Allende samples—whole rock, matrix, chondrules, white inclusions–range from 3.8 AE for matrix of ?5 AE for some white inclusions, but cluster strongly near 4.53 AE. This age marks the dominant KAr resetting of Allende materials. Age spectra show disturbances due to ³⁹Ar recoil or some other argon redistribution processes. Possible explanations for the apparent presolar ages (>4.6 AE) include: ?20% loss of ³⁹Ar; ?40% loss of ⁴⁰K ～3.8 AE ago with no loss of ⁴⁰Arl trapped argon of unique ⁴⁰Ar/³⁶Ar isotopic composition; admixture of “very old” presolar grains.