Roche limit for homogeneous incompressible masses

The aim of the present investigation has been to establish the minimum distance (commonly referred to as the ‘Roche limit’), to which a small satellite can approach its central star without the loss of its stability. In order to do so, we shall depart from hydrodynamical equations governing small oscillations of stellar structures, and set out to establish the limit at which their distorted form of equilibrium can no longer vibrate periodically in response to arbitrary perturbations. To this end, such equations will be rewritten in terms of curvilinear Clairaut coordinates (Kopal, 1980) in which the gravitational potential defining equilibrium surfaces plays the role of the radial coordinate; and their solution constructed for the classical Roche problem in which the oscillating satellite of infinitesimal mass consists of material which is homogeneous and incompressible, while its primary component acts gravitationally as a mass-point. The outcome of such a solution agrees satisfactorily with that previously established by Chandrasekhar (1963) on the basis of the virial theorem; but the method employed by us lends itself more readily to a generalization of the Roche limit to systems of finite mass ratios and consisting of the components of finite size.     

Book reviews

Astrophysics and Space Science -     

Jesenice—A new meteorite fall from Slovenia

Abstract– On April 9, 2009, at 3:00 CEST, a very bright fireball appeared over Carinthia and the Karavanke Mountains. The meteoroid entered the atmosphere at a very steep angle and disintegrated into a large number of objects. Two main objects were seen as separate fireballs up to an altitude of approximately 5 km, and witnesses reported loud explosions. Three stones were found with a total weight of approximately 3.611 kg. The measured activity of short‐lived cosmogenic radionuclides clearly indicates that two specimens result from a very recent meteorite fall. All cosmogenic radionuclide concentrations suggest a rather small preatmospheric radius of <20 cm; a nominal cosmic‐ray exposure age based on ²¹Ne is approximately 4 Ma, but the noble gas and radionuclide results in combination indicate a complex irradiation. Jesenice is a highly recrystallized rock with only a few relic chondrules visible in hand specimen and thin section. The texture, the large grain size of plagioclase, and the homogeneous compositions of olivines and pyroxenes clearly indicate that Jesenice is a L6 chondrite. The bulk composition of Jesenice is very close to the published average element concentration for L ordinary chondrites. The chondrite is weakly shocked (S3) as indicated by the undulatory extinction in olivine and plagioclase and the presence of planar fractures in olivine. Being weakly shocked and with gas retention ages of >1.7 Ga (⁴He) and approximately 4.3 Ga (⁴⁰Ar), Jesenice seems not to have been strongly affected by the catastrophic disruption of the L‐chondrite parent body approximately 500 Ma ago.     

Giant solar arches and coronal mass ejections in November 1980

Using data from the SOLWIND coronagraph and photometers aboard HELIOS-A we examine coronal mass ejections from an active region which produced a series of giant post-flare coronal arches. HXIS X-ray observations reveal that in several cases underlying flares did not disrupt these arch structures, but simply revived them, enhancing their temperature, density and brightness. Thus we are curious to know how these quasi-stationary X-ray structures could survive in the corona in spite of recurrent appearances of powerful dynamic flares below them. We have found reliable evidence that two dynamic flares which clearly revived the preexisting giant arch were not associated with any mass ejection. After two other flares, which were associated with mass ejections, the arch might have been newly formed when the ejection was over. In one of these cases, however, the arch had typical characteristics of a revived structure so that it is likely that it survived a powerful mass ejection nearby. In a magnetic configuration of the arch which results from potential-field modelling (Figure 1(b)) such a survival seems possible.     

Open magnetic fields in active regions

Soft X-ray observations confirm that some of the dark gaps seen between interconnecting loops and inner cores of active regions may be loci of open fields, as it has been predicted by global potential extrapolation of photospheric magnetic fields. It seems that the field lines may open only in a later state of the active region development.Skylab Solar Workshop Post-Doctoral Appointee, 1975–1977. The Skylab Solar Workshops are sponsored by NASA and NSF and managed by the High Altitude Observatory, National Center for Atmospheric Research.