On the variational approach to the periodic n-body problem

This expository paper gathers some of the results obtained by the author in recent works in collaboration with Davide Ferrario and Vivina Barutello, focusing on the periodic n-body problem from the perspective of the calculus of variations and minimax theory. These researches were aimed at developing a systematic variational approach to the equivariant periodic n-body problem in the two and three-dimensional space. The purpose of this paper is to expose the main problems and achievements of this approach. The material here was exposed in the talk that given at the Meeting CELMEC IV promoted by SIMCA (Società italiana di Meccanica Celeste).     

Critical inclination in the main problem of a massive satellite

The classical problem of the critical inclination in artificial satellite theory has been extended to the case when a satellite may have an arbitrary, significant mass and the rotation momentum vector is tilted with respect to the symmetry axis of the planet. If the planet’s potential is restricted to the second zonal harmonic, according to the assumptions of the main problem of the satellite theory, two various phenomena can be observed: a critical inclination that asymptotically tends to the well known negligible mass limit, and a critical tilt that can be attributed to the effect of transforming the gravity field harmonics to a different reference frame. Stability of this particular solution of the two rigid bodies problem is studied analytically using a simple pendulum approximation.     

General relativistic analysis of structure and stability of charged fluid disks around compact objects

In this paper we give a detailed general relativistic formulation of the study of structure and stability of charged fluid disks around compact objects like black holes neglecting the self-gravitation of the disk itself. Having presented the general equations for equilibrium as well as for perturbations we solve explicitly the cases of rigidly and differentially rotating thin disks, with constant charge density and zero pressure, confined to the equatorial plane of the black hole. By using normal mode analysis we have analysed the stability of such disks under purely radial perturbations and find that the disks are generally stable. On leave of absence from Government College, Jagadalpur 494005     

Using Strong Solar Coronal Emission Lines as Coronal Flux Proxies

We investigate the possibility that strong EUV lines observed with the Goddard Solar EUV Rocket Telescope and Spectrograph (SERTS) provide good proxies for estimating the total coronal flux over shorter wavelength ranges. We use coordinated SERTS and Yohkoh observations to obtain both polynomial and power-law fits relating the broad-band soft X-ray fluxes to the intensities of Fexvi 335 Ú and 361 Ú, Fexv 284 Ú and 417 Ú, and Mgix 368 Ú measured with SERTS. We found that the power-law fits best cover the full range of solar conditions from quiet Sun through active region, though not surprisingly the cooler Mgix 368 Ú line proves to be a poor proxy. The quadratic polynomial fits yield fair agreement over a large range for all but the Mgix line. However, the linear fits fail conspicuously when extrapolated into the quiet-Sun regime. The implications of this work for the Heii 304 Ú line formation problem are also briefly considered.     

The Filament Disappearance of 7 May 1992 (the Ebi)

The 7 May 1992 filament disappearance in the low corona is analyzed. The cool and hot components of this event are studied, using H, soft X-ray and radio data. We first show the general effect of the disparition brusque (DB) on the life of the filament, which was a quiescent filament in the vicinity of an active region, and then give the history of the development of the 7 May event. The main stages of the event are: (i) the formation of hot arches spanning the cool filament; (ii) rise of the filament, with plasma ejection into the corona, in which we note some spreading of loops from the main body, with two distinct rising velocity phases of the H filament; (iii) formation of X-ray arches below the filament, the foot points of the arcades being two-ribbon H flare patches. The dynamics of H and X-rays features are given.     

Evidence for the depletion of ammonia in the Uranus atmosphere

The theoretical disk brightness temperature spectra for Uranus are computed and compared with the observed microwave spectrum. It is shown that the emission observed at short centimeter wavelengths originates deep below the region where ammonia would ordinarily begin to condense. We demonstrate that this result is inconsistent with a wide range of atmospheric models in which the partial pressure of NH₃ is given by the vapor-pressure equation in the upper atmosphere. It is estimated that the ammonia mixing ratio must be less than 10^?6 in the 150 to 200°K temperature range. This is two orders of magnitude less than the expected mixing ratio based on solar abundances. The evidence for this depletion and a possible explanation are discussed.