Equations of motion of the restricted problem of three bodies with variable mass

In this paper we have deduced the differential equations of motion of the restricted problem of three bodies with decreasing mass, under the assumption that the mass of the satellite varies with respect to time. We have applied Jeans law and the space time transformation contrast to the transformation of Meshcherskii. The space time transformation is applicable only in the special casen=1,k=0,q=1/2. The equations of motion of our problem differ from the equations of motion of the restricted three body problem with constant mass only by small perturbing forces.     

Nature of solar-cycle and heliomagnetic-polarity dependence of cosmic rays, inferred from their correlation with heliomagnetic spherical surface harmonics in the period 1976–1985

Correlation of cosmic-ray intensity (I) with the solar magnetic field expanded into the spherical surface harmonics, B_ns(n 9), by Hoeksema and Scherrer has been studied using the following regression equation:

, where are subgroups of B_ns classified in ascending order of n, and τ_i is the time lag of I behind correlation coefficient between the observed and simulated intensities (I_obs, I_sml) in the period 1976–1985 is 0.87 and considerably better than that derived from any single index of solar activity. The lag time τ₃ is greater than others, indicating that the higher order magnetic disturbances effective to the cosmic-ray modulation have a longer lifetime in space than the lower order disturbances. The rigidity spectrum of the cosmic-ray intensity variation responsible for A_I due to the dipole moment is harder than those for others (A₂,A₃), indicating that the lowest order (i.e. largest scale) magnetic disturbances can modulate cosmic rays more effectively than the higher order disturbances. As another result of the present analysis, it has been found that the intensity depends also on the polarity of the polar magnetic field of the Sun; the residual (I_obs−I_sml) of the simulation changes its sign from positive to negative with a time lag (0–5 Carrington rotation periods) behind the directional change of the solar magnetic dipole moment from northward to southward, and has a softer rigidity spectrum than A_iS. The dependence is consistent with the result having been obtained in the previous period, 1936–1976, by one (K.N.) of the present authors. The polarity dependence can be found also in the 22-year variation of the time lags obtained every solar cycle in the period 1936–1985. The theoretical interpretation of these polarity dependences is discussed on the basis of the diffusion-convection-drift model.     

Molecular line mapping of the giant molecular cloud associated with RCW 106 – II. Column density and dynamical state of the clumps

We present a fully sampled C¹⁸O (1–0) map towards the southern giant molecular cloud (GMC) associated with the H  ii region RCW 106, and use it in combination with previous ¹³CO (1–0) mapping to estimate the gas column density as a function of position and velocity. We find localized regions of significant ¹³CO optical depth in the northern part of the cloud, with several of the high-opacity clouds in this region likely associated with a limb-brightened shell around the H  ii region G333.6−0.2. Optical depth corrections broaden the distribution of column densities in the cloud, yielding a lognormal distribution as predicted by simulations of turbulence. Decomposing the ¹³CO and C¹⁸O data cubes into clumps, we find relatively weak correlations between size and linewidth, and a more sensitive dependence of luminosity on size than would be predicted by a constant average column density. The clump mass spectrum has a slope near −1.7, consistent with previous studies. The most massive clumps appear to have gravitational binding energies well in excess of virial equilibrium; we discuss possible explanations, which include magnetic support and neglect of time-varying surface terms in the virial theorem. Unlike molecular clouds as a whole, the clumps within the RCW 106 GMC, while elongated, appear to show random orientations with respect to the Galactic plane.     

Fluctuational mechanism of formation of proton vortices in the “npe” phase of a neutron star

The superfluid core (“npe” phase) of a neutron star, consisting of superfluid neutrons, superconducting protons, and normal electrons, is considered. The Gibbs thermodynamic potential of a superconducting proton vortex in a proton superconductor of the second kind, interacting with the normal core of a neutron vortex of radius r ≪ λ parallel to it (λ is the depth of penetration), is calculated. It is shown that under this assumption, the capture by the core of only one vortex turns out to be energetically favored. The force exerted on the proton vortex by the entrainment current, always directed toward the core, is found. The corresponding force for a proton antivortex is directed outward toward the outer boundary of the neutron vortex. It is shown that the fluctuational formation of a vortex-antivortex pair is possible at a large distance from the core under the action of the entrainment current. Under the action of the entrainment current, the antivortex travels outward, while the vortex remains inside the neutron vortex. It is shown that the formation of new proton vortices is possible only in the region in which the entrainment magnetic field strength is H(ρ) > H_cl (H_cl is the first critical field). Translated from Astrofizika, Vol. 42, No. 2, pp. 225–234, April–June, 1999     

A deep seismic profile of 800 km length recorded in southern Queensland, Australia

Summary. In 1984, the Australian Bureau of Mineral Resources and the Geological Survey of Queensland recorded a regional seismic reflection profile of over 800 km length from the eastern part of the Eromanga Basin to the Beenleigh Block east of the Clarence Moreton Basin. A relatively transparent upper crustal basement with an underlying, more reflective lower crust is characteristic of much of the region. Prominent westerly dipping reflectors occur well below the sediments of the eastern margin of the Clarence Moreton Basin and the adjacent Beenleigh Block, and provide some of the most interesting features of the entire survey. A wide angle reflection/refraction survey of 192 km length and an expanding reflection spread of 25 km length were recorded across the Nebine Ridge. The only clear deep reflectors are interpreted as P-to-SV or SV-to-P converted reflections from a mid-crustal boundary at a depth of about 17 km. The combined Nebine Ridge data provide well-constrained P and S wave velocity models of the upper crust, and suggest a crustal structure quite different from that beneath the adjacent Mesozoic basins.     

Heliospheric Observations of STEREO-Directed Coronal Mass Ejections in 2008?–?2010: Lessons for Future Observations of Earth-Directed CMEs

We present a study of coronal mass ejections (CMEs) which impacted one of the STEREO spacecraft between January 2008 and early 2010. We focus our study on 20 CMEs which were observed remotely by the Heliospheric Imagers (HIs) onboard the other STEREO spacecraft up to large heliocentric distances. We compare the predictions of the Fixed-?? and Harmonic Mean (HM) fitting methods, which only differ by the assumed geometry of the CME. It is possible to use these techniques to determine from remote-sensing observations the CME direction of propagation, arrival time and final speed which are compared to in-situ measurements. We find evidence that for large viewing angles, the HM fitting method predicts the CME direction better. However, this may be due to the fact that only wide CMEs can be successfully observed when the CME propagates more than 100^° from the observing spacecraft. Overall eight CMEs, originating from behind the limb as seen by one of the STEREO spacecraft can be tracked and their arrival time at the other STEREO spacecraft can be successfully predicted. This includes CMEs, such as the events on 4 December 2009 and 9 April 2010, which were viewed 130^° away from their direction of propagation. Therefore, we predict that some Earth-directed CMEs will be observed by the HIs until early 2013, when the separation between Earth and one of the STEREO spacecraft will be similar to the separation of the two STEREO spacecraft in 2009??C?2010.