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.     

The C1XS X-ray Spectrometer on Chandrayaan-1

The Chandrayaan-1 X-ray Spectrometer (C1XS) is a compact X-ray spectrometer for the Indian Space Research Organisation (ISRO) Chandrayaan-1 lunar mission. It exploits heritage from the D-CIXS instrument on ESA's SMART-1 mission. As a result of detailed developments to all aspects of the design, its performance as measured in the laboratory greatly surpasses that of D-CIXS. In comparison with SMART-1, Chandrayaan-1 is a science-oriented rather than a technology mission, leading to far more favourable conditions for science measurements. C1XS is designed to measure absolute and relative abundances of major rock-forming elements (principally Mg, Al, Si, Ca and Fe) in the lunar crust with spatial resolution ?25 FWHM km, and to achieve relative elemental abundances of better than 10%.     

Petrography and mineral chemistry of neovolcanics occurring between Pacific and Nazca Plate boundaries

Mid-Oceanic Ridge Basalt (MORB) samples collected from southern East Pacific Rise (SEPR) have been investigated. These highly phyric plagioclase basalts (HPPB) and moderately phyric plagioclase basalts (MOPB) show rare cumulate and vitrophyric textures with plagioclase (>10% as phenocryst) and abundant glass (>72%). Electron Probe Micro Analysis (EPMA) showed large compositional variations in the megacrysts as well as microcrysts of plagioclase (An₆₂ to An₈₂), olivine (Fo₇₈ to Fo₈₇), pyroxene (ferroaugite to augite) and iron oxides, mostly titaniferous magnetite. Olivine grains show high Mg# (>80%) and distinctly low in NiO (0.01–0.2%). Ferroan trevorite (NiO =16.22 and FeO_(t) =83.06) a characteristic meteoritic mineral has been identified from the olivine megacrysts of MORB, possibly attributed to Ni-enrichment, resulted from heterogeneity of the lower mantle. Wide range of An composition in plagioclase is indicative of large pressure range of crystal nucleation under decompression at a depth of ∼70 km (An₈₂) up to the ocean spreading centre. Absence of zoning observed in all the minerals present in the MORB samples, possibly attributed to unmixing and dominant fractionation process.     

High heat producing radioactive granites of malani igneous suite at northeast of Jodhpur,northwestern India

The Malani igneous suite, a terrain showing crustal formation as late as in Neoproterozoic, shows some pink and grey granites in the northeast of the desert city of Jodhpur, in northwestern, India. The average heat generation value of 15.925 HGU for these granites that is much higher than the average known value (3.8 HGU) for the continental crust has been reported here. The concentration of uranium determined is four times higher than the average continental crust. Thorium is still higher than U and K. The radioelement concentration (Ur) varies from 15.58 to 73.48 in the granites with an average of 45.671, clearly indicates a ‘hot crust’. Hence it is favourable for the formation of mineralization of HFS elements like, Nb, Ce, REE and U and Th, which need to be explored in the terrain as an economic deposit.     

Topographic Constraints on Deviatoric Stress Field in the Indo-Eurasian Collision Region: Seismo-Tectonic Implications

The deviatoric stress field are computed from the inversion of Gravitational Potential Energy (GPE) for the Indo-Eurasian plate collision region including the Himalaya and the Tibet Plateau. The resulting stress pattern in combination with stress and strain rates obtained by inverting, respectively, the focal mechanism solution of large earthquakes and GPS derived plate motions are used to study the nature of the present-day deformations. A narrow belt bordering the Himalayan collision zone from the south is characterized by strong compressive stresses. The variations in stress pattern along this belt coincide with arc-normal ridges extending into the Himalaya and are able to explain arc-parallel segmentation of seismicity. Gravitational collapse seems to play an important role in the southeastern Tibet Plateau. Depth sensitivity of the seismic derived stresses and GPS derived surface strain rates coupled with evidence of arcuate shaped high electrical conductivity favour strong ductile flow around the Eastern Himalaya Syntaxis (EHS) at mid-crustal depth. The deflection of crustal flow indicted by the viscous resistance offered by the rigid Sichuan basin adds to the traction stresses to cause clockwise rotation of the block around EHS.     

Geochronological (Rb-Sr and Sm-Nd) studies on intrusive gabbros and dolerite dykes from parts of Northern and Central Indian cratons: Implications for the age of onset of sedimentation in Bijawar and Chattisgarh basins and uranium mineralisation

The Dargawan gabbros intrusive into the Moli Subgroup of Bijawar Group, yielded Rb-Sr whole rock isochron age of 1967 ± 140 Ma. Based on the oldest age from overlying Lower Vindhyan (1.6Ga) and the underlying youngest basement ages (2.2 Ga), the time range of Bijawar sedimentation may be assigned as 2.1–1.6 Ga (Paleoproterozoic). Sm-Nd Model ages (T_DM), obtained, for Dargawan gabbros, is c. 2876–3145 Ma. High initial ⁸⁷Sr/ ⁸⁶Sr ratio of 0.70451 (higher than the contemporary mantle) and negative ɛ_Ndi (at 1.9 Ga) value of −1.5 to − 4.5, indicate assimilation of Archaean lower crustal component by the enriched mantle source magma at the time of gabbroic intrusion. The dolerite, from Damdama area, which is intrusive into the basement and overlying sediments of Chandrapur Group in the central Indian craton, yielded Rb-Sr internal isochron age of 1641 ± 120 Ma. The high initial ⁸⁷Sr/⁸⁶Sr ratio of 0.7098 and ɛ_Ndi value of −3.5 to −3.7 (at 1.6 Ga) is due to contamination of the mantle source magma with the overlying sediments. These dolerites have younger Sm-Nd Model ages (T_DM) than Dargawan gabbros as c. 2462–2675 Ma, which is similar to the age of the Sambalpur granite, from which probably sediments to this part of Chattisgarh basin are derived. Hence mixing of sediments with the Damdama dyke during its emplacement, gives rise to high initial ⁸⁷Sr/⁸⁶Sr and low initial ¹⁴³Nd/¹⁴⁴ ratios for these dykes. The c. 1600 Ma age indicates minimum age of onset of the sedimentation in the Chandrapur Group of Chattisgarh basin. Both the above mafic intrusions might have taken place in an intracratonic rift related (anorogenic) tectonic setting. This study is the first reliable age report on the onset of sedimentation in the Chandrapur Group. The total minimum time span of Chandrapur and Raipur Group may be 1.6 Ga to 1.0 Ga (Mesoproterozoic). The unconformably underlying Shingora Group of rocks of Chhattisgarh Supergroup thus indicates Paleoproterozoic age (older than 1.6 Ga). Most part of the recently classified Chattisgarh Supergroup and Bijawar-Vindhyan sequence are of Mesoproterozoic-Paleoproterozoic age and not of Neoproterozoic-Mesoproterozoic age as considered earlier. Petrographic study of basic dykes from Damdama area (eastern margin of Chattisgarh Supergroup) indicated presence of primary uranium mineral brannerite associated with goethite. This is the evidence of mafic intrusive providing geotherm and helping in scavenging the uranium from the surrounding and later alterations causing remobilisation and reconcentration of pre-existing uranium in host rocks as well as in mafic dyke itself otherwise mafic rocks are poor source of uranium and can not have primary uranium minerals initially. It can be concluded that mafic dykes have role in uranium mineralisation although indirectly.     

Clay mineralogical studies on Bijawars of the Sonrai basin: Palaeoenvironmental implications and inferences on the uranium mineralization

Clays associated with the Precambrian unconformity-related (sensu lato) uranium mineralization that occur along fractures of Rohini carbonate, Bandai sandstone and clay-organic rich black carbonaceous Gorakalan shale of the Sonrai Formation from Bijawar Group is significant. Nature and structural complexity of these clays have been studied to understand depositional mechanism and palaeoenvironmental conditions responsible for the restricted enrichment of uranium in the Sonrai basin. Clays (<2 μm fraction) separated from indurate sedimentary rocks by disaggregation, chemical treatment and centrifugation were examined using X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM). Presence of tv-1M type illite is inferred from the Rohini and Bandai Members of the Sonrai Formation, indicative of high fluid/rock interaction and super-saturation state of the fluids available in proximity with the uranium mineralization. It is observed that the Sonrai Formation is characterized by kaolinite > chlorite > illite > smectite mineral assemblages, whereas, Solda Formation contains kaolinite > illite > chlorite clays. It has been found that the former mineral assemblage resulted from the alteration process is associated with the uranium mineralization and follow progressive reaction series, indicating palaeoenvironmental (cycles of tropical humid to semi-arid/arid) changes prevailed during maturation of the Sonrai basin. The hydrothermal activity possibly associated with Kurrat volcanics is accountable for the clay mineral alterations.     

A review of the seismicity and seismotectonics of Delhi and adjoining areas

Understanding of seismicity and seismotectonics of Delhi and adjoining areas is essential as these areas lie in the seismic zone IV and are geologically confined to the Delhi Fold Belt (DFB), juxtaposed to the Himalayan Frontal Thrust Fold Belt. Owing to the set-up, seismicity in this area is ascribed to the Himalayan Thrust System and activation of DFB Fault Systems. Considerably improved instrumental seismic monitoring in this area and data analysis had resolved three regions of pronounced seismicity that lie close to Sonepat, Rohtak and western part of the NCT Delhi, attributed to activation of various portions of the fault systems of the DFB. Based on seismic telemetry network data, the seismicity pattern analysis revealed that the Mahendragarh Dehradun Sub-Surface Fault (MDSSF) and Delhi Sargodha Ridge (DSR) are the two major zones of structural importance for the nucleation of seismicity in this region. These revelations were corroborated with the fault plane solution of the earthquakes. The dominant mechanism in nucleation of seismicity in DFB is the thrust with minor strike slip. The seismicity and seismotectonics of Delhi and adjoining areas endemic to activation of DFB is reviewed and presented in this paper.     

The ice sheet dynamics around Dakshin Gangotri glacier,Schirmacher Oasis,East Antarctica vis-à-vis topography and meteorological parameters

Recession of the snout of Dakshin Gangotri glacier in the western part of Schirmacher Oasis, East Antarctica has been recorded over two decades. However, the rate of retreat is not uniform and varies at different locations. The ice wall forming the western flank of the glacier has shown an average retreat of 17.07 m between 2001 and 2009 while the snout had gone back by 6.94 m (average) during the same period. Before 2001, the snout had shown a complete recession of 3.13 m (average). The snout occupies valley area receiving less amount of solar radiation as compared to the western wall, which is a vertical cliff receiving maximum amount of solar radiation. The notable difference in the rate of recession in different parts of the Dakshin Gangotri glacier overriding Schirmacher Oasis can be attributed to combined effect of natural factors, including meteorological parameters, ice sheet dynamics and geomorphology of that area.