Integrability of motion around galactic razor-thin disks

We consider the three-dimensional bounded motion of a test particle around razor-thin disk configurations, by focusing on the adiabatic invariance of the vertical action associated with disk-crossing orbits. We find that it leads to an approximate third integral of motion predicting envelopes of the form \(Z(R)\propto [\varSigma (R)]^{-1/3}\), where R is the radial galactocentric coordinate, Z is the z-amplitude (vertical amplitude) of the orbit and \(\varSigma \) represents the surface mass density of the thin disk. This third integral, which was previously formulated for the case of flattened 3D configurations, is tested for a variety of trajectories in different thin-disk models.     

Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.     

Line-of-Sight Anisotropies in the Cosmic Dawn and Epoch of Reionization 21-cm Power Spectrum

The line-of-sight direction in the redshifted 21-cm signal coming from the cosmic dawn and the epoch of reionization is quite unique in many ways compared to any other cosmological signal. Different unique effects, such as the evolution history of the signal, non-linear peculiar velocities of the matter etc. will imprint their signature along the line-of-sight axis of the observed signal. One of the major goals of the future SKA-LOW radio interferometer is to observe the cosmic dawn and the epoch of reionization through this 21-cm signal. It is thus important to understand how these various effects affect the signal for its actual detection and proper interpretation. For more than one and half decades, various groups in India have been actively trying to understand and quantify the different line-of-sight effects that are present in this signal through analytical models and simulations. In many ways the importance of this sub-field under 21-cm cosmology have been identified, highlighted and pushed forward by the Indian community. In this article, we briefly describe their contribution and implication of these effects in the context of the future surveys of the cosmic dawn and the epoch of reionization that will be conducted by the SKA-LOW.     

Petrology,mineralogy, and oxygen isotope compositions of aluminum‐rich chondrules from CV3 chondrites

Bulk major element composition, petrography, mineralogy, and oxygen isotope compositions of twenty Al‐rich chondrules (ARCs) from five CV3 chondrites (Northwest Africa [NWA] 989, NWA 2086, NWA 2140, NWA 2697, NWA 3118) and the Ningqiang carbonaceous chondrite were studied and compared with those of ferromagnesian chondrules and refractory inclusions. Most ARCs are marginally Al‐richer than ferromagnesian chondrules with bulk Al₂O₃ of 10–15 wt%. ARCs are texturally similar to ferromagnesian chondrules, composed primarily of olivine, pyroxene, plagioclase, spinel, Al‐rich glass, and metallic phases. Minerals in ARCs have intermediate compositions. Low‐Ca pyroxene (Fs_0.6–8.8Wo_0.7–9.3) has much higher Al₂O₃ and TiO₂ contents (up to 12.5 and 2.3 wt%, respectively) than that in ferromagnesian chondrules. High‐Ca pyroxene (Fs_0.3–2.0Wo_33–54) contains less Al₂O₃ and TiO₂ than that in Ca,Al‐rich inclusions (CAIs). Plagioclase (An_77–99Ab_1–23) is much more sodic than that in CAIs. Spinel is enriched in moderately volatile element Cr (up to 6.7 wt%) compared to that in CAIs. Al‐rich enstatite coexists with anorthite and spinel in a glass‐free chondrule, implying that the formation of Al‐enstatite was not due to kinetic reasons but is likely due to the high Al₂O₃/CaO ratio (7.4) of the bulk chondrule. Three ARCs contain relict CAIs. Oxygen isotope compositions of ARCs are also intermediate between those of ferromagnesian chondrules and CAIs. They vary from ?39.4‰ to 13.9‰ in δ¹⁸O and yield a best fit line (slope = 0.88) close to the carbonaceous chondrite anhydrous mineral (CCAM) line. Chondrules with 5–10 wt% bulk Al₂O₃ have a slightly more narrow range in δ¹⁸O (?32.5 to 5.9‰) along the CCAM line. Except for the ARCs with relict phases, however, most ARCs have oxygen isotope compositions (>?20‰ in δ¹⁸O) similar to those of typical ferromagnesian chondrules. ARCs are genetically related to both ferromagnesian chondrules and CAIs, but the relationship between ARCs and ferromagnesian chondrules is closer. Most ARCs were formed during flash heating and rapid cooling processes like normal chondrules, only from chemically evolved precursors. ARCs extremely enriched in Al and those with relict phases could have had a hybrid origin (Krot et al. 2002) which incorporated refractory inclusions as part of the precursors in addition to ferromagnesian materials. The occurrence of melilite in ARCs indicates that melilite‐rich CAIs might be present in the precursor materials of ARCs. The absence of melilite in most ARCs is possibly due to high‐temperature interactions between a chondrule melt and the solar nebula.     

Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the <Emphasis Type="Italic">N</Emphasis>-body problem

We study the neighborhood of the equal mass regular polygon relative equilibria in the N-body probem, and show that this relative equilibirum is isolated among the co-circular configurations (in which each point lies on a common circle) for which the center of mass is located at the center of the common circle. It is also isolated in the sense that a sufficiently small mass cannot be added to the common circle to form a \(N+1\)-body relative equilibrium. These results provide strong evidence for a conjecture that the equal mass regular polygon is the only co-circular relative equilibrium with its center of mass located at the center of the common circle.     

The equations of relative motion in the orbital reference frame

The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced.     

Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.     

Petrogenesis of the Northwest Africa 4898 high‐Al mare basalt

Northwest Africa (NWA) 4898 is the only low‐Ti, high‐Al basaltic lunar meteorite yet recognized. It predominantly consists of pyroxene (53.8 vol%) and plagioclase (38.6 vol%). Pyroxene has a wide range of compositions (En_12–62Fs_25–62Wo_11–36), which display a continuous trend from Mg‐rich cores toward Ca‐rich mantles and then to Fe‐rich rims. Plagioclase has relatively restricted compositions (An_87–96Or_0–1Ab_4–13), and was transformed to maskelynite. The REE zoning of all silicate minerals was not significantly modified by shock metamorphism and weathering. Relatively large (up to 1 mm) olivine phenocrysts have homogenous inner parts with Fo ~74 and sharply decrease to 64 within the thin out rims (~30 μm in width). Four types of inclusions with a variety of textures and modal mineralogy were identified in olivine phenocrysts. The contrasting morphologies of these inclusions and the chemical zoning of olivine phenocrysts suggest NWA 4898 underwent at least two stages of crystallization. The aluminous chromite in NWA 4898 reveals that its high alumina character was inherited from the parental magma, rather than by fractional crystallization. The mineral chemistry and major element compositions of NWA 4898 are different from those of 12038 and Luna 16 basalts, but resemble those of Apollo 14 high‐Al basalts. However, the trace element compositions demonstrate that NWA 4898 and Apollo 14 high‐Al basalts could not have been derived from the same mantle source. REE compositions of its parental magma indicate that NWA 4898 probably originated from a unique depleted mantle source that has not been sampled yet. Unlike Apollo 14 high‐Al basalts, which assimilated KREEPy materials during their formation, NWA 4898 could have formed by closed‐system fractional crystallization.     

Study of the Cosmic-Ray Modulation During the Passage of ICMEs and CIRs

We compare the cosmic-ray response to interplanetary coronal mass ejections (ICMEs) and corotating interaction regions (CIRs) during their passage in near-Earth space. We study the relative importance of various structures/features identified during the passage of the ICMEs and CIRs observed during Cycle 23 (1995?–?2009). The identified ICME structures are the shock front, the sheath, and the CME ejecta. We isolate the shock arrival time, the passage of the sheath region, the arrival of ejecta, and the end time of their passage. Similarly, we isolate the CIR arrival, the associated forward shock, the stream interface, and the reverse shock during the passage of a CIR. For the cosmic-ray intensity, we utilize the data from high counting rate neutron monitors. In addition to neutron monitor data, we utilize near-simultaneous and same time-resolution data of interplanetary plasma and field, namely the solar-wind velocity, the interplanetary magnetic field (IMF) vector, and its variance. Further, we also utilize some derived interplanetary parameters. We apply the method of the superposed-epoch analysis. As the plasma and field properties are different during the passage of different structures, both in ICMEs and CIRs, we systematically vary the epoch time in our superposed-epoch analysis one by one. In this way, we study the role and effects of each of the identified individual structures/features during the passage of the ICMEs and CIRs. Relating the properties of various structures and the corresponding variations in plasma and field parameters with changes of the cosmic-ray intensity, we identify the relative importance of the plasma/field parameters in influencing the amplitude and time profiles of the cosmic-ray intensity variations during the passage of the ICMEs and CIRs.     

冬季西太平洋暖池与华南降水关系的年代际变化

利用1951-2010年全国台站冬季降水观测资料、Hadley环流中心逐月海表温度资料以及NCEP/NCAR再分析月平均资料,探讨了西太平洋暖池与我国华南地区冬季降水的关系。结果表明,西太平洋暖池与我国华南冬季降水的年际关系在1972年发生了明显的年代际转折,20世纪70年代前两者弱的负相关未通过信度检验,而70年代后两者相关系数达到-0.5~-0.6。回归分析显示,70年代前,暖池对产生华南冬季降水的水汽条件以及动力条件等的影响不显著,因此其与华南冬季降水的关系不明显。70年代后,暖池偏暖时,在菲律宾海区域激发出一个显著的气旋性环流,该环流西北侧的偏北风不利于南海地区水汽向我国华南地区输送,华南地区水汽辐散增强,而且南支槽地区对流减弱,南支扰动不活跃且扰动不能向下游地区传播,华南地区扰动活动减弱,此外暖池偏暖使北半球经向环流显著增强,且下沉支位于我国华南地区,加强了华南地区的下沉运动,因而华南地区冬季降水显著偏少;暖池偏冷时,情况相反。