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.     

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.     

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.     

热带风压场平衡特征及其对GRAPES系统中同化预报的影响研究I:平衡特征分析

本文基于GRAPES全球模式的短期预报误差样本,利用赤道波动正规模态研究了热带风、压场平衡特征,并根据这些特征分析了线性平衡方程(LBE)在该区域应用时存在的问题。结果表明:(1)赤道波动能成功解释热带短期预报误差样本的大部分分量,对流层中层为60%~80%,对流层顶和平流层低层为80%以上。(2)在可解释的误差方差中,赤道罗斯贝波(ER)占比仅为30%~55%,其他赤道波动的作用不可忽视。(3)在ER模态基础上引入其他赤道波动会大幅削弱原有风、压场平衡约束,重力惯性波与Kelvin波的作用最为显著。此时,对流层中层位势高度h与u风、v风间的约束接近于零,而平流层低层h-u的平衡特征由Kelvin波主导。(4)LBE主要表达了ER模态下的风、压场平衡特征,与实际情形相比高估了热带风、压场的耦合程度,进一步的改进中需削弱这一虚假平衡,使得热带风、压场分析变得更加独立。     

华北地区一次中尺度对流系统上方的Sprite放电现象及其对应的雷达回波和闪电特征

利用低光度相机首次观测到了2013年7月31日华北地区一次中尺度对流系统(MCS)上空产生的中高层Sprite放电现象。结合闪电定位、天气雷达等同步观测, 对一次MCS诱发的Sprite的形态学特征及其对应的母体闪电和雷暴系统的雷达回波特征等进行了详细分析。研究除发现了2例圆柱型、3例胡萝卜型和1例舞蹈型 Sprite外, 还发现了2例发光主体发育不完全的Y字型Sprite。估算的Sprite的底部平均高度低于61.8±3.5 km, 顶部平均高度为84.3±6.8 km。Sprite持续时间算术平均值为25.7±9.8 ms, 几何平均值为24.4 ms。Sprite的母体闪电均为正地闪, 峰值电流在+62.5～+106.2 kA之间, 算术平均值为+77.1±22.2 kA, 是本次MCS所有正地闪平均峰值电流的1.4倍。Sprite母体闪电的脉冲电荷矩变化(iCMC)在+475～+922 C km之间, 几何平均值为+571.0 C km。Sprite母体闪电发生在MCS雷达回波25～35 dBZ的层状云降水区, 弱回波(<30 dBZ)面积的突然增加对Sprite的产生有重要指示作用。Sprite易发生在MCS成熟—消散阶段正地闪比例(POP)显著增加的时段。在本次MCS消散阶段中, 有两个时间段可能有利于产生Sprite。在Sprite集中发生时间段, 北京闪电综合探测网(BLNET)探测到的正地闪比例为54.2%, 正地闪连续电流比例70.24%, 连续电流持续时间为58.17±50.31 ms, 有利于Sprite的产生。     

闪电和固、液态降水关系差异的数值模拟

为了进一步认识闪电和固、液态降水的关系,本文利用三维雷暴云动力-电耦合数值模式,通过设置敏感性试验组,模拟了一次雷暴过程,分析雷暴中闪电和降水的特征,以及闪电和固、液态降水对垂直风速的依赖关系,探讨闪电与固、液态降水的时空分布关系和单次闪电表征的降水量(RPF:rainyields per flash)。结果表明:对流云降水中,液态降水占主要部分,但固态降水比液态降水对于垂直风速的依赖性更强。随着对流的增强,固态降水在总降水中占的比重越来越大。首次放电时间不断提前,闪电峰值落后垂直风速峰值,总闪数一开始随对流的增强而增加,对流一旦增强到一定程度,总闪数则逐渐减小。固态降水和液态降水的开始时间和峰值时间均随着对流的增强而不断提前,而液态降水出现时间和峰值时间均提前于固态降水。雷暴云首次放电的时间滞后于液态降水,而闪电峰值提前固态降水峰值或与固态降水峰值同时产生。雷暴云中的放电活动集中在强降水区域前缘的较弱降水区,强降水区对应的闪电较少,对流的增强会使降水区域面积、降水量和降水强度增加。由于液态降水总量远大于固态降水总量,固、液态RPF的数值相差达到一个量级,但单位时间内固态降水和液态降水增加的速率相近。在单位时间内闪电次数越多,RPF则越小,而固态RPF和闪电次数的线性相关性明显好于液态RPF,所以利用固态降水可以更好地预报闪电。这些结果有助于进一步认识闪电和降水的关系,并可为闪电预报提供新的思路。