Evolution of the Radio Luminosities of the Tycho and Kepler Supernovae Remnants

Radio emission of the historical supernovae remnants Tycho (SNR1572) and Kepler (SNR1604) and evolution of their luminosity are considered. Measurement data of secular luminosity decrease rate, obtained earlier by the authors, were corrected with account of variation in time of the flux density of the reference sources. As a result, it is found that the SNR1604 luminosity at 1667 MHz is weakening with an annual mean rate equal to (0.2 ± 0.07)%. The corresponding rate for SNR1572 is (0.47 ± 0.05)%. Since the radio luminosity evolution, as well as energy densities of magnetic field and relativistic electrons inside SNR1604 and SNR1572 are essentially different, these remnants should be considered as different types of supernovae. Bandiera classified SN1604 as type SNIb or SNII.     

Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

月球典型撞击坑溅射物研究及对月球地质编图的意义

撞击坑是月表最典型的地质单元,其溅射物作为撞击坑的坑外组成部分可分布到距离坑中心10个直径距离之外的区域,因此撞击溅射物也是月球地质编图中最重要的表达要素之一。本文使用月球勘测轨道器(LRO)的激光高度计(LOLA)数据、广角相机(WAC)影像、窄角相机(NAC)影像以及Clementine的UVVIS多光谱数据,研究了哥白尼纪正面月海区直径31km的Kepler撞击坑和背面月陆区直径30km的Necho撞击坑。哥白尼纪撞击坑溅射沉积物可以分为三个相:连续溅射沉积相(CE)、不连续溅射沉积相(DE)和辐射纹(CR)。连续溅射沉积相分布在最大约2.6个半径范围之内,不连续溅射沉积相分布在最大近11个半径范围之内,辐射纹分布在最大近29个半径范围之内。本文强调了多源数据结合在识别撞击坑溅射沉积物中的作用,对Kepler坑和Necho坑溅射沉积物进行了填图,不对称分布的特征表明这两个坑可能形成于倾斜撞击。     

微扰Kepler系统轨道微分方程的近似Lie对称性与近似不变量

把极角θ视为独立变量,得到Kepler系统的轨道微分方程. 首先讨论Kepler系统轨道微分方程的Lie对称性和不变量,微扰Kepler系统轨道微分方程的精确Lie对称性和精确不变量,其次讨论微扰Kepler系统轨道微分方程的近似Lie对称性和近似不变量,并得到了微扰Kepler系统的9个一阶近似Lie对称性和6个一阶近似不变量,其中1个实为精确不变量,而其余5个分别等于微扰系数ε乘以Kepler系统相应的5个不变量.     

Adiabatic invariants for the nonconservative Kepler's problem

This paper considers adiabatic invariants for the classical Kepler problem with resisting forces. The analysis is based on the theory of integrating factors and theory of adiabatic invariants in the Krylov-Bogoliubov-Mitropolski variables. The adiabatic invariants are series with respect to a small parameter. Also, for every particular case of nonconservative forces, it is shown that, with a complete set of adiabatic invariants, an approximate solution of the problem can be obtained. Four problems are analyzed in detail where approximate solutions are compared with numerical.     

The accelerated Kepler problem

The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.     

The Kepler problem: A unifying view

This paper is an attempt to bring unity in the study of the classical Kepler problem by combining, through simple vectorial and quaternionic techniques, its two peculiar aspects: the determination of the constants of the motion and the regularization at the origin.Research supported by the Consiglio Nazionale delle Ricerche of Italy (C.N.R.-G.N.F.M.).     

Zonal-Harmonics Perturbations

A recently developed iterative technique for solving the perturbed Kepler problem is explained, in a step-by-step detail, using the simple example of oblateness perturbations. The results are then extended to deal with higher-degree zonal harmonics.     

Perturbations of the Kepler Problem in Global Coordinates: A Program

The present paper is a brief report of how, along the lines of a previous paper, the implementation of the program KEPLER¹, for the numerical integration of the perturbations of the Kepler problem, has been carried out.     

The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on and . An analog of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of a Newtonian center moving along a geodesic on and (the restricted two-body problem). For the case of a small curvature, the pericenter shift is computed using the perturbation theory. We also present the results of numerical analysis based on an analogy with the motion of a rigid body.