The Artificial Earth Satellite Motion in an Oblate,Rotating Atmosphere with Symmetrical Diurnal Effect

The equations describing the disturbed motion of an artificial Earth satellite in the atmosphere are integrated by using a new variable instead of the true anomaly. The atmospheric flattening and rotation, the linear variation of the density scale height with the altitude, the symmetrical diurnal effect and the variation of its amplitude with the heigth are taken into account. Approximate formulae for the perturbations in all the orbital elements over a revolution of the satellite are given.     

The Prograde C7 Resonance for Earth and Mars Satellite Orbits

The resonance C7 is a 1:1 eccentricity (apsidal) resonance between the longitude of a satellite's pericentre and the mean longitude of the Sun. A previous paper by the author (Breiter, 1999) identified it as the strongest of the lunisolar apsidal resonances. After the reduction to a single degree of freedom, the problem is studied qualitatively for the prograde orbits around the Earth and Mars. Pitchfork, saddle-node, and saddle connection bifurcations give rise to a complicated phase flow, which may involve up to nine critical points. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytical Study of The Resonance Caused by Solar Radiation Pressure on a Spacecraft

The resonance terms produced by the effect of direct solar radiation pressure on the motion of a spacecraft in the oblate field of the earth are analyzed. The spacecraft was assumed axially symmetric with a despun antenna and solar panels. A canonical transformation technique is developed, based on the Bohlin technique of expansion in fractional powers, using Lie series and transformation as well as the concept of the Delaunay anomaly. The developed technique, applied to the problem averaged over the mean anomaly, is suitable in the presence of more than one resonant vector.     

Satellite Orbital Precessions Caused by the Octupolar Mass Moment of a Non-Spherical Body Arbitrarily Oriented in Space

I consider a satellite moving around a non-spherical body of mass M and equatorial radius R, and calculate its orbital precessions caused by the body’s octupolar mass moment J ₄. I consider only the effects averaged over one orbital period T of the satellite. I give exact formulas, not restricted to any special values of either the eccentricity e or the inclination i of the satellite’s orbit. I do not assume any preferential orientation for the body’s spin axis ${\boldsymbol{\hat{{\mathbf{k}}}}}$ because in many cases of potential interest (exoplanets, neutron stars, black holes) it is poorly known or unknown at all.     

地球卫星VLBI观测研究进展

随着地球卫星在资源、导航定位、授时、跟踪以及数据中继等经济和军事领域的作用不断增强,传统的测距测速技术已无法满足对卫星定位精度的实际需求。由于VLBI技术具有高精度角分辨率的特点,人们尝试将其应用于人造地球卫星的观测。针对卫星VLBI观测方面,首先介绍了卫星VLBI观测技术的基本原理及其与传统河外射电源VLBI观测的差异,然后介绍了中外学者应用VLBI技术进行地球卫星观测的研究进展及相关成果,最后对以往近地卫星VLBI观测研究存在的问题进行总结,并讨论了目前以及将来可能的解决方案。     

在卫星授时中电离层误差实时改正的双极化方法

在卫星定位与授时中，电离层折射误差的影响是十分重要的．目前采用的主要改正方法是双频法，还有电离层模型法．双频法要求卫星发射两个工作频率，而电离层模型法的偏差又较大，这对于使用单频接收机的用户来讲，电离层折射改正就成为一个严重问题，笔者提出的双极化法正好可以解决单频接收机所遇到的问题．双极化法是基于电离层的双折射特性．一个线极化波在电离层中传播时被分裂成两个圆极化波，即左旋圆极化波和右旋圆极化波传播，左旋与右旋圆极化波在电离层中传播的速度不同，则到达接收点的时间也就不同，通过测量两个圆极化波到达接收点的传播时廷差，即可确定电离层折射误差的改正量．     

On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.     

Satellite particle exospheres of planets: Application to Earth

Neutral planetary exospheres are built up by three different kinds of gas particles, namely ballistic, hyperbolic and elliptic particles. Elliptic particles have their origin exclusively in exospheric regions of the planet where they are fed into satellite orbits by different physical processes. It has been suggested that elliptic particles that do not enter the collision-dominated planetary gas regions represent an important fraction of the particles constituting the outer parts of planetary exospheres. Here we develop a theoretical concept for a rigorous calculation of elliptic particle distributions using Boltzmann equation kinetic approaches. Taking into account realistic gain and loss processes a general procedure for the determination of satellite particle densities for the terrestrial case is presented. We give representative height profiles of the satellite particle density in the exosphere for weak and strong solar activity. Our results are compared with those obtained by simplified theoretical approaches; pronounced deviations are obvious. It is shown that satellite particles are more relevant in low temperature exospheres leading to an order-of-magnitude difference above 1500 km between the densities for weak and strong solar activity. There is a general tendency for satellite particles to become increasingly important with increasing height.     

Generation of the Stressed State of the Lithosphere of the Earth and Mars Caused by the Reorientation of Their Figures

The computer simulation of the reorientation of the Earth and Mars lithosphere figure has been performed, which due to the dynamic redistribution of masses, allowed to reveal certain regularities of the structure-forming processes. It has been shown that the shape of the lithosphere surface has a different orientation relatively to the geoids’ (aroids) figure. This causes redistribution of masses leading to a strained state of the lithosphere as a result of endogenous and gravitational-rotational forces action in the evolutionary processes of planet’s self-development. The solution of this problem is considered on the example of lithosphere surface heights approximation by a biaxial ellipsoid with seven parameters. The acting horizontal forces in the upper shell of the planet has been calculated, introducing the concept of “evolutionary deviation of the plumb” and assuming that the tangential forces are proportional to the angle, which is defined as the angle between the direction of the plumb line in the past geological epoch and the plumb line direction at a given point. The calculated fields of tangential force vectors show good consistency with the direction of space-time displacement of Earth’s continents and tectonic plates and consistent with the results of the horizontal movements of GNSS stations. This is quite convincing evidence that under the long-term action of vortex rotationalgravitational forces, the lithospheres masses acquire the properties of creep. All this leads to the fact that interacting blocks and plates within the vortex rotational-gravitational model can be interconnected to elastic fields that creates a single planetary geodynamic field that forms the evolutionary state of the geo-environment.     

同步卫星运动引起时延测量值变化的特性

讨论了陕西天文台卫星电视传递时间频率系统所测得的时延值变化特性,依据实测数值给出时延值日变化的模式并与实际结果做了比较。把连续6天这个模式的结果再进行二次多项式回归,可以预报后6天的时延值,精度为几微秒。     

Challenges From Solid Earth Dynamics for Satellite Gravity Field Missions in the Post-Goce Era

Examples from four main categories of solid-earth deformation processes are discussed for which the GOCE and GRACE satellite gravity missions will not provide a high enough spatial or temporal resolution or a sufficient accuracy. Quasi-static and episodic solid-earth deformation would benefit from a new satellite gravity mission that would provide a higher combined spatial and temporal resolution. Seismic and core periodic motions would benefit from a new satellite mission that would be able to detect gravity variations with a higher temporal resolution combined with very high accuracies.     

Symmetric and Asymmetric Librations in Planetary and Satellite Systems at the 2/1 Resonance

Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites of Jupiter for the case m₁>m₂, the system HD82943 for the new masses, for the case m₁=m₂ and the same system HD82943 for the values of the masses m₁<m₂ given in previous work. In the case m₁≥ m₂ there is a family of asymmetric orbits that bifurcates from a family of symmetric periodic orbits, but there exist also an asymmetric family that is independent of the symmetric families. In the case m₁<m₂ all the asymmetric families are independent from the symmetric families. In many cases the asymmetry, as measured by and by the mean anomaly M of the outer planet when the inner planet is at perihelion, is very large. The stability of these asymmetric families has been studied and it is found that there exist large regions in phase space where we have stable asymmetric librations. It is also shown that the asymmetry is a stabilizing factor. A shift from asymmetry to symmetry, other elements being the same, may destabilize the system.     

Kinematical modeling of the Earth rotation,focusing on the Oppolzer terms in a rigid Earth and the Oppolzer-like terms in an elastic Earth

Under perturbations from outer bodies, the Earth experiences changes of its angular momentum axis, figure axis and rotational axis. In the theory of the rigid Earth, in addition to the precession and nutation of the angular momentum axis given by the Poisson terms, both the figure axis and the rotational axis suffer forced deviation from the angular momentum axis. This deviation is expressed by the so-called Oppolzer terms describing separation of the averaged figure axis, called CIP (Celestial Intermediate Pole) or CEP (Celestial Ephemeris Pole), and the mathematically defined rotational axis, from the angular momentum axis. The CIP is the rotational axis in a frame subject to both precession and nutation, while the mathematical rotational axis is that in the inertial (non-rotating) frame. We investigate, kinematically, the origin of the separation between these two axes—both for the rigid Earth and an elastic Earth. In the case of an elastic Earth perturbed by the same outer bodies, there appear further deviations of the figure and rotational axes from the angular momentum axis. These deviations, though similar to the Oppolzer terms in the rigid Earth, are produced by quite a different physical mechanism. Analysing this mechanism, we derive an expression for the Oppolzer-like terms in an elastic Earth. From this expression we demonstrate that, under a certain approximation (in neglect of the motion of the perturbing outer bodies), the sum of the direct and convective perturbations of the spin axis coincides with the direct perturbation of the figure axis. This equality, which is approximate, gets violated when the motion of the outer bodies is taken into account.     

Relativistic Gravitational Experiment in the Earth Orbit: Concept,Technology, and Configuration of Satellite Constellation

An arrangement of the orbital experiment on the measurement of the light propagation delay in the gravitational field of the Earth (Shapiro effect) using laser interferometry based on a cluster of small spacecraft (SC) is proposed. SC layouts, launch technology, and high-precision measurements of their orbital parameters are considered.     

Tidal Winds on Titan Caused by Saturn

The influence of Saturn's gravitational tide on the atmosphere of Titan is investigated by means of a three-dimensional general circulation model. Titan's orbital eccentricity of 0.0292 gives rise to time-dependent radial and librational tide whose potential circles eastward on Titan. Unlike atmospheric tides on terrestrial planets, Saturn's tide on Titan has a large impact on the dynamic meteorology down to the surface. The surface pressure oscillates by up to 1.5 hPa through the orbit. Near the surface the tidal wind dominates the atmospheric flow and exhibits strong temporal and spatial variation. The superposition of the annually present, thermally forced latitudinal pressure gradient and tidally caused pressure variation produces a unique wind pattern near the surface characterized by equatorward flow and high-latitude whirls. At higher levels the tidal wind manifests itself as eastward traveling planetary-scale wave of wavenumber 2 superposed on the background wind. In general tidal winds are more significant in the troposphere, where other forcing mechanisms are weak. Meridional tidal winds become as fast as 5 m s⁻¹ in the troposphere and change direction periodically through the orbit and along the parallel of latitude. Except in the lower troposphere, zonal winds always remain prograde because the tidal wind amplitude is usually smaller than the mean zonal wind. The tide also has a large impact on the mean zonal circulation in the stratosphere. A meridional drift of the descending Huygens Probe in the troposphere would be the easiest way to verify the tidal wind on Titan, but more complete observations of tropospheric wind and surface pressure by a future mission would be required to unveil the complete details of the tidal wind.     

Development and Parameters of a Non-Self-Similar CME Caused by the Eruption of a Quiescent Prominence

The eruption of a large quiescent prominence on 17 August 2013 and an associated coronal mass ejection (CME) were observed from different vantage points by the Solar Dynamics Observatory (SDO), the Solar-Terrestrial Relations Observatory (STEREO), and the Solar and Heliospheric Observatory (SOHO). Screening of the quiet Sun by the prominence produced an isolated negative microwave burst. We estimated the parameters of the erupting prominence from a radio absorption model and measured them from 304 Å images. The variations of the parameters as obtained by these two methods are similar and agree within a factor of two. The CME development was studied from the kinematics of the front and different components of the core and their structural changes. The results were verified using movies in which the CME expansion was compensated for according to the measured kinematics. We found that the CME mass (\(3.6 \times 10^{15}\mbox{ g}\)) was mainly supplied by the prominence (\(\approx 6 \times 10^{15}\mbox{ g}\)), while a considerable part drained back. The mass of the coronal-temperature component did not exceed \(10^{15}\mbox{ g}\). The CME was initiated by the erupting prominence, which constituted its core and remained active. The structural and kinematical changes started in the core and propagated outward. The CME structures continued to form during expansion, which did not become self-similar up to \(25~\mathrm{R}_{\odot }\). The aerodynamic drag was insignificant. The core formed during the CME rise to \(4~\mathrm{R}_{\odot }\) and possibly beyond. Some of its components were observed to straighten and stretch outward, indicating the transformation of tangled structures of the core into a simpler flux rope, which grew and filled the cavity as the CME expanded.     

卫星黑子衰减触发的喷流事件

详细分析了一次太阳低层大气磁场重联触发的喷流事件.这次喷流发生在2014年8月1日,爆发自美国国家海洋和大气管理局(National Oceanic and Atmospheric Administration, NOAA)活动区12127边缘的一个卫星黑子处.该喷流爆发包括日浪、紫外喷流、极紫外高温和低温喷流.大熊湖太阳天文台(Big Bear Solar Observatory,BBSO)的Goode Solar Telescope (GST)高分辨率氧化钛(TiO)谱线的光球观测显示,喷流爆发过程中,卫星黑子一直衰减.到喷流结束,卫星黑子面积共减少了80%.在此过程中,太阳动力学天文台(Solar Dynamics Observatory, SDO)日球磁场成像仪(Helioseismic and Magnetic Imager, HMI)的视向磁场观测表明,该卫星黑子对应的负极磁场与相邻的正极磁场发生明显对消,产生喷流足部亮点.根据SDO卫星太阳大气成像仪(Atmospheric Imaging Assembly, AIA)的多波段观测,该足部亮点首先出现在紫外1600?波段.待紫外(1600?)喷流从紫外足部亮点顶部向上喷发,在极紫外波段也观测到相应的亮源.随着足点源亮度突然增强,有明显的极紫外低温喷流和日浪从足部亮点侧面喷发.从GST的高分辨率Hα图像上,可见日浪由许多精细纤维组成,这些纤维扎根在足点源的东南侧.根据从光球层过色球层再到日冕层的多波段高分辨率观测,色球中下层的磁场对消触发了这次喷流事件.向上喷发的物质流可以携带能量进入上层大气,并加热上层大气.研究结果表明,低层大气磁重联可能对解决日冕加热问题起重要作用.     

A Hill Problem with Oblate Primaries and Effect of Oblateness on Hill Stability of Orbits

We introduce a new version of Hill's problem to include the effect of oblateness of the primaries, and briefly discuss its equilibrium points and zero velocity curves. As a first application we use this to study Hill stability of direct orbits around the small primary. This can be employed to study the stability of a planet's moon perturbed by an oblate Sun, or of a star's planet perturbed by a distant disk-shaped galaxy. Oblateness of the `Sun' is found to decrese the maximum distance of Hill stable direct `moon' orbits. This revised version was published online in July 2006 with corrections to the Cover Date.