地球卫星轨道的椭圆函数解

分析了引力势作用下地球卫星的轨道．结果表明,在考虑地球扁平率后,地球卫星的轨道可用椭圆余弦函数表示,其平衡位置近似在一椭圆上．     

地球静止轨道卫星的数值模拟

在理论力学框架下,考虑科里奥利力和惯性离心力,对地球静止轨道卫星的漂移、调整和同步的过程进行了详细的数值模拟,并借此领略发射地球静止轨道卫星的精湛技术.     

质点在有心力场中运动轨道的稳定性

本文探讨质点在有心力场中运动轨道的稳定性问题．运用李亚普诺夫关于运动的稳定和不稳定性定理，证明在幂次定律形式的 力场中，质点在平方反比场中运动的椭圆、抛物线和双曲线三种轨道都是稳定的，这是这种 力场所具有的性质；质点在弹性引力场中运动的椭圆轨道也是稳定的，而在弹性斥力场中运动的轨道一般是不稳定的．文中对其它有心力场也作了一些讨论．     

地球扁率对卫星轨道平面的影响——兼谈卫星的太阳同步轨道

讨论地球扁率对人造地球卫星轨道平面的影响,介绍卫星的太阳同步轨道设计原理.     

美国研制3.6万公里高的静止轨道光学侦察卫星

正日前,有媒体报道称,美国国防部正在研究地球静止轨道光学侦察卫星,该卫星运行在3.6×104km高的地球同步轨道,可对地球40%的面积进行持续侦察。由于地球静止轨道光学侦察卫星拥有超强的持续侦察能力,因此有"间谍卫星之王"的称号。目前,世界各国现役光学侦查卫星的运行轨道高度一般集     

论卫星抛射点在椭圆运动轨道上的位置

详细分析了人造地球卫星的椭圆轨道方程和在各种情况下卫星的抛射点在其椭圆运动轨道上的位置.     

倾斜轨道卫星在三维场景下运动规律的研究

利用椭圆的偏近点角和极角的相关知识, 推导了倾斜轨道卫星在三维场景中运动时间关于偏近点角和 运动时间关于极角的表达式, 并用了数值模拟     

在轨卫星星等建模与计算

星等的大小代表了星体对于人眼的可观测程度。卫星星等的理论计算对于观测跟踪卫星光学系统设计等具有重要的指导意义。结合天文学、轨道动力学、辐射度学、光度学和计算数学理论,建立了计算人造卫星星等的物理数学模型。计算了卫星的可见光反射能量随轨道运行的瞬时特征,结合人眼的视觉特性,推导出了轨道卫星星等的计算方法,并进一步针对卫星表面为灰体的情况给出了一种计算卫星星等的方法及星下点卫星星等的周期性计算曲线,结果表明:星下点观测的卫星星等随卫星在轨道上位置的变化非常显著,对同一卫星,不同星下点观测到的星等差异仅在日照区就可达5个等级之多。     

地球只受木星引力作用时的运动轨道的探讨

讨论了如果太阳突然消失,而且地球只受木星引力作用时的运动轨道,结果表明,这时地球相对木星的运动轨道为双曲线或直线．     

基准星辐射定标的轨道预报研究

轨道预报是指根据空间目标初始时刻的状态,利用轨道力学建立的数学模型来预测未来某一时刻的轨道信息。简单介绍了基准星辐射定标系统(PSRCS)和定标轨道预报流程。研究了定标空间位置设计方法和辐射传递模型,在此基础上提出一种基于基准星定标的轨道预报方法,用来为待定标卫星选取适合的定标弧段,并精确预报定标时刻基准星、待定标卫星的轨道信息。通过分析基准星定标轨道约束条件,以高分一号(GF-1)太阳同步轨道卫星作为基准星轨道,仿真出满足定标条件的不同待定标卫星轨道上的定标可见时段。结果验证了基准星定标轨道预报方法的可行性。     

Chaotic attitude oscillations of a satellite filled with a rotating ellipsoidal mass of liquid subject to gravity-gradient torques

The Hamiltonian equations of a liquid-filled satellite subject to gravity-gradient torques in terms of the generalized Deprit variables are established for applying the Melnikov theory formally. The heteroclinic orbits of the torque-free symmetric liquid-filled satellite are found. A criterion for the heteroclinic transversal intersections at the onset of chaotic attitude is formulated using Melnikov's integral. The results from the Melnikov theory are crosschecked with simulation.     

On the Behavior of Eisenstein Series Through Elliptic Degeneration

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane \mathbbH{\mathbb{H}}, and let M = G\\mathbbH{M = \Gamma\backslash \mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.     

Hyperbolic structure and stickiness effect: A case of a 2D area-preserving twist mapping

The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect. We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures. Using a two-dimensional area-preserving twist mapping as the model, we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit. We show how the stickiness effect and the orbital diffusion speed are related to the angle.     

A new method for determination of satellite orbits by transfer

The original idea of a new method for determination of satellite orbits by transfer is from Two-Way Satellite Time and Frequency Transfer (TWSTFT). The original method is called “determination of satellite orbit by transfer”. The method is not only for determination of satellite orbit but also for the time transfer with high accuracy and precision. The advantage is that the accuracy and the precision for determination of satellite orbit are very high and the new method is favorable for various applications. The combination of various signals disseminated and received forms various modes of satellite orbit determinations. If receivers at stations receive the own station-disseminated signals via a satellite transponder, it forms an orbit determination mode called “receiving the own station-disseminated signals mode”. If receivers at all stations receive the signals disseminated from the master station via satellite transponders, it forms an orbit determination mode called “receiving the master station-disseminated signals mode”. If all of receivers at stations receive all stations-disseminated signals via satellite transponders, it forms an orbit determination mode called “receiving all stations-disseminated signals mode”. Also there are other combinations of signals for satellite orbit determination. For different orbit determination modes with different signal combinations, their rigorous formulae of processing are hereby presented in this paper. The accurate and the precise satellite orbit determination for both of the modes, “receiving the own station-disseminated signals mode” and “receiving the master station-disseminated signals mode” is attempted. It shows that the accuracy and precision for both of modes are nearly the same, the ranging accuracy is better than 1 cm, and the observation residuals of satellite orbit determination are better than 9 cm in the observation duration of 1 day. Supported by the National Basic Research and Development Program of China (Grant No. 2007CB815503100453001)     

Inelastic gravitational billiards

We present an experimental investigation of gravitational billiards where the particle undergoes inelastic collisions with its boundary. The motion is mapped for an inelastic particle contained within parabolic, wedge, and hyperbolic boundaries. For the parabola, stable orbits are found and the wedge demonstrates a characteristic instability for its vertex angle. In the instance of the hyperbola, there are several features of the dynamics similar to the parabola at low driving and the wedge for higher driving. However, the low driving case for a hyperbola can only be completely understood by considering inelasticity effects predicted by a numerical simulation and the observation that the velocity dependent inelasticity allows the particle to sample several nearby trajectories for fixed driving.     

Retarded lower trace on satellite ionograms as new means for studies of the ionospheric macro-irregularities

Experimental data on radio sounding of the ionosphere from satellites at heights below its main maximum are presented. In these data, additional retarded lower trace (RLT) is observed in the ionograms. It is interpreted as a trace of a probing radio signal reflected obliquely from the Earth and coming back to the satellite after refraction by sharp horizontal ionospheric irregularities. Horizontal and vertical cuts of these irregularities as well as the electron-density gradients at their side walls are determined using quantitative methods. Two sequences of ionograms for two adjacent orbits of a satellite are presented and processed for which the critical-frequency maps corrected according to the experiment are constructed. The method of weighted interpolation of approximated values at the adjacent points is used. The horizontal size of the retrieved macro-irregularity and the velocity of its motion above the Earth’s surface are obtained. A conclusion is drawn that RLT ionograms allow one to diagnose additional parameters of the ionosphere. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 9–20, January 2006.     

Analytical study of chaos and applications

We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic Hénon map, where chaos appears mainly around the origin, which is an unstable periodic orbit. In this case the chaotic orbits around the origin are represented by analytic series (Moser series). We find the domain of convergence of these Moser series and of similar series around other unstable periodic orbits. The asymptotic manifolds from the various unstable periodic orbits intersect at homoclinic and heteroclinic orbits that are given analytically. Then we consider some Hamiltonian systems and we find their homoclinic orbits by using a new method of analytic prolongation. An application of astronomical interest is the domain of convergence of the analytical series that determine the spiral structure of barred-spiral galaxies.     

The motion of a stationary satellite in the neighbourhood of the equilibrium points of a central potential perturbed by theJ22 term

Summary We study in this paper the position and the characteristics of the equilibrium points of a planet gravitational potential as functions of theJ ₂₂ parameter under the assumption that the potential is truncated to the first tesseral harmonicV=V _o+J₂₂V₂₂. The variational equations are solved analytically in the neighbourhood of these points to determine the possible periodic orbits of a stationary satellite in the equatorial plane. A numerical investigation of the problem is reported with the presentation of some periodic orbits of different families of stable and unstable type.

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Riassunto Nel presente articolo si studiano i punti di equilibrio del potenziale gravitazionale di un pianeta in funzione del parametroJ ₂₂ e nell'ipotesi che detto potenziale sia troncato alla prima armonica tesserale. Si risolvono inoltre le equazioni variazionali nell'intorno di detti punti al fine di determinare le possibili orbite periodiche di un satellite stazionario nel piano equatoriale. è riportata pure un'indagine numerica del problema con la presentazione di alcune orbite periodiche stabili ed instabili appartenenti a diverse famiglie.

     

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system

A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination(MPOD)method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service(IGS) analysis centers(ACs) show that the reference time difference between BeiDou time(BDT) and golbal positoning system(GPS) time(GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10.12, which is similar to the GPS IIR.