一种解析定轨方法

本文给出了人造地球卫星轨道计算的一种解析方法,定轨方案中摄动计算考虑了地球引力场非球形摄动的J2,J3,J4的长期项,长周期项,J2短周期项,大气阻力,太阳光压及日月引力摄动的长期项。初始根数改正量估计采用微分轨道改进算法。在定轨迭代收敛后,残差的均方根误差在5″左右,资料使用率超过80%。     

月球探测器过渡轨道的短弧定轨方法

论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考．     

人卫长弧定轨中的摄动计算问题

人卫精度定轨中摄动星历表的计算，常采用数值方法，对于长弧定轨，将会遇到数值稳定问题，有人提出采用Ｅｎｃｋｅ特别摄动法，但要保持数值稳定，关键在于坐标摄动法数值计算中参考轨道的选取，而不是用不用Ｅｎｃｋｅ变换，更有效的方法是一般数值方法中采用稳定化措施。     

土星卫星的精密定轨方案

由于星际探测事业的发展,对土星卫星的定位精度要求愈来愈高,经典的分析法定轨方法已难以适应,在当今计算技术条件高度发展的背景下,本文给出了土星卫星的数值法定轨方案,采用了土星卫星运动的高精度力学模型,并运用１８７４－１９８９这１００多年间的观测资料,引用现代最小二乘估计,对土星卫生进行精密定轨。该方案可以在引用同样的力学模型的前提下,对土星各颗卫星进行定轨,亦可同时进行多颗卫星的定轨。相应的软件比较     

星载GPS自主定轨的长期稳定性

通过模拟长达100天的星载GPS伪距观测资料,进行卡尔曼滤波定轨仿真计算．重点研究：1)采用简化的动力学模型与简化状态转移矩阵,是否保证滤波的长期稳定性；2)模型误差矩阵Q的选取对滤波定轨精度的影响；3)与事后最小二乘批处理相比较,在简化模型下自主定轨的精度．同时给出了相应的结论．     

小行星初轨计算的Fortran程序设计

由改进的Laplace和Gauss方法分别给出小行星初轨计算的程序,通过两程序的比较测试得出结论——两方法适用于三次长时间间隔的角观测资料。为实现一天内角观测资料的小行星初轨计算与位置预报,对改进的Laplace方法流程进行了调整。通过增加迭代方程右矩阵的调整,预报结果可用于指导小行星的跟踪观测,文中给出调整后的流程图及预报效果数值验证。     

光压摄动计算中地影间断的处理

人卫精密定轨中受摄星历（或称精密星历,即状态转移）,可由分析解或数值解提供,相应的定轨方法亦有分析法定轨与数值法定轨之称。对于后者,在一般情况下,现有的常微分方程数值解法（或称积分器）已能满足精度要求,除长弧定轨外,有一定问题是值得注意的,即地影“间断”问题的处理,这关系到如何在保证星历精度的前提下提高计算效率的问题。本文针对这一问题,给出了相应的改进算法,并通过数值验证表明算法的有效性。     

两种观测技术综合精密定轨的探讨

利用T／P卫星的SLR和DORIS实测资料,对两种观测技术综合精密定轨中的加权及其对定轨影响的问题作了初步的探讨。根据所提出的一种经验性的加权方法进行了综合定轨计算,结果表明：对于两种不同技术的观测,相对权选取的恰当与否将影响综合定轨的精度;综合定轨的最优加权不仅依赖于观测资料的精度,还与观测资料的多少和几何分布有关;通过选用最优加权,可使得综合轨的精度优于仅用其中一种技术的定轨精度,综合定轨能有效地提高定轨精度。     

任意倾角的共轨运动研究

共轨运动天体与摄动天体的半长径相同,处于1:1平运动共振中.太阳系内多个行星的特洛伊天体即为处于蝌蚪形轨道的共轨运动天体,其中一些高轨道倾角特洛伊天体的轨道运动与来源仍未被完全理解.利用一个新发展的适用于处理1:1平运动共振的摄动函数展开方式,对三维空间中的共轨运动进行考察,计算不同初始轨道根数情况下共轨轨道的共振中心、共振宽度,分析轨道类型与初始轨道根数的关系.并将分析方法所得结果与数值方法的结果相互比较验证,得到了广阔初始轨道根数空间内共轨运动的全局图景.     

Geosat卫星定轨中的大气阻力摄动

在利用卫星测高资料定轨的过程中，大气阻力摄动的影响较大。本文在比较几种常用大气密度模型误差对定轨影响的基础上，将密度改正公式引入到Geosat卫星的精密定轨中。结果显示，该公式可以有效地提高卫星的径向定轨精度。     

Application of the extended Kalman filter in satellite prediction

The extended Kalman filter is used in this paper to process single-station laser ranging data over a few revolutions to improve the satellite orbit. The aim is to provide accurate short-term predictions of the satellite position. The dynamical model includes the perturbations due to the Earth's oblateness, air drag, solar radiation pressure and the gravitational attractions of the Sun and the Moon.The proposed method is tested with simulated and real LAGEOS data. The results show that the above aim is achievable. Moreover, the computing program based on the present method can be realized on mini-computers.     

Study of the Earth's oblateness and rotating atmosphere effects upon an artificial satellite in terms of KS-regular variables

This paper is concerned with an orbit prediction with the KS-regular variables. Perturbations due to the gravitational oblateness of the Earth, and the rotating atmosphere are considered. Application of the method for the perturbed motion are illustrated by numerical and graphical examples for a test case of the orbit.     

Determination of the parabolic orbit for a body moving in the plane of the ecliptic,by the Laplace method

A modification of the Laplace method for the determination of a preliminary orbit of a body moving in the plane of the ecliptic is presented. It is shown that on the basis of three close positions on the celestial sphere, the parabolic orbit can be determined in cases, when the classical Laplace method is not suitable. The numerical estimation of the number of possible solutions is carried out, and their spatial distribution depending on initial conditions is shown. An example of the determination of an orbit for the comet C/2007 N3 (Lulin) is given.     

Oblateness effect of Saturn on periodic orbits in the Saturn-Titan restricted three-body problem

We explore the effect of oblateness of Saturn (more massive primary) on the periodic orbits and the regions of quasi-periodic motion around both the primaries in the Saturn-Titan system in the framework of planar circular restricted three-body problem. First order interior and exterior mean motion resonances are located. The effect of oblateness is studied on the location, nature and size of periodic and quasi-periodic orbits, using the numerical technique of Poincare surface of sections. Some of the periodic orbits change to quasi-periodic orbits due to the effect of oblateness and vice-versa. The stability of the orbits around Saturn, Titan and both varies with the inclusion of oblateness. The centers of the periodic orbits around Titan move towards Saturn, whereas those around Saturn move towards Titan. For the orbit around Titan at C=2.9992, x=0.959494, the apocenter becomes pericenter. By incorporating oblateness effect, the orbit around Titan at C=2.99345, x=0.924938 is captured by Saturn, remains in various trajectories around Saturn, and as time progresses it spirals away around both the primaries.     

Radius and limb topography of Mercury obtained from images acquired during the MESSENGER flybys

Analysis of images obtained by the MESSENGER spacecraft during its three flybys of Mercury yields a new estimate for the planet's mean radius of 2439.25±0.69 km, in agreement with results from Mariner 10 and Earth-based observations, as well as with MESSENGER altimeter and occultation data. The mean equatorial radius and polar radius are identical to within error, suggesting that rotational oblateness is negligible when compared with other sources of topography. This result is consistent with the small gravitational oblateness of the planet. Minor differences in radius obtained at different locations reflect regional variations in topography. Residual topography along three limb profiles has a dynamic range of 7.4 km and a root-mean-square roughness of 0.8 km over hemispherical scales. Following MESSENGER's entry into orbit about Mercury in March 2011, we expect considerable additional improvements to our knowledge of Mercury's size and shape.     

Preliminary orbits with line-of-sight correction for LEO satellites observed with radar

We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in Gronchi et al. (Mon Not R Astron Soc 451(2):1883–1891, 2015b), which uses a pure Keplerian dynamical model. Since the effect of the Earth oblateness is strong at low altitudes, its inclusion in the model can sensibly improve the initial orbit, giving a better starting guess for differential corrections and increasing the chances to obtain their convergence. The input set consists of two tracks of radar observations, each one composed of at least four observations taken during the same pass of the satellite. A single observation gives the topocentric position of the satellite, where the range is very accurate, while the line-of-sight direction is poorly determined. From these data, we can compute by a polynomial fit the values of the range and range rate at the mean epochs of the two tracks. In order to obtain a preliminary orbit, we wish to compute the angular velocity, which is the rate of change of the line of sight. In the same spirit of Gronchi et al. (Mon Not R Astron Soc 451(2):1883–1891, 2015b), we also wish to correct the values of the angular measurements, so that they fit the selected dynamical model if the same holds for the radial distance and velocity. The selected model is a perturbed Keplerian dynamics, where the only perturbation included is the secular effect of the \(J_2\) term of the geopotential.     

Analytical solutions to the four post-Newtonian effects in a near-Earth satellite orbit

On the basis of the results by Huang et al. (1990), this paper further discusses and analyses the four post-Newtonian effects in a near-Earth satellite orbit: the Schwarzschild solution, the post-Newtonian effects of the geodesic precession, the Lense-Thirring precession and the oblateness of the Earth. A full analytical solution to the effects including their direct perturbations and mixed perturbations due to the Newtonian oblateness (J ₂) perturbation and the Schwarzschild solution is obtained using the quasi-mean orbital element method analogous to the Kozai's mean orbital element one. Some perturbation properties of the post-Newtonian effects are revealed. The results obtained not only can provide a sound scientific basis for the precise determination of a man-made satellite orbit but also is suitable for similar mechanics systems, such as the motions of planets, asteroids and natural satellites.     

Second-order state transition for relative motion near perturbed,elliptic orbits

This paper develops a tensor and its inverse, for the analytical propagation of the position and velocity of a satellite, with respect to another, in an eccentric orbit. The tensor is useful for relative motion analysis where the separation distance between the two satellites is large. The use of nonsingular elements in the formulation ensures uniform validity even when the reference orbit is circular. Furthermore, when coupled with state transition matrices from existing works that account for perturbations due to Earth oblateness effects, its use can very accurately propagate relative states when oblateness effects and second-order nonlinearities from the differential gravitational field are of the same order of magnitude. The effectiveness of the tensor is illustrated with various examples.     

On the convergence of elliptic motion

The convergence of Lagrange series is studied on a part of the elliptical orbit for values of eccentricity exceeding the Laplace limit. The regions in the vicinity of the two apses of the orbit are identified in which the Lagrange series converge absolutely and uniformly for the values of the eccentricity greater than the Laplace limit. The obtained results are of practical interest for astronomy when studying motions of stellar bodies in orbits with high eccentricity. In particular, these series may be used to calculate the orbits of comets or asteroids with high eccentricity as they pass through the neighborhood of perihelion or to calculate the orbits of artificial satellites with high eccentricity “hanging” in the vicinity of apogee. In stellar dynamics, these series may be used in cases of close binary stars, many of which move in orbits with an eccentricity greater than the Laplace limit.