Allowance for the phase of Jupiter when determining the contact times in some phenomena of its Galilean satellites

We suggest a new method for predicting the phenomena observed in Jovian system of Galilean satellites that takes into account the planet’s phase effect. The method allows one to determine the geocentric times of the contacts of the satellite and its shadow with the illuminated part of the planet’s visible disk that occur near its inferior geocentric and inferior heliocentric conjunctions, respectively. The calculation is performed in the orthographic approximation for the geometric center of the satellite and its shadow by taking into account the curvature of the satellite’s orbit and the visible flattening of Jovian disk. The correction for the phase to the satellite’s contact time is determined from the phase shift of the center of the planet’s disk.     

低轨通信卫星多普勒定位性能分析

为了研究低轨通信卫星多普勒定位性能,首先分析了低轨卫星的对地覆盖特性、信号传输特性以及多普勒频移特性,推导了多普勒定位原理和方法,提出了适用于多普勒定位的精度因子.基于已在轨的铱星和全球星系统,解算了全球范围可见卫星数和定位精度因子,并对相应测站进行了定位仿真实验和误差分析.结果表明:对于铱星和全球星系统,随着纬度降低,卫星可见数减小,多普勒几何精度因子变大;多普勒定位结果精度同时受到频率测量精度、卫星位置误差以及卫星速度误差影响,当卫星位置误差小于10 m、卫星速度误差小于0.1 km·s^-1时,对定位结果影响不大,此时频率测量精度成为影响定位精度的决定性因素,且当频率测量精度为0.01 Hz时,定位精度可达1.18 m.     

Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth’s satellites

We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth’s satellites. We describe parameters of the motion model used for the artificial Earth’s satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.     

转发器式卫星测轨方法

提出了转发器式卫星测轨方法。发射信号和接收信号的不同组合,形成不同模式的转发器式卫星测轨方法,并给出了不同模式下归算转发器式卫星测轨的公式。自发自收模式下的转发器式卫星测轨方法的观测和计算结果表明,定轨观测残差小于9cm。用转发器式卫星测轨方法,不但能给出高精度时间比对结果,而且能给出高精度卫星轨道和卫星预报轨道。     

The general equilibria of a spinning satellite in a circular orbit

Let a rigid satellite move in a circular orbit about a spherically symmetric central body, taking into account only the main term of the gravitational torque. We shall investigate and find all solutions of the following problem: Let the satellite be permitted to spin about an axis that is fixed in the orbit frame; the satellite need not be symmetric, the spin not uniform, and the spin axis not a principal axis of inertia. The complete discussion of this type of spin reveals that the cases found by Lagrange and by Pringle - and the well-known spin about a principal axis of inertia orthogonal to the orbit plane — are essentially the only ones possible; the only further (degenerate) case is uniform spin of a two-dimensional, not necessarily symmetric satellite about certain axes that are orthogonal to the plane containing the body and to the orbit of the satellite around the central body.     

Numerical investigation of collision orbits of lunar satellites

In the present study an investigation of the collision orbits of natural satellites of the Moon (considered to be of finite dimensions) is developed, and the tendency of natural satellites of the Moon to collide on the visible or the far side of the Moon is studied. The collision course of the satellite is studied up to its impact on the lunar surface for perturbations of its initial orbit arbitrarily induced, for example, by the explosion of a meteorite. Several initial conditions regarding the position of the satellite to collide with the Moon on its near (visible) or far (invisible) side is examined in connection to the initial conditions and the direction of the motion of the satellite. The distribution of the lunar craters-originating impact of lunar satellites or celestial bodies which followed a course around the Moon and lost their stability - is examined. First, we consider the planar motion of the natural satellite and its collision on the Moon's surface without the presence of the Earth and Sun. The initial velocities of the satellite are determined in such a way so its impact on the lunar surface takes place on the visible side of the Moon. Then, we continue imparting these velocities to the satellite, but now in the presence of the Earth and Sun; and study the forementioned impacts of the satellites but now in the Earth-Moon-Satellite system influenced also by the Sun. The initial distances of the satellite are taken as the distances which have been used to compute periodic orbits in the planar restricted three-body problem (cf. Gousidou-Koutita, 1980) and its direction takes different angles with the x-axis (Earth-Moon axis). Finally, we summarise the tendency of the satellite's impact on the visible or invisible side of the Moon.     

Orbit determination of satellite “Tance 1” with VLBI data

The satellite “Tance 1” of the “Double-Star Program” is the first truly scientific experimentation satellite of China. Its orbit is the farthest so far launched in China, with a geocentric apogee reaching 78 thousand kilometers. The tracking of “Tance 1” and of more distant space targets, such as the lunar exploration craft, can be realized with the VLBI technique of radio astronomy. In order to test and verify the role which the VLBI technique plays in the lunar exploration program of China, Shanghai Astronomical Observatory organized the only 3 tracking stations in China (located at Shanghai, Urumqi and Kunming), to carry out test tracking of “Tance 1,” and used the time delay data obtained to determine the orbit of “Tance 1” over a two-day period, so providing a preliminary assessment of the possibility of VLBI orbit determination. The fitting error of the orbit so obtained is about 5.5 m in the time delay and about 2 cm/s in the delay rate (this for checking only), much better than is provided by the preliminary orbit (used merely for ensuring tracking) in which the corresponding figures are around 2 km and 15 cm/s. Further, if the orbit is determined by using both the time delay and time delay rate data (with weights according to their internal accuracies), then the residuals are 5.5 m in the time delay and 2 cm/s in the delay rate. For an appreciation of the true accuracy of the VLBI orbit determination, we used simulation data (of the observed two-day VLBI data) and found the results depended greatly on the error in the dynamic model of the satellite which, however, is difficult to assess, while the formal residuals are of the order of 1 kin in the delay and of cm/s in the delay rate. The simulation computation also indicates that a joint determination using both VLBI and USB data will have an improved accuracy.     

大气模式动态测定的研究

利用12万组大气阻力资料，对DTM－1994模式进行改造，获得了一个新的大气模式，该模式的特点是：1．利用2阶周日峰效应，代替了原来模式中的复杂的周日效应表达式，减少了模式参数（少于50个），并使模式参数均具有明确的物理意义，2．分清了模式的主要参数和次要参数，在主要参数中，又分清了利用了阻力资料可以改进的参数和可能改不好的参数．3．与MSIS－1990和DTM－1994模式相比，其互差可以被接受，说明使用卫星阻力资料可以进行大气模式动态改正，不仅能测定大气总密度，并且能测定大气的分密度，4．与卫星轨道相比较，改进有显优于MSIS－1990模式，在120km轨道附近，改进模式密度比MSIS－1990模式大10％，同时我们在卫星陨落期预报中发现，MSIS－1990模式密度比实际大气密度小9％，这说明改进模式的密度与实际大气的密度基本接近。     

An analytic algorithm for global coverage of the revisiting orbit and its application to the CFOSAT satellite

This paper addresses a new analytic algorithm for global coverage of the revisiting orbit and its application to the mission revisiting the Earth within long periods of time, such as Chinese-French Oceanic Satellite (abbr., CFOSAT). In the first, it is presented that the traditional design methodology of the revisiting orbit for some imaging satellites only on the single (ascending or descending) pass, and the repeating orbit is employed to perform the global coverage within short periods of time. However, the selection of the repeating orbit is essentially to yield the suboptimum from the rare measure of rational numbers of passes per day, which will lose lots of available revisiting orbits. Thus, an innovative design scheme is proposed to check both rational and irrational passes per day to acquire the relationship between the coverage percentage and the altitude. To improve the traditional imaging only on the single pass, the proposed algorithm is mapping every pass into its ascending and descending nodes on the specified latitude circle, and then is accumulating the projected width on the circle by the field of view of the satellite. The ergodic geometry of coverage percentage produced from the algorithm is affecting the final scheme, such as the optimal one owning the largest percentage, and the balance one possessing the less gradient in its vicinity, and is guiding to heuristic design for the station-keeping control strategies. The application of CFOSAT validates the feasibility of the algorithm.     

同步卫星短弧定轨

同步卫星受到摄动力的影响,它的实际轨道有一点漂移．卫星需要不断的调轨调姿,以保证其正常运行．为了研究卫星在几小时,甚至更短的时间内的轨迹情况,采用短弧段定轨法．用动力学方法进行短弧定轨,分别研究1小时和15分钟定轨并进行比较,目的是为了在同步轨道卫星变轨后,能尽快地为卫星提供精密的预报轨道．此外,在系列短弧定轨后,得到精密轨道系列,为研究轨道变化的力学因素及研究短弧中卫星转发器时延变化规律等提供依据．     

A numerical-analytical method for studying the orbital evolution of distant planetary satellites

We describe an approximate numerical-analytical method for calculating the perturbations of the elements of distant satellite orbits. The model for the motion of a distant satellite includes the solar attraction and the eccentricity and ecliptic inclination of the orbit of the central planet. In addition, we take into account the variations in planetary orbital elements with time due to secular perturbations. Our work is based on Zeipel’s method for constructing the canonical transformations that relate osculating satellite orbital elements to the mean ones. The corresponding transformation of the Hamiltonian is used to construct an evolution system of equations for mean elements. The numerical solution of this system free from rapidly oscillating functions and the inverse transformation from the mean to osculating elements allows the evolution of distant satellite orbits to be studied on long time scales on the order of several hundred or thousand satellite orbital periods.     

Stability and evolution of primeval lunar satellite orbits

There are several independent sources of evidence which suggest that the multiring basins of the lunar surface were created by the impact of natural satellites of the Moon, early in solar system history. If this hypothesis is correct the orbits of these primeval satellites would need to be stable for significant periods, to account for the known age differences of these basins. The stability of these primeval satellite orbits is considered. We find constraints on the satellite masses and initial orbits for long-term and short-term orbit stability. Dissipation due to lunar tidal friction may contribute significantly to the stability of close orbits.     

Luni-solar perturbations of an Earth satellite

Luni-solar perturbations of the orbit of an artificial Earth satellite are given by modifying the analytical theory of an artificial lunar satellite derived by the author in recent papers. Expressions for the first-order changes, both secular and periodic, in the elements of the geocentric Keplerian orbit of the earth satellite are given, the moon's geocentric orbit, including solar perturbations in it, being found by using Brown's lunar theory.The effects of Sun and Moon on the satellite orbit are described to a high order of accuracy so that the theory may be used for distant earth satellites.     

On the band-to-continuum intensity ratio in the infrared spectra of interstellar carbonaceous dust

Published interpretations of the relative intensity variations of the unidentified infrared bands (UIBs) and their underlying continuum are discussed. An alternative model is proposed, in which a single carrier for both emits (a) mostly a continuum when it is electronically excited by photons (visible or UV), or (b) exclusively the UIBs, when only chemical energy is deposited by H capture on its surface, inducing only nuclear vibrations. The bands will dominate in atomic H regions but will be overcome by thermal continuum radiation when the ambient field is strong but lacks dissociating photons (900–1100 Å). The model applies to photodissociation regions as well as to limbs of molecular clouds in the interstellar medium and agrees quantitatively with recent satellite observations. It gives indications on atomic H density and UIB intensity provided the ambient radiation field is known. It invokes no chemical, electronic, structural or size change to interpret the observed intensity variations.     

基于轨道改正的卫星电视时间传递

利用在模拟卫星电视信号中插入的时间信息可实现时间传递,但由于它常采用固定的卫星位置,限制了时间传递精度。为此,研究了基于轨道改正的卫星电视时间传递方法,并给出了在轨道改正的基础上实现单向和共视时间传递的计算公式。将该方法应用于我国的模拟卫星电视时间传递中,计算了从中央电视台到国家授时中心的单向时间传递结果。     

Perturbations of a spheroidal satellite due to direct solar radiation pressure

The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime.     

A method for averaging the perturbing function in Hill’s problem

A modified method for averaging the perturbing function in Hill’s problem is suggested. The averaging is performed in the revolution period of the satellite over the mean anomaly of its motion with a full allowance for a variation in the position of the perturbing body. At its fixed position, the semimajor axis of the satellite orbit during the revolution of the satellite is constant in view of the evolution equations, while the remaining orbital elements undergo secular and long-period perturbations. Therefore, when the motion of the perturbing body is taken into account, the semimajor axis of the satellite orbit undergoes the strongest perturbations. The suggested approach generalizes the averaging method in which only the linear (in time) term is included in the perturbing function. This method requires no expansion in powers of time. The described method is illustrated by calculating the perturbations of the semimajor axes for two distant satellites of Saturn, S/2000 S 1 and S/2000 S5. An approximate analytic solution is compared with the results of numerical integration of the averaged system of equations of motion for these satellites.     

Ridge formation and de-spinning of Iapetus via an impact-generated satellite

We present a scenario for building the equatorial ridge and de-spinning Iapetus through an impact-generated disk and satellite. This impact puts debris into orbit, forming a ring inside the Roche limit and a satellite outside. This satellite rapidly pushes the ring material down to the surface of Iapetus, and then itself tidally evolves outward, thereby helping to de-spin Iapetus. This scenario can de-spin Iapetus an order of magnitude faster than when tides due to Saturn act alone, almost independently of its interior geophysical evolution. Eventually, the satellite is stripped from its orbit by Saturn. The range of satellite and impactor masses required is compatible with the estimated impact history of Iapetus.     

The potential of an electrostatically clean geostationary satellite and its use in plasma diagnostics

Electrostatic charging has given rise to problems on several geostationary spacecraft. This has led to a rigorous electrostatic cleanliness approach in the case of the scientific geostationary satellite GEOS in order to secure correct electric field and low energy plasma measurements. The present paper outlines the relevant charging mechanism, describes a new method for the determination of the equilibrium potential, and reports on actual potential measurements. The potentials observed are very closely related to the actual plasma conditions at the geostationary orbit. It is generally possible to use the potential measurements to characterize the particle population encountered by the spacecraft.Measurements carried out over a period of 4 years are presented by way of examples. A careful analysis shows that the chosen examples are representative and reflect the conditions observed on all other days of the mission. The results lead to the overall conclusion that the equilibrium potential of GEOS in sunlight is always moderately positive and only rarely exceeds + 10 V with respect to ambient space. At no instance in the sunlit portion of the orbit does the spacecraft assume a negative potential. We find that the observed moderate positive equilibrium potential generally is a function of cold plasma density. During the night and early morning part of the orbit we can, however, identify periods where the high energy particle population dictates the equilibrium potential. The electrostatic cleanliness design of GEOS avoids negative charging also under these conditions. In eclipse, a negative potential cannot be avoided but here the electrostatic cleanliness approach chosen for GEOS prevents any differential charging and avoids potentials of several thousand volts which have appeared on other satellites. The cost, in time and effort, of the precautions employed has clearly been justified. The specially developed techniques have since been used on other satellites and the lessons learned have also been applied successfully to operational spacecraft such as METEOSAT 2.     

Qualitative features of the evolution of some polar satellite orbits

Two special cases of the problem of the secular perturbations in the orbital elements of a satellite with a negligible mass produced by the joint influence of the oblateness of the central planet and the attraction by its most massive (or main) satellites and the Sun are considered. These cases are among the integrable ones in the general nonintegrable evolution problem. The first case is realized when the plane of the satellite orbit and the rotation axis of the planet lie in its orbital plane. The second case is realized when the plane of the satellite orbit is orthogonal to the line of intersection between the equatorial and orbital planes of the planet. The corresponding particular solutions correspond to those polar satellite orbits for which the main qualitative features of the evolution of the eccentricity and pericenter argument are described here. Families of integral curves have been constructed in the phase plane of these elements for the satellite systems of Jupiter, Saturn, and Uranus.